Search Results for sun

Biographies

1. Sun Zi biography
   
   • Sun Zi .
     
   • Nothing is known about Sun Zi except his text Sunzi suanjing (Sun Zi's Mathematical Manual).
     
   • In the 17th century Sun Zi was identified with Sun Wu, a famous military expert of the sixth century BC who wrote Sun Zi's art of war.
     
   • The Ruan Yuan in his Chouren zhuan or Biographies of astronomers and mathematicians (1799) certainly realised that references in certain problems in the Sunzi suanjing meant that the identification with Sun Wu was incorrect.
     
   • He placed Sun Zi around 250 BC but knew that there was still problems with this dating which he said would have to be studied later.
     
   • During the third century Sun Zi, an author of considerable note, published his Sunzi suanjing.
     
   • 19 (4) (1984), 397-405.',4)">4] say 'About 400 AD a Chinese mathematician, Sun Zi, took up the problem ..
     
   • 38 (2) (1988), 101-108.',6)">6] says 'Sun Zi (somewhere between the 3rd and 5th centuries AD) ..
     
   • Leaving the question of the date let us look briefly at the content of the treatise, before finally trying to make some guesses about Sun Zi based purely on the text.
     
   • Sun Zi explains how to do multiplication on a counting board:- .
     
   • Sun Zi then explains how to do division on a counting board:- .
     
   • Let us mention one further major contribution by Sun Zi.
     
   • (1) (1987), 22-27.',11)">11], gives a detailed description of the algorithm used by Sun Zi for the extraction of roots and compares it with the method described in the Nine Chapters on the Mathematical Art.
     
   • Xu argues convincingly that Sun Zi's procedure differs from the earlier method in significant ways and so should be recognized as an outstanding and original contribution.
     
   • Can we deduce anything of Sun Zi himself? Perhaps the most significant fact is that nothing is known.
     
   • How can this tell us anything? Well first notice that since the work of modern historians has placed the Sunzi suanjing much later than was thought in ancient times, we can now see that as nothing was known of Sun Zi within say 100 years of his death.
     
   • Unlike many Chinese mathematicians, Sun Zi cannot have been an important government official, nor to have been from a family of high social standing.
     
   • http://www-history.mcs.st-andrews.ac.uk/Biographies/Sun_Zi.html .
     

2. Aristarchus biography
   
   • Aristarchus was certainly both a mathematician and astronomer and he is most celebrated as the first to propose a sun-centred universe.
     
   • He is also famed for his pioneering attempt to determine the sizes and distances of the sun and moon.
     
   • You King Gelon are aware the 'universe' is the name given by most astronomers to the sphere the centre of which is the centre of the earth, while its radius is equal to the straight line between the centre of the sun and the centre of the earth.
     
   • His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface.
     
   • The only surviving work of Aristarchus, On the Sizes and Distances of the Sun and Moon, is not based on the sun centred theory and unfortunately his work on that sun centred theory referred to by Archimedes has been lost.
     
   • On the Sizes and Distances of the Sun and Moon provides the details of his remarkable geometric argument, based on observation, whereby he determined that the Sun was about 20 times as distant from the Earth as the Moon, and 20 times the Moon's size.
     
   • He knew that the moon shines by reflected sunlight, so he argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances.
     
   • and deduced that the sun was between 18 to 20 times as far away as the moon.
     
   • In fact at the moment of half illumination the angle between the moon and the sun is actually 89° 50' and the sun is actually about 400 times further away than the moon.
     
   • Rather strangely Aristarchus uses values for the angle subtended by the sun and moon to be 2°.
     
   • He correctly uses the evidence of eclipses to state that the sun and moon subtend the same angle.
     
   • However, Archimedes quotes a value of 1/2° for the angle subtended by the sun and attributes this figure to Aristarchus.
     
   • We can only assume that Aristarchus wrote On the Sizes and Distances of the Sun and Moon early in his career, then later on he adopted his hypothesis of a sun centred universe and computed a much more accurate value of the angle subtended by the sun.
     

3. Chang biography
   
   • Sun-Yung Alice Chang .
     
   • Sun-Yung Alice Chang was born in China at the time when the Communists were rapidly taking control of the country.
     
   • The Ruth Lyttle Satter Prize is awarded to Sun-Yung Alice Chang for her deep contributions to the study of partial differential equations on Riemannian manifolds and in particular for her work on extremal problems in spectral geometry and the compactness of isospectral metrics within a fixed conformal class on a compact 3-manifold.
     
   • Honours awarded to Sun-Yung Alice Chang .
     

4. Clavius biography
   
   • An event which had a large influence on him was an eclipse of the sun which occurred on 21 August 1560.
     
   • I shall cite two remarkable eclipses of the Sun, which happened in my own time and thus not long ago.
     
   • One of these I observed about midday at Coimbra in Lusitania [Portugal] in the year 1559 [sic], in which the Moon was placed between my sight and the Sun with the result that it covered the whole Sun for a considerable length of time.
     
   • The quotation from In sphaeram Ioannis de Sacro Bosco Commentarius which we gave above begins by referring to 'two remarkable eclipses of the Sun'.
     
   • The other I saw at Rome in the year 1567 also about midday in which although the Moon was placed between my sight and the Sun it did not obscure the whole Sun as previously but (a thing which perhaps never before occurred at any other time) a certain narrow circle was left on the Sun, surrounding the whole of the Moon on all sides.
     
   • The report suggests an annular eclipse with the moon subtending a slightly smaller angle than the sun.
     
   • Hence if the lunar limb was assumed to be accurately circular, the eclipse of 1567 would be only marginally total, the Moon covering the Sun completely for just 14 sec near the central line.
     
   • Far from the least important of the things seen with this instrument is that Venus receives its light from the Sun as does the Moon, so that sometimes it appears to be more like a crescent, sometimes less, according to its distance from the Sun.
     
   • Of course the observations of Venus were the most disturbing since Ptolemy's version of the sun and planets would not account for the observed phases.
     

5. Horrocks biography
   
   • However he rejected Kepler's theory of why the planetary orbits were ellipses, which was based on alternate attraction and repulsion of a planet by the sun.
     
   • Horrocks then proposed that the planets had a tendency to fall towards the sun.
     
   • The sun's conversion doth turn the planet out of this line framing its motion into a circle, but the former desire of the planet to move in a straight line hinders the full conquest of the sun and forces it into an elliptical figure.
     
   • Kepler had died in 1630 but even if he had lived he would not have seen the transit of 1631 since it was not visible in Europe as the sun was below the horizon during the transit.
     
   • Horrocks purchased a simple telescope which he set up to project an image of the sun onto a graduated circle six inches in diameter.
     
   • But during all this time I saw nothing in the sun except a small and common spot ..
     
   • I then beheld a most agreeable spectacle, the object of my sanguine wishes, a spot of unusual magnitude and of a perfectly circular shape, which had already fully centred upon the sun's disc on the left, so that the limbs of the Sun and Venus precisely coincided, forming an angle of contact.
     
   • Although he had only been able to make three observations of the transit from the same site, Horrocks was able to compute the distance of the earth to the sun far more accurately than any previously found.
     
   • He realised that the moon's orbit was perturbed by the sun (remember that he worked before Newton proposed his theory of universal gravitation) and was able to give a lunar theory which was much better than anything available at the time.
     

6. Heraclides biography
   
   • Heraclides of Pontus has achieved fame for a long time as the first to propose that the sun was the centre of the solar system but this has been shown to be due to a misinterpretation of what he wrote.
     
   • Heraclides of Pontus, Plato's famous pupil, is known on clear evidence to have discovered that Venus and Mercury revolve round the sun like satellites.
     
   • Heraclides Ponticus, when describing the circle of Venus as well as that of the sun, and giving the two circles one centre and one mean motion, showed how Venus is sometimes above, sometimes below the sun.
     
   • T H Martin, in 1849, pointed out the significance of the passage saying that Venus is sometimes above, sometimes below the sun clearly means that Heraclides believed that it was in orbit round the sun.
     
   • Schiaparelli accepted Martin's argument and went further to claim that Heraclides must have proposed the theory that the sun revolves round the earth, but the planets revolve round the sun.
     
   • Neugebauer [A history of ancient mathematical astronomy (New York, 1975).',3)">3] shows clearly that the passage indicating that Venus is sometimes above, sometimes below the sun, means that it is sometimes ahead of the sun, sometimes behind it.
     
   • Rather than basing his argument on Calcidius's words, van der Waerden interpreted a diagram in Calcidius to mean that the sun, Venus and the earth all revolve round a common centre.
     

7. Copernicus biography
   
   • This book, usually called the Little Commentary, set out Copernicus's theory of a universe with the sun at its centre.
     
   • The centre of the universe is near the sun.
     
   • The distance from the Earth to the sun is imperceptible compared with the distance to the stars.
     
   • The apparent annual cycle of movements of the sun is caused by the Earth revolving round it.
     
   • The most remarkable of the axioms is 7, for although earlier scholars had claimed that the Earth moved, some claiming that it revolved round the sun, nobody before Copernicus appears to have correctly explained the retrograde motion of the outer planets.
     
   • In De revolutionibus Copernicus states several reasons why it is logical that the sun would be at the centre of the universe:- .
     
   • At the middle of all things lies the sun.
     
   • As the location of this luminary in the cosmos, that most beautiful temple, would there be any other place or any better place than the centre, from which it can light up everything at the same time? Hence the sun is not inappropriately called by some the lamp of the universe, by others its mind, and by others its ruler.
     
   • Copernicus's cosmology placed a motionless sun not at the centre of the universe, but close to the centre, and also involved giving several distinct motions to the Earth.
     
   • Brahe, who did not accept Copernicus's claim that the Earth moved round the sun, nevertheless wrote:- .
     

8. Ptolemy biography
   
   • The Almagest is the earliest of Ptolemy's works and gives in detail the mathematical theory of the motions of the Sun, Moon, and planets.
     
   • It is a view of the world based on a fixed earth around which the sphere of the fixed stars rotates every day, this carrying with it the spheres of the sun, moon, and planets.
     
   • Ptolemy used geometric models to predict the positions of the sun, moon, and planets, using combinations of circular motion known as epicycles.
     
   • [After introducing the mathematical concepts] we have to go through the motions of the sun and of the moon, and the phenomena accompanying these motions; for it would be impossible to examine the theory of the stars thoroughly without first having a grasp of these matters.
     
   • In examining the theory of the sun, Ptolemy compares his own observations of equinoxes with those of Hipparchus and the earlier observations Meton in 432 BC.
     
   • Based on his observations of solstices and equinoxes, Ptolemy found the lengths of the seasons and, based on these, he proposed a simple model for the sun which was a circular motion of uniform angular velocity, but the earth was not at the centre of the circle but at a distance called the eccentricity from this centre.
     
   • This theory of the sun forms the subject of Book 3 of the Almagest.
     
   • Ptolemy also discusses, as Hipparchus had done, the synodic month, that is the time between successive oppositions of the sun and moon.
     
   • Having given a theory for the motion of the sun and of the moon, Ptolemy was in a position to apply these to obtain a theory of eclipses which he does in Book 6.
     

9. Anaxagoras biography
   
   • In about 450 BC Anaxagoras was imprisoned for claiming that the Sun was not a god and that the Moon reflected the Sun's light.
     
   • Under this law they persecuted Anaxagoras, who was accused of teaching that the sun was a red-hot stone and the moon was earth.
     
   • We should examine this teaching of Anaxagoras about the sun more closely for, although it was used as a reason to put him in prison, it is a most remarkable teaching.
     
   • Anaxagoras proposed that the moon shines by reflected light from the "red-hot stone" which was the sun, the first such recorded claim.
     
   • Showing great genius he was also then able to take the next step and become the first to explain correctly the reason for eclipses of the sun and moon.
     
   • His explanation of eclipses of the sun is completely correct but he did spoil his explanation of eclipses of the moon by proposing that in addition to being caused by the shadow of the earth, there were other dark bodies between the earth and the moon which also caused eclipses of the moon.
     
   • The investigation of sun.
     

10. Kepler biography
    
    • The astronomy of the curriculum was, of course, geocentric astronomy, that is the current version of the Ptolemaic system, in which all seven planets - Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn - moved round the Earth, their positions against the fixed stars being calculated by combining circular motions.
      
    • This ties up with Kepler's astronomy to the extent that he apparently found somewhat similar intellectual difficulties in explaining how 'force' from the Sun could affect the planets.
      
    • For instance, the Copernican theory can explain why Venus and Mercury are never seen very far from the Sun (they lie between Earth and the Sun) whereas in the geocentric theory there is no explanation of this fact.
      
    • Kepler concluded that the orbit of Mars was an ellipse with the Sun in one of its foci (a result which when extended to all the planets is now called "Kepler's First Law"), and that a line joining the planet to the Sun swept out equal areas in equal times as the planet described its orbit ("Kepler's Second Law"), that is the area is used as a measure of time.
      
    • Both laws relate the motion of the planet to the Sun; Kepler's Copernicanism was crucial to his reasoning and to his deductions.
      
    • Like most people of the time, Kepler accepted the principle of astrology, that heavenly bodies could influence what happened on Earth (the clearest examples being the Sun causing the seasons and the Moon the tides) but as a Copernican he did not believe in the physical reality of the constellations.
      

11. Anaximander biography
    
    • He appears to have been the first person to argue that the sun, moon, planets and stars revolved around the earth so the sun which rose in the morning was the same sun that had disappeared on the evening of the preceding day.
      
    • The radius of the stars circles was 9 times the radius of the circle on top of the cylindrical earth, the radius of the moons circle was 18 times that of the earth, and the ratio of the sun's to the radius of the earth was 27.
      
    • The sphere of fire split into several wheels which were then the wheels of the stars, moon, and sun.
      
    • He argued that the young earth was covered in seas, some of which began to dry out due to the heat of the sun.
      
    • The first animals had skin covered with spines but after they began to live on dry land, the heat of the sun gradually caused the animals to have fewer spines.
      
    • Since at this time the sun was due south, the gnomon was used to find what we would call today 'the points of the compass'.
      

12. Cassini biography
    
    • Observations would lead him to accept the model of the solar system proposed by Tycho Brahe and, in 1659, he presented an Earth centred system with the moon and sun orbiting the Earth and the other planets orbiting the sun.
      
    • A small hole allowed the rays of the sun to enter the church.
      
    • They formed a small image on a scale on the floor which allowed the position of the sun to be accurately determined.
      
    • He continued with his research in astronomy, proposing a model for atmospheric refraction which turned out to be incorrect, making an intensive study of the sun, publishing tables in 1662, and continuing to search for comets.
      
    • In 1664 he observed a comet which led him to propose a new theory that comets travelled in circular orbits around the sun with the centre of the orbit in the direction of the star Sirius.
      
    • From their data the first accurate value of the solar parallax was found, giving the distance from the Earth to the sun.
      
    • He worked on this as part of a study of the relative motions of the Earth and the sun and proposed this as the curve for planetary orbits rather than the ellipse as proposed by Kepler.
      

13. Brahe biography
    
    • Tycho is perhaps best known today for his theory of the solar system which is based on a stationary Earth round which the Moon and Sun revolve.
      
    • The other planets, according to Tycho's theory, revolve round the Sun.
      
    • In fact in his younger days Tycho had been convinced by Copernicus' Sun centred model but his firm belief that theory must be supported by experimental evidence led him away.
      
    • The problem was, of course, that in the Sun centred model of Copernicus a parallax shift should be observed but despite his attempts to measure such a shift, Tycho could detect none.
      
    • In fact Tycho was not the first to propose the Earth centred model with the planets rotating round the Sun for Erasmus Reinhold had done so a few years earlier.
      
    • Tycho intended that this work should prove the truth of his cosmological model, in which the Earth (with the Moon in orbit around it) was at rest in the centre of the Universe and the Sun went round the Earth (all other planets being in orbit about the Sun and thus carried round with it).
      

14. Al-Battani biography
    
    • He composed a work on astronomy, with tables, containing his own observations of the sun and moon and a more accurate description of their motions than that given in Ptolemy's "Almagest".
      
    • The motions of the sun, moon and five planets are discussed in chapters 27 to 31, where the theory given is that of Ptolemy but for al-Battani the theory appears less important than the practical aspects.
      
    • Al-Battani showed that the farthest distance of the Sun from the Earth varies and, as a result, annular eclipses of the Sun are possible as well as total eclipses.
      
    • However, as Swerdlow points out in [Centaurus 17 (2) (1972), 97-105.',8)">8], the influence of Ptolemy was remarkably strong on all medieval authors, and even a brilliant scientist like al-Battani probably did not dare to claim a different value of the distance from the Earth to the Sun from that given by Ptolemy.
      
    • 53 (1) (1998), 1-49.',5)">5] there is a discussion on how al-Battani managed to produce more accurate measurements of the motion of the sun than did Copernicus.
      
    • For al-Battani refraction had little effect on his meridian observations at the winter solstice because, at his more southerly site of ar-Raqqah, the sun was higher in the sky.
      

15. Gassendi biography
    
    • We also have records of Gassendi and Gaultier observing a comet in 1618, an eclipse of the moon in 1620, and an eclipse of the sun in 1621.
      
    • After returning to Provence from Paris, Gassendi wrote to Galileo with strong support for his argument that the earth revolves round the sun.
      
    • In 1632 Gassendi published Mercury seen on the face of the sun, which described his observations of the transit of Venus which he observed from Paris in November 1631 following the prediction of the event by Kepler in 1629 (the transit actually occurred a month before Kepler's predicted date).
      
    • Gassendi had used a telescope to project the image of the sun onto paper, and so was able to observe the transit.
      
    • He believed in atomism and defended a mechanistic explanation of nature, as for example in On the apparent magnitude of the sun on the horizon and overhead (1635).
      
    • Gassendi was a firm believer in the system of Copernicus and Galileo, and the argument with Morin led to him thinking deeply about the scientific case for a sun centred system.
      

16. Galileo biography
    
    • At one stage in the calculations he became very puzzled since the data he had recorded seemed inconsistent, but he had forgotten to take into account the motion of the Earth round the sun.
      
    • Also in 1610 he discovered that, when seen in the telescope, the planet Venus showed phases like those of the Moon, and therefore must orbit the Sun not the Earth.
      
    • This did not enable one to decide between the Copernican system, in which everything goes round the Sun, and that proposed by Tycho Brahe in which everything but the Earth (and Moon) goes round the Sun which in turn goes round the Earth.
      
    • I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it.
      
    • He declared the Galileo case closed, but he did not admit that the Church was wrong to convict Galileo on a charge of heresy because of his belief that the Earth rotates round the sun.
      

17. Eddington biography
    
    • Its aim was to verify the bending of light passing close to the sun which was predicted by relativity theory.
      
    • At that time such observations of stars close to the sun in the sky could only be made during a total eclipse.
      
    • we began to get a glimpse of the sun.
      
    • They are all good of the sun, showing a very remarkable prominence; but the cloud has interfered with the star images.
      
    • Light rays, when near the Sun, do not go straight.
      

18. Proclus biography
    
    • For example he mentions the hypothesis that the sun is at the centre of the planets as proposed by Aristarchus but rejects it immediately since it contradicted the views of a Chaldean whom he says that it is unlawful not to believe.
      
    • In his astronomical writings, Proclus described how the water clock invented by Heron could be used to measure the apparent diameter of the Sun.
      
    • Water is collected from the clock in a container while the sun rises.
      
    • As soon as the Sun has risen the water is collected in another container and this measurement continues until sunrise the following day.
      
    • Then the ratio of the weights of water in the two containers gives the apparent diameter of the Sun.
      

19. Oenopides biography
    
    • Indeed, if Oenopides did not fix on this or some other figure it is difficult to know in what his achievement consisted, for the Babylonians no less than the Pythagoreans and Egyptians must have realised from early days that the apparent path of the sun was inclined to the celestial equator.
      
    • Originally the "Great Year" was the period after which the motions of the sun and moon came to repeat themselves.
      
    • Later it came to mean the period after which the motions of the sun, moon and planets all repeated themselves so in the period of one Great Year all should have returned to their positions at the beginning of the Great Year.
      
    • His Great Year clearly had reference to the sun and moon only; he merely sought to find the least integral number of complete years which would contain an exact number of lunar months.
      
    • Paul Tannery in [Memoires de la Societe des sciences physiques et naturelles de Bordeaux 4 (1888), 79-96.',5)">5] makes another claim however when he states that Oenopides considered some of the planets as well as the sun and moon as part of his 59 year Great Year.
      

20. Hipparchus biography
    
    • There are two different definitions of a 'year' for one might take the time that the sun takes to return to the same place amongst the fixed stars or one could take the length of time before the seasons repeated which is a length of time defined by considering the equinoxes.
      
    • In addition there is the synodic month, that is the time between successive oppositions of the sun and moon.
      
    • The main reason for his range of values was that he was unable to determine the parallax of the sun, only managing to give an upper value.
      
    • Hipparchus appears to know that 67 earth radii for the distance of the moon comes from this upper limit of solar parallax, while the lower value of 59 earth radii corresponds to the sun being at infinity.
      
    • Hipparchus was also able to give an epicycle model for the motion of the sun (which is easier), but he did not attempt to give an epicycle model for the motion of the planets.
      

21. Boulliau biography
    
    • As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2.
      
    • However he then argues that the sun does not produce a planetary moving force:- .
      
    • I say that the Sun is moved by its own form around its axis, by which form it was ignited and made light, indeed I say that no kind of motion presses upon the remaining planets ..
      

22. Kirchhoff biography
    
    • Fraunhofer had observed bright lines in the spectrum produced by flames and noted that they appeared at similar frequencies to certain dark lines in the spectrum of the sun.
      
    • Kirchhoff and Bunsen went on to examine the spectrum of the sun in 1861 and were able to identify the chemical elements in the sun's atmosphere.
      
    • Kirchhoff is perhaps best known for being the first to explain the dark lines in the sun's spectrum as caused by absorption of particular wavelengths as the light passes through gases in the sun's atmosphere.
      

23. Al-Khazin biography
    
    • We know that in 959/960 al-Khazin was required by the vizier of Rayy, who was appointed by Adud ad-Dawlah, to measure the obliquity of the ecliptic (the angle which the plane in which the sun appears to move makes with the equator of the earth).
      
    • Ptolemy had the sun moving in uniform circular motion about a centre which was not the earth.
      
    • Al-Khazin was unhappy with this model since he claimed that if this were the case then the apparent diameter of the sun would vary throughout the year and observation showed that this were not the case.
      
    • Of course the apparent diameter of the sun does vary but by too small an amount to be observed by al-Khazin.
      
    • To get round this problem, al-Khazin proposed a model in which the sun moved in a circle which was centred on the earth, but its motion was not uniform about the centre, rather it was uniform about another point (called the excentre).
      

24. Nilakantha biography
    
    • The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.
      
    • The fourth and fifth chapters are Treatise on the lunar eclipse and On the solar eclipse and these two chapters treat various aspects of the eclipses of the sun and the moon.
      
    • The sixth chapter is On vyatipata and deals with the complete deviation of the longitudes of the sun and the moon.
      
    • The final chapter On elevation of the lunar cusps examines the size of the part of the moon which is illuminated by the sun and gives a graphical representation of it.
      

25. McCrea biography
    
    • Later, however, he became interested in a theoretical study of the sun.
      
    • In 1929 he was awarded his doctorate after submitting his thesis Problems concerning the outer layers of the sun [The Mathematical Gazette 84 (500) (2000), 318-320.',6)">6]:- .
      
    • At that time, it was still commonly believed that the main constituent of the sun was iron.
      
    • McCrea's later books are Physics of Sun and Stars (1950), Cosmology (1969), The Royal Greenwich Observatory (1975), and History of the Royal Astronomical Society, 1920 to 1980 (1987).
      

26. Al-Biruni biography
    
    • Certainly by the age of seventeen al-Biruni was engaged in serious scientific work for it was in 990 that he computed the latitude of Kath by observing the maximum altitude of the sun.
      
    • al-Khujandi was an astronomer who was working with a very large instrument he had built on the mountain above Rayy to observe meridian transits of the sun near the solstices.
      
    • At Lamghan, north of Kabul, on 8 April 1019 he observed an eclipse of the sun, writing [Encyclopaedia Britannica.
      
    • at sunrise we saw that approximately one-third of the sun was eclipsed and that the eclipse was waning.
      

27. Darwin biography
    
    • In particular, using methods introduced by Laplace and Thomson, he discussed the effects of tidal action on the Sun-Earth-Moon system.
      
    • One of his theories, namely that the Moon was pulled from a molten Earth early in its history by tidal action of the Sun, is now considered incorrect.
      
    • Darwin made a major study of the three-body problem in the case of the orbits of the Sun-Earth-Moon system.
      
    • Despite the fact that we do not accept Darwin's conclusions today, he is important in being the first to apply mathematical techniques to study the evolution of the Sun-Earth-Moon system.
      

28. Cleomedes biography
    
    • It is written to attack the Epicureans who believed among other odd beliefs, that the sun was as large as it looked, namely one foot across.
      
    • He also correctly explains the reports of lunar eclipses seen when both the sun and moon are above the horizon as being due to refraction.
      
    • Of some interest is the remark that the absolute size of fixed stars may reach, or even surpass, the sun ..
      
    • it is [also] said that the earth, seen from the sun, would appear at best a very small star.
      

29. Levi biography
    
    • of a staff of 41/2 feet long and about one inch wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars.
      
    • After he had observed this event he proposed a new theory of the Sun, which he proceeded to test by further observations.
      
    • He described a geometrical model for the motion of the Moon and made other astronomical observations of the Moon, Sun and planets using a camera obscura.
      
    • Of course these beliefs were well wide of the truth such as his belief that the Milky Way was on the sphere of the fixed stars and shines by the reflected light of the Sun.
      

30. Vijayanandi biography
    
    • It deals with the topics of: units of time measurement; mean and true longitudes of the sun and moon; the length of daylight; mean longitudes of the five planets; true longitudes of the five planets; the three problems of diurnal rotation; lunar eclipses, solar eclipses; the projection of eclipses; first visibility of the planets; conjunctions of the planets with each other and with fixed stars; the moon's crescent; and the patas of the moon and sun.
      
    • In particular there was, according to Aryabhata I, a basic period of 4320000 years called a mahayuga and it was assumed that the sun, the moon, their apsis and node, and the planets reached perfect conjunctions after this period.
      
    • All the planets and the node and apsis of the moon and sun had to have an integer number of revolutions in the mahayuga.
      

31. Jyesthadeva biography
    
    • The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.
      
    • The fourth and fifth chapters are Treatise on the lunar eclipse and On the solar eclipse and these two chapters treat various aspects of the eclipses of the sun and the moon.
      
    • The sixth chapter is On vyatipata and deals with the complete deviation of the longitudes of the sun and the moon.
      
    • The final chapter On elevation of the lunar cusps examines the size of the part of the moon which is illuminated by the sun and gives a graphical representation of it.
      

32. Lepaute biography
    
    • The Ephemerides des mouvements celestes gave tables of the sun, the moon and planets covering a period of ten years.
      
    • For this last volume she alone made all the computations for the positions of the sun, moon and planets.
      
    • Alic also claims in [Hypatia\'s Heritage : A history of women in science from antiquity to the late nineteenth century (The Women\'s Press, London, 1986).',1)">1] that Lepaute published a memoir containing observations of the transit of Venus across disk of the sun in 1761.
      
    • Another piece of work which is certainly due to Lepaute is the calculation concerning the annular eclipse of the sun on 1 April 1764.
      

33. Al-Khalili biography
    
    • Al-Khalili was an astronomer associated with the Umayyad Mosque in Damascus in the latter half of the fourteenth century, who compiled an extensive corpus of tables for timekeeping by the sun and regulating the astronomically defined time of Muslim prayer ..
      
    • tables for reckoning time by the sun, for the latitude of Damascus; tables for regulating the time of Muslim prayer, for the latitude of Damascus; tables of auxiliary mathematical functions for timekeeping by the sun for all latitudes; tables of auxiliary mathematical functions for solving the problems of spherical astronomy for all latitudes; a table for displaying ..
      
    • Tables for reckoning time by the sun and tables for regulating the time of Muslim prayer, computed for the latitude of Cairo, had been earlier computed by ibn Yunus.
      

34. Wilson Alexander biography
    
    • Using a geometric argument, he showed that sunspots were depressions in the Sun, publishing his results in papers of 1774 and 1783 in the Philosophical Transactions of the Royal Society of London.
      
    • The model of the Sun proposed by Wilson was of a dark body surrounded by a shell of highly luminous material.
      
    • This model was accepted as true for 100 years and Wilson's theory that sunspots were depressions was 'proved' on 1861 when the first stereoscopic photographs of the sun were taken.
      

35. Jabir ibn Aflah biography
    
    • In [Centaurus 19 (2) (1975), 85-107.',4)">4] Lorch explains Jabir ibn Aflah's most famous criticism, namely Ptolemy's placement of Venus and Mercury below the Sun.
      
    • Ptolemy claimed that these planets could never be on a line between an observer on Earth and the sun., but ibn Aflah states that this is an error, and that Venus and Mercury are above the Sun.
      

36. Cowling biography
    
    • His first paper On the radial limitation of the Sun's magnetic field (1929) actually criticised Chapman's theory that the magnetic field of the sun had radial limitations.
      
    • Certainly showing inconsistencies in Chapman's theory of the sun's magnetic field did not hinder collaboration between the two men, and they published a major classic text The Mathematical Theory of Non-uniform Gases in 1939.
      

37. Thales biography
    
    • It is reported that Thales predicted an eclipse of the Sun in 585 BC.
      
    • The cycle of about 19 years for eclipses of the Moon was well known at this time but the cycle for eclipses of the Sun was harder to spot since eclipses were visible at different places on Earth.
      
    • without trouble or the assistance of any instrument [he] merely set up a stick at the extremity of the shadow cast by the pyramid and, having thus made two triangles by the impact of the sun's rays, ..
      

38. Kirch biography
    
    • In case the reader thinks of a calendar as simply giving the days of the week together with a pretty picture for each month, we should explain that the Kirch calendars included information on the phases of the moon, the setting of the sun, eclipses, and the position of the sun and the planets.
      
    • For example she published her observations on the Aurora Borealis in 1707 and, in 1709, she published a work Von der Conjunction der Sonne des Saturni und der Venus on the conjunction of the Sun, Saturn, and Venus which would occur in 1712.
      

39. Wolf biography
    
    • He observed the Sun because he was trying to find a planet inside the orbit of Mercury.
      
    • His idea was to detect it when it crossed the disk of the Sun so he began to make a systematic record of the spots on the Sun, every day when visibility allowed, beginning in 1826.
      

40. Picard Jean biography
    
    • Picard devised a micrometer to measure the diameters of celestial objects such as the Sun, Moon and planets.
      
    • The value Picard, working with Jean-Dominique Cassini, and Jean Richer, deduced for the distance from the Earth to the sun underestimates the true value by 8.5%.
      
    • Also at the Paris Observatory, Picard tried to measure the parallax of nearby stars and so verify the fact that the Earth orbits the sun.
      

41. Diocles biography
    
    • Pythian the Thasian geometer wrote a letter to Conon in which he asked him how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet the circumference of a circle.
      
    • And when Zenodorus the astronomer came down to Arcadia and was introduced to us, he asked us how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet a point and thus cause burning.
      
    • In On burning mirrors Diocles also studies the problem of finding a mirror such that the envelope of reflected rays is a given caustic curve or of finding a mirror such that the focus traces a given curve as the Sun moves across the sky.
      

42. Lalande biography
    
    • The observations of its orbit made by Halley had been used to predict its return based on the assumption that the comet's orbit was not affected by any bodies in the solar system except the sun.
      
    • Again observations taken from different places on the Earth of the precise timing of the passage of the planet in front of the sun would allow parallax measurements to be made and the distance from the Earth to the sun to be calculated.
      

43. Hooke biography
    
    • He then invented a helioscope to attempt to measure the rotation of the sun using sunspots.
      
    • He observed several comets and asked a number of important questions about them, including why the tail points away from the sun, and how if the comet is burning it could burn for so long and burn in a place where there is no air.
      
    • In 1672 Hooke attempted to prove that the Earth moves in an ellipse round the Sun and six years later proposed that inverse square law of gravitation to explain planetary motions.
      

44. Callippus biography
    
    • The Sun, Moon, Mercury, Venus and Mars each had five spheres while Jupiter and Saturn had four and the stars had one.
      
    • Callipus tried to make the system of concentric spheres suit the phenomena more exactly by adding other spheres; he left the number of spheres at four in the case of Jupiter and Saturn, but added one each to the other planets and two each in the case of the sun and the moon ..
      
    • He accounted for this in his model by making the velocity of the Sun vary through the year and this was achieved with the two extra spheres described above.
      

45. Aryabhata I biography
    
    • Aryabhata gives the radius of the planetary orbits in terms of the radius of the Earth/Sun orbit as essentially their periods of rotation around the Sun.
      
    • He correctly explains the causes of eclipses of the Sun and the Moon.
      

46. Autolycus biography
    
    • Again eclipses of the sun were sometimes total, sometimes annular where moon appears smaller than the sun and a ring of the sun is visible right round the moon.
      

47. Al-Farisi biography
    
    • Ibn al-Haytham had proposed that light from the sun is reflected by a cloud before reaching the eye.
      
    • Al-Farisi, on the other hand, proposed a model where the ray of light from the sun was refracted twice by a water droplet, one or more reflections occurring between the two refractions.
      
    • Next, the blended image diminishes and becomes a darker and darker red until it disappears when the sun is outside the cone of rays refracted after one reflection.
      

48. Posidonius biography
    
    • Posidonius also made calculations of the size and distance to the moon, and the size and distance to the sun.
      
    • As to his calculations of the sun, Neugebauer writes [A history of ancient mathematical astronomy (New York, 1975).',3)">3]:- .
      
    • Posidonius's attempts (according to Cleomedes) to determine the size of the sun are rather naive and make it difficult to understand that his astronomy was not ridiculed by authors like Cicero and Pliny who pretend to know the work of Hipparchus.
      

49. Fizeau biography
    
    • He approached the two friends in 1845 and suggest that they might attempt to make photographs of an image of the sun produced by a telescope.
      
    • They were highly successful and produced the first ever photograph of the sun.
      
    • Arago was delighted with the success of Fizeau and Foucault in photographing the sun, and suggested to them that they try to calculate the speed of light with an earth based experiment.
      

50. Harriot biography
    
    • he solved the problem of reconciling the sun and pole star observations for determining latitude, introduced the idea of using solar amplitude to determine magnetic variation and, as well as improving methods and devices for observation of solar or stellar altitudes, he recalculated tables for the sun's declination on the basis of his own astronomical observations.
      
    • From the data he collected he was able to deduce the period of the Sun's rotation.
      

51. Ibrahim biography
    
    • He also studied the apparent motion of the Sun and the geometry of shadows.
      
    • On the motions of the sun is an astronomical work which discusses of the motion of the solar apogee.
      
    • It also provides a critical analysis of the observations underlying Ptolemy's solar theory, and Ibrahim ibn Sinan provides his own theory of the sun.
      

52. Wittich biography
    
    • They observed the partial eclipse of the sun on 22 October 1579 and a total eclipse of the moon on 31 January 1580.
      
    • By the end of the 1570s, Tycho had found an orbit for the comet of 1577 that tallied well with the older view that Mercury and Venus circled around the Sun.
      
    • Wittich's diagrams are semigeoheliocentric, and therefore retain the solid crystalline spheres, only because they fail to solve completely the problem of the possible collision between the Sun and a planet such as Mars.
      

53. Freundlich biography
    
    • Freundlich was interested in measuring the deflection in a light ray passing close to the sun since again Einstein's incomplete theory of relativity suggested that this test could be used to check the validity of the theory and show that Newton's theory was incorrect.
      
    • During this period Freundlich planned three further expeditions to observe an eclipse and measure the deflection of light passing close to the sun.
      
    • he was a tall impressive man, and when we walked side by side through the streets of St Andrews people would say: "Here come the Sun and Moon".
      

54. Plateau biography
    
    • Unfortunately, the same year [1829], his ardour for experimentation pushed him to carry out a very dangerous experiment consisting in looking directly into the bright sun during approximately twenty-five seconds.
      
    • Although Plateau had carried out his experiment of staring at the sun in 1829, he had retained reasonable vision until 1841.
      

55. Bjerknes Vilhelm biography
    
    • He also produced the theory, in 1926, that sun spots are the erupting ends of magnetic vortices broken by the sun's differential rotation.
      

56. Empedocles biography
    
    • Empedocles says that the light from the Sun arrives first in the intervening space before it comes to the eye, or reaches the Earth.
      
    • But any given time is divisible into parts; so that we should assume a time when the sun's ray was not as yet seen, but was still travelling in the middle space.
      

57. Luoxia Hong biography
    
    • In seven of the 19 years an extra month was inserted making it a calendar based both on the sun and on the moon.
      
    • Luoxia Hong's calendar was much more than simply an attempt to bring the sun and moon into a common system for he also gave predictions for the positions of the planets and predictions of eclipses.
      

58. Halley biography
    
    • He proposed using transits of Mercury (and even better of Venus) to determine the distance of the Sun and therefore the scale of the solar system using Kepler's third law.
      
    • Earlier observations of the Moon were made only at conjunction or at opposition to the Sun and it was these earlier observations on which Newton's lunar theory had been based.
      

59. Anthemius biography
    
    • To contrive that a ray of the sun (admitted through a small hole or window) shall fall in a given spot, without moving away at any hour and season.
      
    • This is contrived by constructing an elliptical mirror one focus of which is at the point where the ray of the sun is admitted while the other is at the point to which the ray is required to be reflected at all times.
      

60. Yunus biography
    
    • The Muslim religion required considerable knowledge of the moon and the sun to determine the times of prayer during the year.
      
    • The Muslin lunar calendar required that the new months be determined by actual visibility of the lunar crescent rather than duration of the lunar month, so it was necessary to know a number of different details such as how far the moon was from the sun to determine when it became visible.
      

61. Thomson biography
    
    • This seems too extreme a view, but Thomson's refusal to accept atoms, his opposition to Darwin's theories, his incorrect speculations as to the age of the Earth and the Sun, and his opposition to Rutherford's ideas of radioactivity, certainly put him on the losing side of many arguments later in his career.
      
    • Kelvin on the sun .
      

62. Zu Chongzhi biography
    
    • In seven of the 19 years an extra month was inserted making it a calendar based both on the sun and the moon with 235 months in 19 years.
      
    • Because of the precession of the equinoxes the tropical year is shorter by about 21 minutes than the sidereal year (the time taken by the Sun to return to the same place against the background stars).
      

63. Cusa biography
    
    • For example he claimed that the Earth moved round the Sun.
      
    • Cusa published improvements to the Alfonsine Tables which gave a practical method to find the position of the Sun, Moon and planets using Ptolemy's model.
      

64. Herschel biography
    
    • The parallax is the apparent change in position of a relatively nearby star against the background of very distant stars due to the change in position of the earth in its orbit around the sun.
      
    • He recognised that the comet was being subjected to major forces other than gravitation and he was able to calculate that the force was one repelling it from the sun.
      

65. Apianus biography
    
    • The book also contains descriptions of five comets, in particular Halley's comet, and in Astronomicon Caesareum Apian is the first to make the important observation that a comet's tail always points away from the Sun.
      
    • With the volvelles that were supplied readers could solve calendar problems and find the positions of the sun, moon and the planets.
      

66. Archimedes biography
    
    • He states that Aristarchus has proposed a system with the sun at the centre and the planets, including the Earth, revolving round it.
      
    • as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him.
      

67. Sampson biography
    
    • He worked for the two years 1891-93 in Cambridge on astronomical spectroscopy and published a major paper On the rotation and mechanical state of the Sun [Obituary Notices of Fellows of the Royal Society 3 (8) (1940), 220-226.',2)">2]:- .
      
    • In addition to the usual assumption that the angular velocity increases inwards along all radii, he laid down postulates for a new theory of the distribution of the sun's internal temperature; being somewhat dissatisfied with the theory of convective equilibrium, he laid stress on the effects of radiation and absorption.
      

68. Avicenna biography
    
    • For example he observed Venus as a spot against the surface of the Sun and correctly deduced that Venus must be closer to the Earth than the Sun.
      

69. Eratosthenes biography
    
    • He assumed that the sun was so far away that its rays were essentially parallel, and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.
      
    • Eratosthenes also measured the distance to the sun as 804,000,000 stadia and the distance to the Moon as 780,000 stadia.
      

70. Foucault biography
    
    • He approached Foucault and Fizeau, who he knew personally, in 1845 and asked if they could try to take photographs of the sun.
      
    • They were successful in this and took the first ever photograph of the sun.
      

71. Gregory biography
    
    • Let in the sun's rays by a small hole to a darkened house, and at the hole place a feather (the more delicate and white the better for this purpose), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (if I mistake them not) whereof one is somewhat white (to wit, the middle which is opposite the sun) and all the rest severally coloured.
      

72. Bruno Giordano biography
    
    • Oxford seemed a place of learning that looked attractive to Bruno who visited there in the summer of 1583 and gave a series of lecturers on Copernicus's theory that the Earth rotated round the fixed Sun.
      
    • His ideas on cosmology are quite remarkable for he not only argued for a moving Earth, but he also argued for an infinite universe containing other stars like the Sun and other worlds like the Earth.
      

73. Scherk biography
    
    • These included talks on astronomy on topics such as: meteors and comets; the movements of the nebulas; the distance between the sun and earth; sunspots; the determination of the parallax of the sun with the transit of the Venus on 16 March 1874; and one to commemorate the 400th birthday of Nikolaus Copernicus in February 1873.
      

74. Lehmer Derrick N biography
    
    • Lehmer wrote two operas: The Necklace of the Sun : A Mayan Drama had its premiere at the Scottish Rite Auditorium, Oakland, on 28 February 1935.
      
    • He also published many collections of songs which he composed including Seven Indian Songs from the Yosemite Valley (1924), Down the stream and other Indian songs (1927), Indian camp-fire songs (1930), Indian songs from the Northland (1931), Fingers of the sun and other Indian songs from the Sierra slopes (1931), Songs from the Mesas (1932), Songs from the Tundras (1932), The Ballad of San Francisco Bay (1937), and Five Little songs (1937).
      

75. Roberval biography
    
    • In this work he praises Aristarchus's heliocentric system but he did not totally reject Ptolemy's earth centered system with the sun and planets circling the earth, or Tycho Brahe's system which has the earth at the centre, but has the planets circling a sun which circles the earth.
      

76. Bessel biography
    
    • Clearly to succeed it was important to choose a star which was close to the Sun.
      
    • Bessel functions appear as coefficients in the series expansion of the indirect perturbation of a planet, that is the motion caused by the motion of the Sun caused by the perturbing body.
      

77. Pappus biography
    
    • However, we now know that both the above sources are wrong, for Rome (see [Commentaires de Pappus et de Theon d\'Alexandrie sur l\'Almageste (Rome, 1931).',6)">6]) showed that it can be deduced from Pappus's commentary on the Almagest that he observed the eclipse of the sun in Alexandria which took place on 18 October 320.
      
    • When Ptolemy in the chapter on the apparent diameter of the sun, moon and shadow simply remarks that the tangential cones in question contact the spheres within a negligible error in great circles, then Pappus refers to Euclid's "Optics" to show that the circle of contact has a smaller diameter than the sphere, only to add a lengthy argument to demonstrate that the error committed in Ptolemy's construction is nevertheless negligible.
      

78. Sundman biography
    
    • In this work Sundman examined the perturbations of minor planets whose period of revolution round the sun is in the ratio of 1:2 of that of Jupiter.
      
    • He published La gravitationuniverselle et sa vitesse de propogation (1929), Demonstration nouvelle du theoreme de Poisson sur l'invariabilite des grands axes (1940), and The Motions of the Moon and the Sun at the Solar Eclipse of 1945, July 9th (1948).
      

79. Theodosius biography
    
    • Theodosius considered that it was 'day' if the sun was less than 15° below the horizon for then no stars were visible and he seemed to fail to understand that in the polar regions the sun can move almost parallel to the horizon.
      

80. Qin Jiushao biography
    
    • Although there is no evidence of progress on such problems in China since the work of Sun Zi which was 800 years earlier, Qin now shows how to handle the case where the mk are not pairwise coprime.
      
    • We should not underestimate [Qin's] revolutionary advance, because from [Sun Zi's] single remainder problem, we come at once to the general procedure for solving the remainder problem, even more advanced than Gauss's method, and there is not the slightest indication of gradual evolution.
      

81. Hevelius Johannes biography
    
    • He was off to study law at the University of Leyden, but his fascination with astronomy was enhanced when an eclipse of the sun occurred while he was on board the ship.
      
    • This half succeeded but the event which sealed things was an eclipse of the sun which occurred on 1 June 1639.
      

82. Le Verrier biography
    
    • Le Verrier, however, attributed this to a planet, which he called Vulcan, closer to the Sun than Mercury or to a second asteroid belt so close to the Sun as to be invisible.
      

83. Newton biography
    
    • He further demonstrated that the planets were attracted toward the Sun by a force varying as the inverse square of the distance and generalised that all heavenly bodies mutually attract one another.
      
    • Newton explained a wide range of previously unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon as perturbed by the gravity of the Sun.
      

84. Chapman biography
    
    • To counter this trend, Chapman began to analyse data relating to the way that the Sun and Moon influence terrestrial phenomena.
      
    • These interpreted magnetic variations using a dynamo theory driven by tidal flows in the ionosphere resulting from the influence of the Sun and Moon.
      

85. Guo Shoujing biography
    
    • The reason that interpolation was required was that the motion of the sun through the stars throughout the year is irregular.
      
    • Guo looked at the accumulated difference, namely the difference in degrees moved by the sun in a day compared with the expected degrees moved if the motion was constant.
      

86. Milne biography
    
    • He calculated the amount of darkening of the limb resulting from a given energy distribution in the star's spectrum, and compared his theoretical results with the known values for the sun.
      
    • for his researches on the atmosphere of the Earth and the sun, on the internal constitution of the stars, and on the theory of relativity.
      

87. Peurbach biography
    
    • The astrologer wanted to know the precise position of the sun, moon and planets at the time of a person's birth to draw up a chart which was believed foretold a person's future.
      
    • Peurbach believed that the planets were in solid crystalline spheres although he believed that their motions were controlled by the Sun.
      

88. Buffon biography
    
    • Buffon proposed a method of creation of the planets which involved the collision of a comet with the sun.
      
    • Also in 1777 he attempted to calculate the probability that the sun would continue to rise after having been observed to rise n days in a row; see [Arch.
      

89. Talbot biography
    
    • The apparatus being armed with a sensitive paper, was taken out in a summer afternoon, and placed about one hundred yards from a building favourably illuminated by the sun.
      
    • He visited Edinburgh in the early 1840s and published Sun Pictures of Scotland in 1845 which contains photographs of Scotland including the Scott Monument on Princes Street in Edinburgh.
      

90. Hardy biography
    
    • Since Hardy thought that God would then have the sun shine all day to spite him, he would be able to enjoy the cricket in perfect sunshine.
      
    • But those who formed the idea that he was merely an absent-minded professor would receive a shock in conversation, where he displayed amazing vitality on every subject under the sun.
      

91. Schwarzschild biography
    
    • He also worked on radiation pressure from the sun and, with the assumption that the tails of comets consisted of spherical particles which reflected light well, he calculated the size of the particles in the tails.
      
    • In 1906 he studied the transport of energy through a star by radiation and published an important paper on radiative equilibrium of the atmosphere of the sun.
      

92. Jackson biography
    
    • There was a total eclipse of the sun in South Africa on 1 October 1940.
      
    • He was president of the Royal Astronomical Society from 1953 to 1955 and during this time he went to Stromatad in Sweden to observe the total eclipse of the sun on 30 June 1954.
      

93. Plato biography
    
    • Plato's beliefs as regards the universe were that the stars, planets, Sun and Moon move round the Earth in crystalline spheres.
      
    • The sphere of the Moon was closest to the Earth, then the sphere of the Sun, then Mercury, Venus, Mars, Jupiter, Saturn and furthest away was the sphere of the stars.
      

94. Kamalakara biography
    
    • It deals with the topics of: units of time measurement; mean motions of the planets; true longitudes of the planets; the three problems of diurnal rotation; diameters and distances of the planets; the earth's shadow; the moon's crescent; risings and settings; syzygies; lunar eclipses, solar eclipses; planetary transits across the sun's disk; the patas of the moon and sun; the "great problems"; and a final chapter which forms a conclusion.
      

95. Ferrel biography
    
    • An event which heightened Ferrel's scientific interests and encouraged him to pursue his education further was the partial eclipse of the sun which he witnessed in 1832.
      
    • that the action of the moon and sun upon the tides must have a tendency to retard the earth's rotation on its axis.
      

96. Gauss biography
    
    • Unfortunately, Piazzi had only been able to observe 9 degrees of its orbit before it disappeared behind the Sun.
      
    • Because of the survey, Gauss invented the heliotrope which worked by reflecting the Sun's rays using a design of mirrors and a small telescope.
      

97. Einstein biography
    
    • In fact 1911 was a very significant year for Einstein since he was able to make preliminary predictions about how a ray of light from a distant star, passing near the Sun, would appear to be bent slightly, in the direction of the Sun.
      

98. Maskelyne biography
    
    • This was important since accurate measurements would allow the distance from the Earth to the Sun to be accurately measured and the scale of the solar system determined.
      

99. Mahler biography
    
    • He was without any pretensions and one could discuss anything under the sun with him, though preferably mathematics, photography or Chinese (in that order).
      

100. Wang Xiaotong biography
     
     • There was disagreement between Wang and another calendar expert Fu Renjun about certain aspects of the calendar and in fact Wang's ideas were not particularly good since he wished to ignore the irregularity of the sun's motion and he also wanted to ignore the precession of the equinoxes which had first been incorporated in calendar calculations by Zu Chongzhi in the fifth century.
       

101. Kac biography
     
     • where there is more sun and less ice ..
       

102. Sporus biography
     
     • Sporus also wrote on the size of the Sun and on comets.
       

103. Stokes biography
     
     • He suggested these were caused by atoms in the outer layers of the Sun absorbing certain wavelengths.
       

104. Reynolds biography
     
     • He also worked on electromagnetic properties of the sun and of comets, and considered tidal motions in rivers.
       

105. Eudemus biography
     
     • the cycle of the great year after which all the heavenly bodies are found in the same relative positions; the realisation by Anaximander that the earth is a heavenly body moving about the middle of the universe; the discovery by Anaximenes that the moon reflects the light of the sun and the explanation of lunar eclipses; and the inequality of the times between the solstices and the equinoxes.
       

106. Stevin biography
     
     • In De Hemelloop, published in 1608, he wrote on astronomy and strongly defended the sun centred system of Copernicus.
       

107. Al-Haytham biography
     
     • He explained twilight by refraction of sunlight once the Sun was less than 19° below the horizon.
       

108. Jeans biography
     
     • Instead he proposed a tidal theory based on a star passing close to the Sun and pulling matter out which condensed into the planets.
       

109. Todd John biography
     
     • One was a terrestrial globe, about a foot in diameter, driven by a 24-hour clock, which rotated in front of a brass sun.
       

110. Torricelli biography
     
     • He had also read almost everything that the contemporary mathematicians Brahe, Kepler and Longomontanus had written and, he told Galileo, he was convinced by the theory of Copernicus that the Earth revolved round the sun.
       

111. Commandino biography
     
     • In the same year he published his Latin edition of Aristarchus' Sizes and distances of the Sun and Moon again with commentary.
       

112. Al-Jayyani biography
     
     • He wrote on the morning and evening twilight, computing the fairly accurate value of 18° for the angle of the sun below the horizon at the start on morning twilight and at the end of the evening twilight.
       

113. Stormer biography
     
     • Birkeland, one of Stormer's colleagues, had put forward a theory in 1896 that auroras were caused by electrons emitted by the sun which interacted with the earth's magnetic field.
       

114. Lavanha biography
     
     • His book Regimento nautico gives rules for determining latitude and tables of declination of the Sun.
       

115. Lalla biography
     
     • The first volume, On the computation of the positions of the planets, was in thirteen chapters and covered topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; syzygies; risings and settings; the shadow of the moon; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; the patas of the moon and sun, and a final chapter in the first volume which forms a conclusion.
       

116. Harley biography
     
     • She has published tables for finding the time at sea by altitude of the sun and stars.
       

117. Sitter biography
     
     • De Sitter's work led directly to Arthur Eddington's 1919 expedition to measure the gravitational deflection of light rays passing near the Sun, results which, at that time, could only be obtained during an eclipse.
       

118. La Hire biography
     
     • He also produced tables giving the movements of the Sun, Moon and the planets which he published in 1687, publishing further such tables in 1702.
       

119. Aepinus biography
     
     • Other achievements of Aepinus include improvements to the microscope, and his demonstration of the effects of parallax in the transit of a planet across the Sun's disk (1764).
       

120. Descartes biography
     
     • He assumes that the universe is filled with matter which, due to some initial motion, has settled down into a system of vortices which carry the sun, the stars, the planets and comets in their paths.
       

121. Banu Musa biography
     
     • They also made many observations of the sun and the moon from Baghdad.
       

122. Cassini Dominique biography
     
     • If Galileo, Newton or Kepler were to descend from heaven and appear at the Academy, they would not comprehend a word in the presentation of Citizen Lalande when he told them that on 20 brumaire, the moon, in a 200 degree opposition to the sun, passed the meridian at five hours ..
       

123. Wren biography
     
     • Also in his lecture Wren talked of the discoveries which had recently been made concerning the sun, moon and planets using the telescope.
       

124. Werner biography
     
     • In addition, Werner suggested using the position of the Moon between the stars or the distance of the Moon from the Sun to allow an absolute time to be calculated.
       

125. Heath biography
     
     • Greek astronomical work also attracted Heath's attention and in 1913 he published a translation of Aristarchus' On the sizes and distances of the sun and moon again with an important preface, this time giving a thorough account of Greek astronomy.
       

126. Stefan Josef biography
     
     • Stefan then applied it to determine the approximate temperature of the surface of the Sun.
       

127. Bacon biography
     
     • So we might also cause the Sun, Moon and stars in appearance to descend here below..
       

128. Aryabhata II biography
     
     • The topics included in these twelve chapters are: the longitudes of the planets, eclipses of the sun and moon, the projection of eclipses, the lunar crescent, the rising and setting of the planets, conjunctions of the planets with each other and with the stars.
       

129. Theon of Smyrna biography
     
     • From these observations Theon made estimates of the greatest angular distance that Mercury and Venus can reach from the Sun.
       

130. Ledermann biography
     
     • he was a tall impressive man, and when we walked side by side through the streets of St Andrews people would say: "Here come the Sun and Moon".
       

131. Zenodorus biography
     
     • And when Zenodorus the astronomer came down to Arcadia and was introduced to us, he asked us how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet a point and thus cause burning.
       

132. Molyneux Samuel biography
     
     • After this the two scientists set about trying to measure the parallax of a star, the one final step which was required to prove that the earth orbited the sun and was also a necessary step in deducing a scale for the universe.
       

133. Friedmann biography
     
     • As Copernicus made the Earth go round the Sun, so Friedmann made the Universe expand.
       

134. Li Chunfeng biography
     
     • His contributions arose through his astronomical work, in particular in computing the angular speed of the sun's apparent motion.
       

135. Auzout biography
     
     • He also considered the question of why, in the last eclipse of the sun, the diameter of the moon appeared larger towards the end of the eclipse that at the beginning.
       

136. Danti biography
     
     • In order to calibrate the astronomical year Danti had to calculate accurately the height of the noon sun, which he achieved by making a small hole in the round window of the church to act as a camera obscura.
       

137. Xenocrates biography
     
     • He also believed that people die twice, once on Earth, then for a second time on the Moon when the mind separates from the soul and travels to the Sun.
       

138. Stewart biography
     
     • Two years later, he wrote the supplement The Distance of the Sun from the Earth determined by the Theory of Gravity.
       

139. Hadley biography
     
     • This motivated Hadley to tackle the problem and in 1730 he invented the reflecting octant which measured the altitude of the sun or of a star.
       

140. Al-Khujandi biography
     
     • During the year 994 al-Khujandi used the very large instrument to observe a series of meridian transits of the sun near the solstices.
       

141. Maclaurin biography
     
     • Other topics which Maclaurin wrote on were the annular eclipse of the sun in 1737 and the structure of bees' honeycombs.
       

142. Bhaskara I biography
     
     • It discusses topics such as: the longitudes of the planets; conjunctions of the planets with each other and with bright stars; eclipses of the sun and the moon; risings and settings; and the lunar crescent.
       

143. Albertus biography
     
     • His methods of tracing back the positions of the sun and moon is interesting.
       

144. Landen biography
     
     • He also corrected Stewart's result on the distance of the Sun from the Earth in 1771.
       

145. Leonardo biography
     
     • He understood the fact that the Moon shone with reflected light from the Sun and he correctly explained the 'old Moon in the new Moon's arms' as the Moon's surface illuminated by light reflected from the Earth.
       

146. Bruns biography
     
     • The Earth-Moon-Sun system was the most important astronomical applications for here none of the gravitational forces could be ignored.
       

147. Euler biography
     
     • determination of the orbits of comets and planets by a few observations, methods of calculation of the parallax of the sun, the theory of refraction, consideration of the physical nature of comets, ..
       

148. Hill biography
     
     • Hill was the first to use infinite determinants to study the orbit of the Moon in On the part of the motion of the lunar perigee which is a function of the mean motion of the sun and moon.
       

149. Cataldi biography
     
     • Among his other works were Transformatione geometrica (1611), dedicated to the Grand Duke Cosimo II, and a book which studied problems of the range of artillery which included tables on the rising of the sun and the time of midday for Bologna (1613).
       

150. Bhaskara II biography
     
     • The twelve chapters of the first part cover topics such as: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; syzygies; lunar eclipses; solar eclipses; latitudes of the planets; risings and settings; the moon's crescent; conjunctions of the planets with each other; conjunctions of the planets with the fixed stars; and the patas of the sun and moon.
       

151. Bethe biography
     
     • Nonetheless, his conclusion -- that the CNO cycle drove energy generation in stars much more massive that the sun while the p-p reaction drove energy production in lighter stars -- is a staple of nearly every introductory textbook on astronomy.
       

152. Wallis biography
     
     • Wallis made other contributions to the history of mathematics by restoring some ancient Greek texts such as Ptolemy's Harmonics, Aristarchus's On the magnitudes and distances of the sun and moon and Archimedes' Sand-reckoner.
       

153. Varahamihira biography
     
     • One treatise which Varahamihira summarises was the Romaka-Siddhanta which itself was based on the epicycle theory of the motions of the Sun and the Moon given by the Greeks in the 1st century AD.
       

154. Gan De biography
     
     • Every 12 years Jupiter returns to the same position in the sky; every 370 days it disappears in the fire of the Sun in the evening to the west, 30 days later it reappears in the morning to the east ..
       

155. Conon biography
     
     • discerned all the lights of the vast universe, and disclosed the risings and settings of the stars, how the fiery brightness of the sun is darkened, and how the stars retreat at fixed times.
       

156. Paramesvara biography
     
     • It is a work containing typical topics for Indian mathematical astronomy works of this period: the mean motions of the heavenly bodies; the true motions of the heavenly bodies; miscellaneous mathematical rules; the systems of coordinates, direction, place and time; eclipses of the sun and the moon; and the operation for apparent longitude.
       

157. Ladyzhenskaya biography
     
     • She loved St Petersburg but she was also a sun worshipper and had been due to be in Florida from January 12th during the long dark days of winter in St Petersburg.
       

158. Troughton biography
     
     • For example he observed the transit of Mercury across the disk of the sun in May 1799 and made careful, accurate observations which he published in the scientific literature.
       

159. Herglotz biography
     
     • This was the first asteroid to be discovered that had an orbit closer to the sun than Mars.
       

160. Mastlin biography
     
     • He found, however, a sun centred orbit for the comet of 1577 which he claimed supported Copernicus's heliocentric system.
       

161. Adams biography
     
     • He worked out that an annular eclipse of the Sun would be visible in Lidcot in 1836, and he was there to make the observations.
       

162. Clairaut biography
     
     • He calculated to within a month the return in 1759 of Halley's comet to its perihelion (closest point to the Sun).
       

163. Thom biography
     
     • He had original ideas about everything under the sun.
       

164. Digges biography
     
     • One of his ideas was that the movement of the Earth round the sun meant that the Earth moved towards and then away from the star causing it to brighten and fade.
       

165. Thabit biography
     
     • He also published observations of the Sun.
       

166. Rocard biography
     
     • In fact this was to prove a significant time for Rocard in the development of his scientific ideas, for at this time he learnt that radars in England had been shown to have detected strong radio emission from the Sun.
       

167. Lexell biography
     
     • When William Herschel discovered a new body in the solar system on 13 March 1781, Lexell computed its orbit which showed that it was a planet (later named Uranus) twice as far from the sun as Saturn, rather than a comet as had been thought at first.
       

168. Meshchersky biography
     
     • He began the thesis with a discussion of the many instances in which the mass of a moving body changes, citing as examples the increase of the mass of the earth occasioned by meteorites falling on it; the increase of the mass of an iceberg with freezing and its decrease with thawing; the increase of the mass of the sun through its gathering of cosmic dust and its decrease with radiation; the decrease of the mass of a rocket as its fuel is consumed ..
       

169. Aaboe biography
     
     • 40094 (1969) he gave photographs with a translation of a cuneiform tablet in the British Museum which gives the moment of conjunction of sun and moon each month over a three year period.
       

170. Ball Robert biography
     
     • He wrote a number of popular books on astronomy including A Story of the Heavens (1886) and The Story of the Sun (1893).
       

171. Al-Maghribi biography
     
     • ',4)">4] discusses the three observations of the sun and the mathematical methods which Muhyi l'din used to find the solar eccentricity and apogee.
       

172. Al-Khwarizmi biography
     
     • The main topics covered by al-Khwarizmi in the Sindhind zij are calendars; calculating true positions of the sun, moon and planets, tables of sines and tangents; spherical astronomy; astrological tables; parallax and eclipse calculations; and visibility of the moon.
       

173. Adelard biography
     
     • However, there is a manuscript (written later but a copy of Adelard's translation) which mentions an eclipse of the sun which took place in 1133.
       

174. Tisserand biography
     
     • A transit of Venus is when the planet passed in front of the disc of the sun as viewed from the Earth and Tisserand took a year to make the journey to Japan, make his observations, and return to France.
       

175. Newcomb biography
     
     • The programme of work which I mapped out involved, as one branch of it, a discussion of all the observations of value on the positions of the sun, moon, and planets, and incidentally on the bright fixed stars, made by the leading observatories of the world since 1750.
       

176. Molyneux William biography
     
     • And thus likewise the slow diurnal motion of the sun or stars, which is hardly perceivable by the bare eye ..
       

177. Al-Kashi biography
     
     • detailed tables of the longitudinal motion of the sun, the moon, and the planets.
       

178. Levy Paul biography
     
     • whenever I pass by the Luxembourg gardens, I still see us there strolling, sitting in the sun on a bench; I still hear him speaking carefully his thoughts.
       

179. Xu Yue biography
     
     • Mathematics was used by Liu Hong and others at the Observatory in their studies of astronomy and the related work on the calendar which, of course, was based on the apparent motion of the sun and the moon.
       

180. Boethius biography
     
     • Theodoric employed Boethius to reform the coinage, and to astonish less sophisticated barbarian kings with such devices as sun-dials and water-clocks.
       

181. Mouton biography
     
     • As an astronomical observer he made remarkably accurate observations of the apparent diameter of the sun.
       

182. Peirce Benjamin biography
     
     • force; and the laws under which the tides obey the attractions of the sun and moon are quite undeveloped.
       

183. Dyson biography
     
     • Dyson has also published several books on science/philosophy, including Disturbing the Universe (1979), Weapons and Hope (1984), Origins of Life (1986), Infinite in all Directions (1988), From Erod to Gaia (1992), Imagined Worlds (1997) and The Sun, the Genome and the Internet (1999).
       

184. Waterston biography
     
     • Becoming interested in calculating the age of the sun, he studied the kinetic theory of gases realising that chemical processes alone were insufficient to explain the solar output.
       

185. Hutton James biography
     
     • The Bible was taken as literal truth, despite the acceptance by most that the Earth revolved around the sun.
       

186. Berwald biography
     
     • One could make Berwald very happy if one turned the conversation to his Dalmatian trips - how he loved the hot sun of this stony country.
       

187. Oughtred biography
     
     • Oughtred's other works were Trigonometrie (1657), one of the first works on trigonometry to use concise symbolism, and a number of more minor works on watchmaking, solving spherical triangles by the planisphere and methods to determine the position of the sun.
       

188. Poncelet biography
     
     • At first he was too exhausted, cold and hungry even to think; but when the spring came ("the splendid April sun"), he resolved to utilise his time by recalling all he could of his mathematical education.
       

189. Chandrasekhar biography
     
     • In 1930 Chandra showed that a star of a mass greater than 1.4 times that of the Sun (now known as the Chandrasekhar's limit) had to end its life by collapsing into an object of enormous density unlike any object known at that time.
       

190. Ulugh Beg biography
     
     • He produced data relating to the Sun, the Moon and the planets.
       

191. Brahmadeva biography
     
     • Topics covered include the longitudes of the planets, problems relating to the daily rotation of the heavens, eclipses of the sun and the moon, risings and settings, the lunar crescent, and conjunctions of the planets.
       

192. Cassini Jacques biography
     
     • As to his contributions to astronomy, Cassini published many papers in the journals of the Academie des Sciences and two major treatises in 1740, namely Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn.
       

193. Delambre biography
     
     • In 1786 Delambre recorded a transit of Mercury across the Sun.
       

194. Doppelmayr biography
     
     • In 1698 he completed a dissertation on the sun, then went on to attend lectures on mathematics and natural philosophy by Johann Christoph Sturm who was considered the leading experimental physicist in Germany at the time.
       

195. Scott Elizabeth biography
     
     • It seems inconceivable that the distribution of the true longitude of periastron could depend on whether or not the sun happens to lie in the plane of the orbit.
       

196. Govindasvami biography
     
     • It discussed topics such as the longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent.
       

197. See biography
     
     • [and] showed himself "every inch a natural philosopher" by speculating on the origins of the sun, moon and stars at the tender age of two, never so much as dreaming that he should grow into a little boy with "methodical methods", and one day become "the greatest astronomer in the world".
       

198. Iyanaga biography
     
     • Iyanaga received honours such as being awarded the Rising Sun from Japan in 1976, being elected a member of the Japan Academy in 1978, and receiving the Order of Legion d'Honneur from France in 1980.
       

199. Aristotle biography
     
     • Another passage recalls the fundamental assumption on which Eudoxus based his 'method of exhaustion' for measuring areas and volumes; and, of course, Aristotle was familiar with the system of concentric spheres by which Eudoxus and Callippus accounted theoretically for the independent motions of the sun, moon, and planets.
       

200. Petit Pierre biography
     
     • In particular, late in his life, Petit devised a filar micrometer to measure the diameters of celestial objects such as the Sun, Moon and planets.
       

History Topics

1. Kepler's Laws
   
   • Law I (the Ellipse Law) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.
     
   • Law II (the Area Law) - the time taken by a planet to reach a particular position is represented by the area swept out by the radius vector drawn from the fixed Sun.
     
   • Kepler followed the ancients in always starting to measure at the point furthest from the Sun.) Almost certainly Kepler was responsible for introducing the term 'orbit', in Astronomia Nova Ch.1, and on his behalf we shall precisely define an orbit as possessing a pair of independent constituents: the path or curve, together with a (geometrical) way of representing time.
     
   • it is an outer planet (and therefore it is seldom viewed close to the Sun); .
     
   • it is the nearest to the Sun of the outer planets (and therefore it makes more frequent circuits, producing more observations).
     
   • Since Greek times, the accepted description of the planetary system had been a geometrical one, known as the Ptolemaic theory (a geocentric configuration), which supposed that the Earth was fixed at the centre of the universe, with the Moon, the Sun, and the five known (naked-eye) planets revolving round it.
     
   • In fact, Kepler gave Copernican theory a new, mathematical precision by specifying two fundamental properties that were consistent with his conviction that the Sun was metaphorically the place of God: .
     
   • The Sun is the fixed hub of the universe.
     
   • The Sun is responsible for all celestial motion.
     
   • Thus Kepler's interpretation of heliocentricity provided him with an origin from which to determine the Sun-planet distances and so discover the actual path of the planet.
     
   • In order to transpose the observations from a geocentric to a heliocentric basis, he applied triangulation to ensure that each Mars-distance was measured as if from the fixed Sun.
     
   • Bearing in mind that the observations contained no distance-measurements (as explained in Section 2), this involved expressing all the Mars-Sun distances in terms of the Earth-Sun distance, regarded as a standard unit or 'baseline' (since the path of the Earth is very nearly circular, this approximation happened to be accurate enough for Kepler's purpose); .
     
   • He verified that the path of each planet lay in a plane that passed through the Sun; .
     
   • And because it was expressed geometrically, the solution would potentially be exact - the closed orbit of a single planet in a plane round the fixed Sun.
     
   • He began by assuming a fixed/known line of apsides CD, on which lies the fixed point A (the position of the Sun) at a known 'eccentric' distance AB (all previously determined from Tycho's observations), where B is the midpoint of CD.
     
   • However, he found that this placed the planet too far from the Sun in almost all positions.
     
   • Unless its focus coincides with the fixed Sun (the origin), the investigation would have been too complicated to manage by geometry.
     
   • From a heliocentric point of view, it is especially easy to be aware that planets move more slowly the further they are from the Sun (and faster when nearer).
     
   • Thus, as Kepler realized, a connection exists between a small (micro) interval of time and the corresponding distance of the planet from the Sun.
     
   • Initially, he suggested that this (macro) time (the sum of the micro intervals of time) could be represented geometrically by the sum of all the corresponding distances from the Sun.
     
   • Next, Kepler extended that proposition, and took the distance-sum from the eccentric point (A, the position of the Sun) to be (approximately) proportional to the area of the eccentric sector (the area QAC, shown in Figure (4)).
     
   • Firstly, between 1609 and 1618, he satisfied himself that the orbit of each of the six primary planets was an ellipse with the Sun at one focus.
     
   • radial motion which is measured by the linear variation in distance from the Sun; .
     
   • transradial motion which is measured by the variation in the area swept out: this motion is defined to be circular round the Sun, and thus precisely at right angles to the radial motion.
     
   • This pair of component motions, whose source is the Sun (see Section 3), is contrasted in Figure (6) with the single tangential velocity, shown dashed, which, in Newton's work, superseded and replaced the Keplerian components of motion.
     
   • Kepler could never have supposed that the Sun could exert an attractive force because that concept did not exist in Aristotelian terms.
     
   • Section 10 The Sun's rotation: the cause of transradial motion .
     Go directly to this paragraph
     
   • We will deal first with the cause of the transradial motion because the revolution of the planets round the Sun is the most outstanding feature of a heliocentric universe, and requires a universal cause.
     
   • Kepler accounted for that motion by inventing the rotation of the Sun on its axis.
     
   • Thus, Kepler envisaged that the rays emitted by the rotating Sun would 'hit' or impel each planet continuously round in a circle.
     
   • Naturally, he expected that this impulsion would be less when the planet was further from the Sun, so he reasonably supposed that the action of the rays would vary inverse-linearly (that is, weaken) with distance.
     
   • Because of his Copernican convictions, Kepler extended this idea to suppose that every planet possessed magnetism, and contained a set of 'fibres' fixed within its body which could be activated by the Sun's magnetism; and he further supposed that each set of fibres possessed a unique potential magnetic 'strength' that could be associated with the individual eccentricity of the particular planetary path.
     
   • The radial motion itself was evaluated by taking a small variation (an increment) of the distance from the Sun with respect to a small change in the auxiliary angle: see Summary Table at the end, confirmed by the modern treatment in Planetary motion tackled kinematically.
     
   • Kepler was the first to introduce the concept of causation into astronomy, and in accordance with his Copernican convictions, he naturally believed that the Sun was the generator of all causes.
     
   • Moreover, it seemed common sense to suppose that the Sun could only act (or activate) continuously either in a radial direction or circularly round itself, and this consideration, for Kepler, determined the direction of the causes available and limited their number to two.
     
   • The precedent cause was the action of the Sun's rays, due to its rotation, which produced transradial motion.
     
   • The lesser cause was magnetism, generated by the Sun, which activated the planetary fibres.
     
   • The Sun appeared to function merely as a catalyst to facilitate radial motion - on no account can it be regarded as a Newtonian force (nor as an Aristotelian 'force').
     
   • Therefore, from a modern viewpoint, Kepler's work was purely kinematical, and he was entirely correct to treat each individual planet as if it were the only particle in the universe apart from the fixed Sun.
     
   • Action circularly round Sun:perpendicular to Sun's raysDirectionof componentsActivation in direction of Sun, thoughfibres are supposed fixed in direction .
     
   • 'Impulsion' of Sun's rays proportional 1/r Kepleriancauses[Strength of planet's fibres proportional e] .
     

2. Sundials
   
   • This celestial sphere rotated from east to west, carrying not only the stars but also the sun and the planets.
     
   • Therefore, the sun revolved around the earth.
     
   • The sun did not travel around the earth in a circle at right angles to the earth's axis (which was also the axis of the celestial sphere) as the stars did.
     
   • Rather, the sun traced a circle along the celestial sphere, centred on the earth, known as the ecliptic.
     
   • The circle of the ecliptic more or less intersects the twelve constellations of the zodiac, and the time of year (corresponding to modern months) was reckoned by what sign of the zodiac the sun was traversing.
     
   • (Regardless of the exact location of the zodiac constellations, the ecliptic was divided into 12 equal arcs of 30° each, leaving most of the constellations off-centred and often not entirely in their designated 30° region.) The sun's motion along the ecliptic circle takes a (solar) year.
     
   • The dual motion of the sun (on the celestial sphere and along the ecliptic) means that the sun follows a different path in the sky each day.
     
   • From the perspective of the northern hemisphere, during the summer, the sun is higher in the sky and remains visible for a longer period of time.
     
   • In the winter months, the sun is lower in the sky and visible for a shorter period of time.
     
   • In the early ages of Rome and even down to the middle of the fifth century after the foundation of the city no other divisions of the day were known than sunrise, sunset and midday, which were marked by the arrival of the Sun between the Rostra and a place called Graecostasis.
     
   • A funerary text from 1290 B.C., referring to astronomical events in the 19th century B.C., gives instructions on how to construct a "shadow stick."[Timing the sun in Egypt and Mesopotamia.
     
   • Neither the funerary text nor surviving examples have the crossbar, though one specimen has holes on either side of its upright which may suggest such an addition.[Timing the sun in Egypt and Mesopotamia.
     
   • Two hours are said to have occurred before the sun struck the clock in the morning, and another two hours passed after the sun left the clock but before night began.
     
   • 51-65.',5)" onmouseover="window.status='Click to see reference';return true">5] The markings on the clock indicating the four hours were very inaccurate, and were possibly not based on observation but rather some fallacy of celestial geometry.[Timing the sun in Egypt and Mesopotamia.
     
   • This is perhaps the crudest order of gnomon use and provides little of either theoretical or empirical interest for the Greeks."[Timing the sun in Egypt and Mesopotamia.
     
   • 157-167.',4)" onmouseover="window.status='Click to see reference';return true">4] Further Egyptian development in timekeeping seems to have waned until the Assyrian invasion in the 7th century B.C.[Timing the sun in Egypt and Mesopotamia.
     
   • The instrument was put down on a flat surface, and whenever it was to be used, was turned so that it faced the sun directly.
     
   • At six in the morning the shadow would strike the top of the dial; as the sun rose higher the shadow would decrease in length until at noon it touched the lowest line; it reached the top of the dial again at six in the evening.
     
   • The shadow's tip traced a curve on the dial plane as the sun moved, a curve which changed from summer to winter.
     
   • The sun traces a circular path in the sky in its daily motion.
     
   • The tip of the gnomon is the vertex of a cone with the sun's rays as elements, and since the dial plane cuts the cone, the shadow path is a conic section.
     
   • The ellipse is easy to see as during the Arctic day, the sun makes its full circuit above the horizon, and thus a gnomon's shadow would map out the closed conic section.[Early Sundials and the Discovery of the Conic Sections.
     
   • Specifically, in his book, 'On the Analemma', Ptolemy gives methods for deriving, both by trigonometric and also by graphic means, three pairs of spherical coordinates for the sun relative to a given place on earth, given solar declination, terrestrial latitude, and hour of the day.
     
   • 101-112.',9)" onmouseover="window.status='Click to see reference';return true">9] The basic principle of the spherical sundial was that it mirrored the celestial sphere in which the sun travels.
     

3. Orbits
   
   • The first to propose a system of planetary paths which would set the scene for major advances was Copernicus who in De revolutionibus orbium coelestium (1543), argued that the planets and the Earth moved round the Sun.
     Go directly to this paragraph
     
   • Kepler showed that a planet moves round the Sun in an elliptical path which has the Sun in one of its two foci.
     
   • He also showed that a line joining the planet to the Sun sweeps out equal areas in equal times as the planet describes its path.
     
   • Certainly the motion of the Moon round the Earth was not seen to necessarily be part of the same laws which govern the motion of the planets round the Sun.
     
   • In 1684 Wren, Hooke and Halley discussed, at the Royal Society, whether the elliptical shape of planetary orbits was a consequence of an inverse square law of force depending on the distance from the Sun.
     Go directly to this paragraph
     
   • It remained visible until 5 December 1680 when it moved too close to the Sun to be observed.
     Go directly to this paragraph
     
   • It reappeared two weeks later moving away from the Sun along almost the same path along which it had approached.
     Go directly to this paragraph
     
   • Taking the perturbations into account Halley predicted the comet would return and reach perihelion (the point nearest the Sun) on 13 April 1759.
     Go directly to this paragraph
     
   • He drew up lunar tables in 1744, clearly already studying gravitational attraction in the Earth, Moon, Sun system.
     Go directly to this paragraph
     
   • Precession is caused by the gravitational attraction of the Sun on the equatorial bulge of the Earth, the bulge being predicted by Newton.
     Go directly to this paragraph
     
   • The comet made no reappearance and again Lexell correctly deduced that Jupiter had changed the orbit so much that it was thrown far away from the Sun.
     Go directly to this paragraph
     
   • gave the distances of the 6 known planets from the Sun (taking the Earth's distance to be 1) except there was no planet at distance 2.8.
     
   • The new planet, unobserved by other astronomers, passed behind the Sun and was lost.
     Go directly to this paragraph
     
   • Its distance from the Sun fitted exactly the 2.8 prediction of the Titus-Bode law.
     Go directly to this paragraph
     
   • as did the significant paper published by Jacobi in 1843 where he reduced the problem of two actual planets orbiting a sun to the motion of two theoretical point masses.
     Go directly to this paragraph
     
   • He pointed out that there was a discrepancy of 38" per century between the predicted motion of the perihelion (the point of closest approach of the planet to the Sun) which was 527" per century and the observed value of 565" per century.
     Go directly to this paragraph
     
   • Le Verrier was convinced that a planet or ring of material lay inside the orbit of Mercury but being close to the Sun had not been observed.
     Go directly to this paragraph
     
   • Earlier approaches started with an elliptic orbit of the Moon round the Earth, assuming the Sun had no effect, then perturbing the orbit to take account of the gravitation of the Sun.
     Go directly to this paragraph
     
   • Hill, on the other hand, started with circular orbits for the Sun and Moon about the Earth and went on to examine the perturbations caused by assuming elliptic orbits.
     Go directly to this paragraph
     

4. Size of the Universe
   
   • Why is this such a special time? Well a very rare event is happening as I write, namely a transit of Venus across the Sun.
     
   • Previous such transits have been significant in determining the distance between the Earth and the Sun.
     
   • The transits of June 1761 and 1769 and those of December in 1874 and 1882 were used to obtain an accurate value for the astronomical unit, which is the distance from the Earth to the Sun.
     
   • In the earliest times the universe was considered to consist of the Earth with the Moon, Sun, and planets revolving round it.
     
   • Even before historical records began it was realised that the Moon was closer to the Earth than the Sun, the planets, and the stars, since it was seen to move in front of them.
     
   • The first person that we know to have obtained values for the distances of the Sun and Moon was Aristarchus in the 3rd century BC.
     
   • He estimated that the distance from the Earth to the Moon is 59 times the radius of the Earth and the distance to the Sun is 1,200 times the radius of the Earth, a serious underestimate.
     
   • Using the same method as Hipparchus to determine the distance to the Sun led Ptolemy to the same serious underestimate in its distance.
     
   • In fact Copernicus, although proposing a very different model of the universe from Ptolemy, took essentially the same values for the distances to the Sun and Moon.
     
   • He did improve the value for the distance to the Sun to 1,500 times the radius of the Earth but this is still such a serious underestimate that it is little improvement.
     
   • An argument against the Earth rotating about the Sun had been that in this case the closer stars should appear to move backwards and forwards relative to the distant stars due to the observer moving through the diameter of the Earth's orbit every six months.
     
   • However, he made an important observation regarding the distance to the Sun.
     
   • If, he argued, the distance to the Sun was 1,2000 times the radius of the Earth then Mars, at its closest approach to the Earth, should be closer than this distance.
     
   • However, he did not observe any parallax so deduced that the accepted distance to the Sun was an underestimate.
     
   • Richer made the observations from Cayenne and, after his return to Paris, Cassini reduced the data obtained to give the distance from the Earth to the Sun to be 87 million miles.
     
   • Halley, in 1718, noted that three stars, Sirius, Procyon and Arcturus, had moved relative to the ecliptic (the apparent line of the Sun through the stars) since Hipparchus had measured their positions.
     
   • As we mentioned at the beginning of this article, the use of a transit of Venus to obtain an accurate value for the distance to the Sun had been suggested by Halley.
     
   • Although the method was sound, there was great difficulty in determining the exact moment of contact of the disk of the Sun and the disk of Venus.
     
   • As a result estimates of the distance to the Sun varied by up to 10 million miles.
     
   • Clearly to succeed it was important to choose a star which was close to the Sun.
     
   • The Sun, he estimated, was situated at about 2/3 of the distance from the centre to the outer edge of the galaxy.
     

5. Planetary motion
   
   • Law I (the Ellipse Law) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.
     
   • Law II (the Area Law) - the time taken by a planet to reach a particular position is measured by the area swept out by the radius vector drawn from the fixed Sun.
     
   • This composite solution represents what is in fact the earliest instance of a planetary orbit: it will be succinctly referred to in what follows as 'the Sun-focused ellipse'.
     
   • Unexpectedly, this analysis is carried out in terms of the auxiliary angle of the ellipse, rather than the polar angle (at the Sun) that is invariably used nowadays: this came about for historical reasons - because, until the adoption of the heliocentric view, the position of the Sun did not play an explicit part in planetary theory.
     
   • It is essential to appreciate here that e not only denotes the focal eccentricity (the 'ellipticity') but the polar eccentricity as well, since A is both the focus and the origin or pole of coordinates (which here coincides with the position of the Sun).
     
   • Further, this argument could be generalized by carrying out a similar brief calculation to find the radius vector of any ellipse belonging to the system of conics whose origin is at the Sun (again setting polar distance AB = ae) that has CQD as its auxiliary circle and its typical point lying on QH (still defined by auxiliary angle β).
     
   • This identity acts as the bridging relation (inverse or direct) between the modern treatment by polar angle and the present treatment by auxiliary angle (which will only work effectively in the case of the unique Sun-focused ellipse alone).
     
   • Whatever we call it, this motion is defined to take place round the Sun instantaneously in a circle.
     
   • The constant of proportionality involved (1/2h is standard usage) is expressed mathematically by the following relationship, in which r represents the radius vector measured from the source of motion at the Sun, still taken as the origin of coordinates, again with reference to the figure: .
     
   • We now apply this to the special case of the Sun-focused ellipse, whose total area is πab and periodic time T, in order to evaluate its particular constant.
     
   • Thus for the Sun-focused ellipse alone, we deduce from (10) and (11): .
     
   • Then, by introducing the dimensional constant 1/2 ab, for the Sun-focused ellipse alone, we can easily deduce that time is proportional to area.
     
   • This motion takes place linearly in the direction of the radius vector -- towards or away from the Sun.
     
   • Radial acceleration directed towards the Sun.nnnnnnnnnnnn(15) .
     
   • Radial acceleration = (2π)2a3/T2 cross (1/r2) towards the Sun.
     
   • Acceleration = μ0/r2 towards the Sun.
     

6. Christianity and Mathematics
   
   • Aristotle's view of the world was based on a spherical Earth round which there were crystalline spheres which carried the Sun, Moon and planets.
     
   • The first of these were arguments based purely on logic, for example that the "day" is defined by the passage of the Sun in the sky so to talk, as in Genesis, of several days passing before the Sun was created makes no sense.
     
   • This insistence on circular motion meant that to fit the observations Copernicus had to place the centre of the universe not at the Sun but at a point close to the Sun around which both the Earth and the Sun revolved.
     
   • he seeks to raise the Earth, heavier than the other elements, from its lower place to the sphere where everybody by common consent correctly locates the Sun's sphere, and to caste the sphere of the Sun down to the place of the Earth, contravening the rational order and Holy Writ, which declares that heaven is up, while the Earth is down ..
     
   • He realised the mathematical superiority of Copernicus over Ptolemy but he proposed a modification of Copernicus's system in which the planets revolved around the Sun while the Sun itself moved around the stationary Earth.
     
   • Not only did he accept that the Earth was in orbit round the Sun but he introduced a new brilliant idea, never before postulated, that the heavenly bodies do not travel in circles but in ellipses.
     
   • Piety prevents many people from agreeing with Copernicus out of fear that the Holy Ghost speaking in Scripture will be branded as a liar if we say that the Earth moves and the Sun stands still.
     
   • By 1613 Galileo believed that his telescopic observations of the moons of Jupiter proved that the Earth and planets revolved round the Sun.
     
   • I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it.
     
   • all said that the proposition of a stationary Sun is foolish and absurd in natural philosophy.
     

7. Cosmology
   
   • Four thousand years ago the Babylonians were skilled astronomers who were able to predict the apparent motions of the moon and the stars and the planets and the Sun upon the sky, and could even predict eclipses.
     
   • In the fourth century BC, they developed the idea that the stars were fixed on a celestial sphere which rotated about the spherical Earth every 24 hours, and the planets, the Sun and the Moon, moved in the ether between the Earth and the stars.
     
   • Copernicus constructed a model where the Earth rotated and, together with the other planets, moved in a circular orbit about the Sun.
     Go directly to this paragraph
     
   • There were other practical reasons why many astronomers of the time rejected the Copernican notion that the Earth orbited the Sun.
     Go directly to this paragraph
     
   • He realised that if the Earth was moving about the Sun, then the relative positions of the stars should change as viewed from different parts of the Earth's orbit.
     Go directly to this paragraph
     
   • And if moons could orbit another planet, why could not the planets orbit the Sun? .
     Go directly to this paragraph
     
   • The planets moved in ellipses, not perfect circles, about the Sun.
     Go directly to this paragraph
     
   • But the absence of any observable parallax in the apparent positions of the stars as the Earth rotated the Sun, then implied that the stars must be at a huge distance from the Sun.
     
   • Newton concluded that the Universe must be an infinite and eternal sea of stars, each much like our own Sun.
     
   • The nearest star (other than the Sun) turned out to be about 25 million, million miles away! (By contrast the Sun is a mere 93 million miles away from the Earth.) .
     Go directly to this paragraph
     

8. Classical time
   
   • When should crops be planted? When would the rains come? When would rivers flood? When should one harvest the crops? The natural timekeepers in the sky are the daily passage of the sun and the monthly phases of the moon.
     
   • The heliacal rising is the first appearance of the star after the period when it is too close to the sun to be seen.
     
   • Now units of time require some way of measurement and, not surprisingly, because of their astronomical definitions the early devices to measure time used the sun.
     
   • The problem with the sundial was that the sun took a different path through the sky throughout the year.
     
   • Of course the sun could not be used to tell the time at night and clepsydras or water clocks were in use in Egypt by 1500 BC.
     
   • In a sense this is reasonable since to Aristotle time was measured by the motions of the heavenly bodies so a period of time was represented by the movement of the sun across the sky.
     
   • However, for Aristotle time itself is motion, the flow of time is the motion of the arrow or of the sun and moon across the sky.
     
   • It is a fascinating discussion which essentially asks if time as measured by the sun and the moon is the "same" time.
     
   • The movements of the sun, moon and five planets were shown.
     
   • Eclipses of the sun and moon and phases of the moon were also shown, and there was an astrolabe which was designed on Ptolemy's version of the universe.
     
   • An example would be the prediction of eclipses of the sun and moon which is possible from knowing the positions and motions of the bodies in the solar system and then using Newton's laws.
     

9. Greek astronomy
   
   • when the Pleiades rise it is time to use the sickle, but the plough when they are setting; 40 days they stay away from heaven; when Arcturus ascends from the sea and, rising in the evening, remain visible for the entire night, the grapes must be pruned; but when Orion and Sirius come in the middle of heaven and the rosy fingered Eos sees Arcturus, the grapes must be picked; when the Pleiades, the Hyades, and Orion are setting, then mind the plough; when the Pleiades, fleeing Orion, plunge into the dark sea, storms may be expected; 50 days after the sun's turning is the right time for man to navigate; when Orion appears, Demeter's gift has to be brought to the well-smoothed threshing floor.
     
   • He did not have it orbiting the sun, however, but rather all the heavenly bodies went in circles round a central fire which one could never see since there was a counter earth between the earth and the fire.
     
   • Meton worked in Athens with another astronomer Euctemon, and they made a series of observations of the solstices (the points at which the sun is at greatest distance from the equator) in order to determine the length of the tropical year.
     
   • We know that Aristarchus measured the ratio of the distances to the moon and to the sun and, although his methods could never yield accurate results, they did show that the sun was much further from the earth than was the moon.
     
   • His results also showed that the sun was much larger than the earth, although again his measurements were very inaccurate.
     
   • Some historians believe that this knowledge that the sun was the largest of the three bodies, earth, moon and sun, led him to propose his heliocentric theory.
     
   • His sun-centred universe found little favour with the Greeks, however, who continued to develop more and more sophisticated models based on an earth centred universe.
     
   • Archimedes measured the apparent diameter of the sun and also is said to have designed a planetarium.
     
   • Most telling regarding his understanding of the scientific method is the fact that he proposed a theory of the motion of the sun and the moon yet he was not prepared to propose such a theory for the planets.
     

10. Physical world
    
    • The problem of whether a mathematical model represents reality became highly significant when Copernicus proposed his Sun centred system.
      
    • The Christian Church had no problems with mathematical models, and were quite happy to allow publication of models to "save the appearances" based on a Sun centred model.
      
    • Copernicus, however, maintained that his Sun centred system was superior for it provided an explanation of the retrograde motion of the planets as opposed to Ptolemy's model which was devised to produce the observed effect.
      
    • He argued that the Sun had a driving force which propelled the planets in their orbits.
      
    • This force diminished with distance from the Sun and so the outer planets moved more slowly.
      
    • He tried various algebraic formulas to relate the velocity of a planet round the Sun with its distance from the Sun before he stumbled on: .
      
    • For each of the planets he calculated 1/√r when r is its distance from the Sun.
      
    • Now the distances of the planets Mercury, Venus, Earth, Mars, Jupiter, Saturn from the Sun (taking the distance of the Earth as 1) are .
      

11. Classical light
    
    • Now of course if this were true one could see at night, so Empedocles knew that things were somewhat more complicated than this and postulated an interaction between rays from the eyes and rays from a source such as the sun.
      
    • The light and heat of the sun; these are composed of minute atoms which, when they are shoved off, lose no time in shooting right across the interspace of air in the direction imparted by the shove.
      
    • Now al-Haytham argued quite correctly that we see objects because the sun's rays of light, which he believed to be streams of tiny particles travelling in straight lines, are reflected from objects into our eyes.
      
    • Let in the sun's rays by a small hole to a darkened house, and at the hole place a feather (the more delicate and white the better for this purpose), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (if I mistake them not) whereof one is somewhat white (to wit, the middle which is opposite the sun) and all the rest severally coloured.
      
    • He realised that the reason the time between eclipses of Jupiter's moons by the planet was shorter when the Earth on the same side of the sun as Jupiter and became longer when Earth and Jupiter moved towards opposite sides of the sun was due to the time taken for light to cross the increased distance.
      
    • The sun, said Euler, is "a bell ringing out light".
      
    • It is worth noting that Bradley's work provided first direct evidence that the Earth revolves around the sun.
      

12. Gravitation
    
    • Although we now know that the Moon orbits the Earth and the planets orbit the Sun because of the same force that makes the stone fall, this was not suspected by early scholars.
      
    • Their contributions which we now discuss were not thought at the time to be in any way connected, for Kepler's contribution concerned the orbits of the planets round the Sun while that of Galileo concerned motion and the acceleration of falling objects.
      
    • Kepler's first two laws of planetary motion are: (1) a planet moves round the Sun in an ellipse with the Sun at one focus, and (2) a line joining the planet to the Sun sweeps out equal areas in equal times as the planet describes its orbit.
      
    • These vortices were the cause of gravity; they held the planets in their orbits round the Sun.
      
    • A stone falling to Earth was subject to precisely the same force which kept the Moon in its orbit about the Earth and the planets in their orbits around the Sun.
      
    • Descartes had a rational explanation for why stones fell to Earth and why planets orbited the Sun.
      

13. Forgery 1
    
    • Copernicus had proposed a sun centred system while Kepler had discovered that the planets revolved round the sun in ellipses with the sun at one focus.
      
    • However this left a major question - what kept the planets in their orbits about the sun? .
      
    • According to Descartes, the planets must be linked mechanically to the sun in order that there is a force keeping them in their orbits, so the solar system had to be filled with matter to provide this mechanical link.
      

14. Mayan mathematics
    
    • One suggestion is that since the Maya lived in the tropics the sun was directly overhead twice every year.
      
    • Perhaps they measured 260 days and 105 days as the successive periods between the sun being directly overhead (the fact that this is true for the Yucatan peninsular cannot be taken to prove this theory).
      
    • The Mayan concern for understanding the cycles of celestial bodies, particularly the Sun, the Moon and Venus, led them to accumulate a large set of highly accurate observations.
      
    • Many of the windows of the building are positioned to line up with significant lines of sight such as that of the setting sun on the spring equinox of 21 March and also certain lines of sight relating to the moon.
      

15. Mathematical classics
    
    • Sunzi suanjing (Sun Zi's Mathematical Manual) .
      
    • The Zhoubi suanjing contains calculations of the movement of the sun through the year as well as observations of the moon and stars, particularly the pole star.
      
    • Sunzi suanjing (Sun Zi's Mathematical Manual) .
      

16. Greek astronomy references
    
    • G Abraham, Mean sun and moon in ancient Greek and Indian astronomy, Indian J.
      
    • E Nevill, The early eclipses of the sun and moon, Monthly Notices Roy.
      
    • B L van der Waerden, The motion of Venus, Mercury and the Sun in early Greek astronomy, Arch.
      

17. Greek astronomy references
    
    • G Abraham, Mean sun and moon in ancient Greek and Indian astronomy, Indian J.
      
    • E Nevill, The early eclipses of the sun and moon, Monthly Notices Roy.
      
    • B L van der Waerden, The motion of Venus, Mercury and the Sun in early Greek astronomy, Arch.
      

18. Ten classics
    
    • Sunzi suanjing (Sun Zi's Mathematical Manual) .
      
    • The Zhoubi suanjing contains calculations of the movement of the sun through the year as well as observations of the moon and stars, particularly the pole star.
      
    • Sunzi suanjing (Sun Zi's Mathematical Manual) .
      

19. Chinese numerals
    
    • For example Sun Zi, in the first chapter of the Sunzi suanjing (Sun Zi's Mathematical Manual), gives instructions on using counting rods to multiply, divide, and compute square roots.
      

20. Neptune and Pluto
    
    • On 1 June 1846 Le Verrier published a second paper in which he showed that a variety of other possible causes could not explain the orbit of Uranus, and deduced that the only possible cause could be a planet further from the Sun than Uranus.
      Go directly to this paragraph
      
    • His first solution had depended on assuming a distance for the "new planet" of twice that of Uranus from the Sun.
      Go directly to this paragraph
      

21. U of St Andrews History
    
    • Let in the sun's rays by a small hole to a darkened house, and at the hole place a feather (the more delicate and white the better for this purpose), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (if I mistake them not) whereof one is somewhat white (to wit, the middle which is opposite the sun) and all the rest severally coloured.
      

22. Jaina mathematics
    
    • Before the Jaina period the ideas of eclipses were based on a demon called Rahu which devoured or captured the Moon or the Sun causing their eclipse.
      
    • The Jaina school assumed the existence of two demons Rahu, the Dhruva Rahu which causes the phases of the Moon and the Parva Rahu which has irregular celestial motion in all directions and causes an eclipse by covering the Moon or Sun or their light.
      

23. Chinese overview
    
    • For example Sun Zi (about 400 - about 460) wrote his mathematical manual the Sunzi suanjing which on the whole provides little new.
      
    • This text by Sun Zi was the first of a number of texts over the following two hundred years which made a number of important contributions.
      

24. Longitude2
    
    • The Sun could not be used as a timekeeper since the fact that the Earth's orbit is not circular means that the sundial time would be ahead of accurate clock time for part of the year and behind it at other times.
      
    • Flamsteed used the star Sirius as a timekeeper correcting the sidereal time obtained from successive transits of the star into solar time, the difference of course being due to the rotation of the Earth round the Sun.
      

25. Longitude1
    
    • The clocks were calibrated taking observations of the Sun and of a star.
      
    • The latitude of the place from which the observations were being made was found by calculating the height of the Pole Star and of the Sun at noon and consulting tables of declination.
      

26. Chinese problems
    
    • Problem 4: See Sun Zi .
      
    • Problem 8: See Sun Zi .
      

27. Mathematical games
    
    • If thou art diligent and wise, O Stranger, compute the number of cattle of the Sun..
      
    • In the early 16th Century Cornelius Agrippa constructed squares for n = 3, 4, 5, 6, 7, 8, 9 which he associated with the seven planets then known (including the Sun and the Moon).
      Go directly to this paragraph
      

28. General relativity
    
    • Le Verrier, in 1859, had noted that the perihelion (the point where the planet is closest to the sun) advanced by 38" per century more than could be accounted for from other causes.
      Go directly to this paragraph
      
    • Many possible solutions were proposed, Venus was 10% heavier than was thought, there was another planet inside Mercury's orbit, the sun was more oblate than observed, Mercury had a moon and, really the only one not ruled out by experiment, that Newton's inverse square law was incorrect.
      Go directly to this paragraph
      

29. Greek sources II
    
    • Pythian the Thasian geometer wrote a letter to Conon in which he asked him how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet the circumference of a circle.
      Go directly to this paragraph
      
    • And when Zenodorus the astronomer came down to Arcadia and was introduced to us, he asked us how to find a mirror surface such that when it is placed facing the sun the rays reflected from it meet a point and thus cause burning.
      Go directly to this paragraph
      

30. Sundials references
    
    • J Fermor, Timing the sun in Egypt and Mesopotamia.
      

31. Jaina mathematics references
    
    • J C Sikdar, Eclipses of the Sun and Moon according to Jaina astronomy, in Proceedings of the Symposium on the 1500th Birth Anniversary of Aryabhata I, New Delhi, 1976, Indian J.
      

32. Water-clocks references
    
    • J Fermor, Timing the sun in Egypt and Mesopotamia.
      

33. Sundials references
    
    • J Fermor, Timing the sun in Egypt and Mesopotamia.
      

34. Jaina mathematics references
    
    • J C Sikdar, Eclipses of the Sun and Moon according to Jaina astronomy, in Proceedings of the Symposium on the 1500th Birth Anniversary of Aryabhata I, New Delhi, 1976, Indian J.
      

35. 20th century time
    
    • Dirac was forced into this conclusion based on results of the Large Numbers Hypothesis that threw off age calculations of the Moon and Sun.
      

36. Newton's bucket
    
    • Tie two rocks together with a rope, he suggested, and go into deep space far from the gravitation of the Earth or the sun.
      

37. Decimal time
    
    • Thus, the sun illuminated both poles simultaneously, and in succession the entire globe, on the same day that, for the first time, in all its purity, the flame of liberty, which must one day illuminate all mankind, shone on the French nation.
      

38. Indian mathematics
    
    • He replaced the two demons Rahu, the Dhruva Rahu which causes the phases of the Moon and the Parva Rahu which causes an eclipse by covering the Moon or Sun or their light, with a modern theory of eclipses.
      

39. Arabic mathematics
    
    • Al-Battani (born 850) made accurate observations which allowed him to improve on Ptolemy's data for the sun and the moon.
      Go directly to this paragraph
      

40. Babylonian mathematics
    
    • Their symbols were written on wet clay tablets which were baked in the hot sun and many thousands of these tablets have survived to this day.
      

41. Water-clocks
    
    • The water clock, or klepsydra, probably developed in response to the shortcomings of the sundial, namely the inability of the sundial to work when there was no sun and to maintain a constant division of time.
      

42. Babylonian numerals
    
    • Another hypothesis concerns the fact that the sun moves through its diameter 720 times during a day and, with 12 Sumerian hours in a day, one can come up with 60.
      

43. Infinity
    
    • What happened if one kept travelling in a particular direction? Would one reach the end of the world or could one travel for ever? Again above the earth one could see stars, planets, the sun and moon, but was this space finite or do it go on for ever? .
      

44. Modern light
    
    • In 1919 Eddington made an expedition to Principe Island off the west coast of Africa to observe a solar eclipse and to measure the apparent position of stars observed close to the disk of the eclipsed sun.
      

45. Egyptian mathematics
    
    • The heliacal rising is the first appearance of the star after the period when it is too close to the sun to be seen.
      

46. Water-clocks references
    
    • J Fermor, Timing the sun in Egypt and Mesopotamia.
      

Famous Curves

1. Cassinian
   
   • The curve was first investigated by Giovanni Cassini in 1680 when he was studying the relative motions of the Earth and the Sun.
     
   • Cassini believed that the Sun travelled round the Earth on one of these ovals, with the Earth at one focus of the oval.
     

2. Ellipse
   
   • Kepler, in 1602, said he believed that the orbit of Mars was oval, then he later discovered that it was an ellipse with the sun at one focus.
     
   • In 1705 Halley showed that the comet, which is now called after him, moved in an elliptical orbit round the sun.
     

3. Involute
   
   • The problem was of vital importance since if GMT was known from a clock then, since local time could be easily computed from the Sun, longitude could be easily computed.
     

Societies etc

1. International Congress Speakers
   
   • Adolfe Rome, The Calculation of an Eclipse of the Sun According to Theon of Alexandria.
     
   • Sun-Yung Alice Chang and Paul Chien-Ping Yang, Non-linear Partial Differential Equations in Conformal Geometry.
     

2. AMS Satter Prize
   
   • 1995 Sun-Yung Alice Chang .
     

3. AMS Colloquium Lecturers
   
   • 2004 Sun-Yung Alice Chang .
     

References

1. References for Sun Zi
   
   • References for Sun Zi .
     
   • E I Berezkina, Le traite mathematique de Sun-zi Suan-Jing (Russian), Istor.-Mat.
     
   • W M Li, A preliminary proof of Zi Sun's theorem and the art of solving congruences by Zong Xian Huang (Chinese), in Di Li (ed.), Collected research papers on the history of mathematics 3 (Chinese) (Hohhot, 1992), 112-116.
     
   • X T Xu, Sun Zi suan jing ( Master Sun's arithmetical manual) was the original source for the 'leap forward and regress method of place determination' in the extraction of roots (Chinese), J.
     
   • http://www-history.mcs.st-andrews.ac.uk/References/Sun_Zi.html .
     

2. References for Chang
   
   • References for Sun-Yung Alice Chang .
     

3. References for Hipparchus
   
   • Y Maeyama, Determination of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.
     
   • V M Petersen and O Schmidt, The determination of the longitude of the apogee of the orbit of the sun according to Hipparchus and Ptolemy, Centaurus 12 (1967/1968), 73-96.
     
   • N M Swerdlow, Hipparchus on the distance of the sun, Centaurus 14 (1969), 287-305.
     
   • G J Toomer, Hipparchus on the distances of the sun and moon, Arch.
     

4. References for Ptolemy
   
   • B Chatterjee, Geometrical interpretation of the motion of the sun, moon and the five planets as found in the mathematical syntaxis of Ptolemy and in the Hindu astronomical works, J.
     
   • Y Maeyama, Determination of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.
     
   • V M Petersen and O Schmidt, The determination of the longitude of the apogee of the orbit of the sun according to Hipparchus and Ptolemy, Centaurus 12 (1967/1968), 73-96.
     

5. References for Yang Hui
   
   • K Q Sun, Hui Yang's triangle and determinant (Chinese), Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 17 (4) (1994), 53-57.
     
   • H A Sun, A note on computation of the area of a quadrilateral with different sides (Chinese), J.
     

6. References for Al-Battani
   
   • Y Maeyama, Determination of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.
     

7. References for Regiomontanus
   
   • N M Swerdlow, Regiomontanus's concentric-sphere models for the sun and moon, J.
     

8. References for McCrea
   
   • W Saxon, William Hunter McCrea, 94, Expert on Sun's Ingredients, The New York Times (6 May 1999).
     

9. References for Feynman
   
   • D L Goodstein and J R Goodstein, Feynman's lost lecture : The motion of planets around the sun (New York, 1996).
     

10. References for Brahe
    
    • Y Maeyama, Determination of the Sun's orbit (Hipparchus, Ptolemy, al-Battani, Copernicus, Tycho Brahe), Arch.
      

11. References for Wolf
    
    • D V Hoyt and K H Schatten,, The Role of the Sun in Climate Change (Oxford University Press, 1997).
      

12. References for Varahamihira
    
    • G Abraham, Theories for the motion of the Sun in the Pancasiddhantika, Arch.
      

13. References for Geminus
    
    • The motion of the Sun in the Parapegma of Geminos and in the Romaka-Siddhanta, Arch.
      

14. References for Yunus
    
    • D A King, Ibn Yunus' Very Useful Tables for Reckoning Time by the Sun, Archive for the History of Exact Sciences 10 (1973), 342-394.
      

15. References for Theon
    
    • A Rome, The calculation of an eclipse of the sun according to Theon of Alexandria, in Proceedings of the International Congress of Mathematicians 1950 1 (Providence, R.
      

16. References for Horrocks
    
    • D Sellers, The Transit of Venus: the Quest to Find the True Distance of the Sun (2001).
      

17. References for Yang
    
    • K Q Sun, Hui Yang's triangle and determinant (Chinese), Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 17 (4) (1994), 53-57.
      

18. References for Archimedes
    
    • A E Shapiro, Archimedes's measurement of the sun's apparent diameter, J.
      

19. References for Harriot
    
    • J J Roche, Harriot's 'Regiment of the Sun' and its background in sixteenth-century navigation, British J.
      

Additional material

1. Kelvin on the sun
   
   • Kelvin on the sun .
     
   • He addressed the audience on The Sun's Heat.
     
   • The second part of Thomson's lecture may be found here: Kelvin on the sun 2 .
     
   • The Sun's Heat, Part 1 .
     
   • From human history we know that for several thousand years the sun has been giving heat and light to the earth as at present, possibly with some considerable fluctuations, and possibly with some not very small progressive variation.
     
   • The records of agriculture, and the natural history of plants and animals within the time of human history, abound with evidence that there has been no exceedingly great change in the intensity of the sun's heat and light within the last three thousand years; but for all that, there may have been variations of quite as much as 5 or 10 per cent, as we may judge by considering that the intensity of the solar radiation to the earth is 6 1/2 per cent greater in January than in July; and neither at the equator nor in the northern or southern hemispheres has this difference been discovered by experience or general observation of any kind.
     
   • But as for the mere age of the sun, irrespective of the question of uniformity, we have proof of something vastly more than three thousand years in geological history, with its irrefragable evidence of continuity of life on the earth in time past for tens of thousands, and probably for millions of years.
     
   • The sun, a mere piece of matter of the moderate dimensions which we know it to have, bounded all round by cold ether, has been doing work at the rate of four hundred and seventy-six thousand million million million horse-power for three thousand years; and at possibly a higher, certainly not much lower, rate for a few million years.
     
   • It may be taken as an established result of scientific inquiry that the sun is not a burning fire, and is merely a white hot fluid mass cooling, with some little accession of fresh energy by meteors occasionally falling in, but of very small account in comparison with the whole energy of heat which he gives out from year to year.
     
   • Helmholtz's form of the meteoric theory of the origin of the sun's heat, may be accepted as having the highest degree of scientific probability that can be assigned to any assumption regarding actions of prehistoric times.
     
   • The essential principle of the explanation is this; at some period of time, long past, the sun's initial heat was generated by the collision of pieces of matter gravitationally attracted together from distant space to build up his present mass; and shrinkage due to cooling gives, through the work done by the mutual gravitation of all parts of the shrinking mass, the vast heat-storage capacity in virtue of which the cooling has been, and continues to be, so slow.
     
   • In some otherwise excellent books it is "paradoxically" stated that the sun is becoming hotter because of the condensation.
     
   • The truth is, that it is because the sun is becoming less hot in places of equal density that his mass is allowed to yield gradually under the condensing tendency of gravity and thus from age to age cooling and condensation go on together.
     
   • An essential detail of Helmholtz's theory of solar heat is that the sun must be fluid, because even though given at any moment hot enough from the surface to any depth, however great, inwards, to be brilliantly incandescent, the conduction of heat from within through solid matter of even the highest conducting quality known to us, would not suffice to maintain the incandescence of the surface for more than a few hours, after which all would be darkness.
     
   • Observation confirms this conclusion so far as the outward appearance of the sun is concerned, but does not suffice to disprove the idea which was so eloquently set forth by Sir John Herschel, and which prevailed till thirty or forty years ago, that the sun is a solid nucleus enclosed in a sheet of violently agitated flame.
     
   • In reality, the matter of the outer shell of the sun, from which the heat is radiated outwards, must in cooling become denser, and so becoming unstable in its high position must fall down, and hotter fluid from within must rush up to take its place.
     
   • To form some idea of the amount of the heat which is being continually carried up to the sun's surface and radiated out into space, and of the dynamical relations between it and the solar gravitation, let us first divide that prodigious number (476 cross 1021) of horse-power by the number (6.1 cross 1018) of square metres in the sun's surface, and we find 78,000 horse-power as the mechanical value of the radiation per square metre.
     
   • The same heat would be given out from the square metre surface of the fluid as is given out from every square metre of the sun's surface.
     
   • But now to pass from a practically impossible combination of engines, and a physically impossible paddle and fluid and containing vessel, towards a more practical combination of matter for producing the same effect: still keep the ideal vat and paddle and fluid, but place the vat on the surface of a cool, solid, homogeneous globe of the same size (697,000 kilometres radius) as the sun, and of density (1.4) equal to the sun's mean density.
     
   • Let the pit be a metre square at its upper end, and let it be excavated quite down to the sun's centre, everywhere of square horizontal section, and tapering uniformly to a point in the centre.
     
   • Let the weight be simply the excavated matter of the sun's mass, with merely a little clearance space between it and the four sides of the pit, and with a kilometre or so out off the lower pointed end to allow space for its descent.
     
   • Its heaviness, three-quarters of the heaviness of an equal mass at the sun's surface, is 244 million tons solar surface-heaviness.
     
   • Now a horse-power is, per hour, 270 metre-tons, terrestrial surface-heaviness; or 10 metre-tons, solar surface-heaviness, because a ton of matter is twenty-seven times as heavy at the sun's surface as at the earth's.
     
   • To advance another step, still through impracticable mechanism, towards the practical method by which the sun's heat is produced, let the thread of the screw be of uniformly decreasing steepness from the surface downwards, so that the velocity of the weight, as it is allowed to descend by the turning of the screw, shall be in simple proportion to distance from the sun's centre.
     
   • Now let the whole surface of our cool solid sun be divided into squares, for example as nearly as may be of one square metre area each, and lot the whole mass of the sun be divided into long inverted pyramids or pointed rods, each 697,000 kilometres long, with their points meeting at the centre.
     
   • Let each be mounted on a screw, as already described for the long tapering weight which we first considered; and let the paddle at the top end of each screw-shaft revolve in a fluid, not now confined to a vat, but covering the whole surface of the sun to a depth of a few metres or kilometres.
     
   • The whole fluid will, by the work which the paddles do in it, be made incandescent, and it will give out heat and light to just about the same amount as is actually done by the sun.
     
   • If the fluid is a few thousand kilometres deep over the paddles, it would be impossible, by any of the appliances of solar physics, to see the difference between our model mechanical sun and the true sun.
     
   • To do away with the last vestige of impracticable mechanism in which the heavinesses of all parts of each long rod are supported on the thread of an ideal screw cut on a vertical shaft of ideal matter, absolutely hard and absolutely frictionless: first, go back a step to our supposition of just one such rod and screw working in a single pit excavated down to the centre of the sun, and let us suppose all the rest of the sun's mass to be rigid and absolutely impervious to heat.
     
   • We should thus have a pit from the sun's surface to his centre, of a square metre area at the surface, full of incandescent fluid, which we may suppose to be of the actual ingredients of the solar substance.
     
   • If the solidified matter floats on the fluid, at the same temperature, below it, the crust would simply thicken as ice on a lake thickens in frosty weather; but if, as is more probable, solid matter, of such ingredients as the sun is composed of, sinks in the liquid when both are at the melting temperature of the substance, thin films of the upper crust would fall in, and continue falling in, until, for several metres downwards, the whole mass of mixed solid and fluid becomes stiff enough (like the stiffness of paste or of mortar) to prevent the frozen film from falling down from the surface.
     
   • Suppose the whole complex mass to be rotating at the rate of once round in twenty-five days, which is, about as exactly as we know it, the time of the sun's rotation about his axis.
     
   • Now at the instant when the paddle stops let all the partitions be annulled, so that there shall be perfect freedom for currents to flow unresisted in any direction, except so far as resisted by the viscosity of the fluid, and leave the piece of matter, which we may now call the Sun, to himself.
     
   • Of course the observer might have to wait a few years for sunspots, and a few quarter-centuries to discover periods of sunspots, but they would, I think I may say probably, all be there just as they are, because I think we may feel that it is most probable that all these actions are due to the sun's own substance, and not to external influences of any kind.
     
   • It is, however, quite possible, and indeed many who know most of the subject think it probable, that some of the chief phenomena due to sunspots arise from influxes of meteoric matter circling round the sun.
     
   • The energy of chemical combination is as nothing compared with the gravitational energy of shrinkage, to which the sun's activity is almost wholly due.
     
   • A body falling forty-six kilometres to the sun's surface or through the sun's atmosphere, has as much work done on it by gravity, as corresponds to a high estimate of chemical energy in the burning of combustible materials.
     
   • But chemical combinations and dissociations may, as urged by Lockyer, in his book on the 'Chemistry of the Sun,' just now published, be thoroughly potent determining influences on some of the features of non-uniformity of the brightness in the grand phenomena of sunspots, hydrogen flames, and corona, which make the province of solar physics.
     
   • What concerns us as to the explanation of sun-light and sun-heat may be summarised in two propositions:- .
     
   • Gigantic currents throughout the sun's liquid mass are continually maintained by fluid, slightly cooled by radiation falling down from the surface, and hotter fluid rushing up to take its place.
     
   • The work done in any time by the mutual gravitation of all the parts of the fluid, as it shrinks in virtue of the lowering of its temperature, is but little less than (so little less than, that we may regard it as practically equal to) the dynamical equivalent of the heat that is radiated from the sun in the same time.
     
   • If we wish to carry our calculations much farther back or forward than two hundred thousand years, we must reckon by differences of the reciprocal of the sun's radius, and not by differences simply of the radius, to take into account the change of density (which, for example, would be three per cent for one per cent change of the radius).
     
   • If in past time there has been as much as fifteen million times the heat radiated from the sun as is at present radiated out in one year, the solar radius must have been four times as great as at present.
     
   • If the sun's effective thermal capacity can be maintained by shrinkage till twenty million times the present year's amount of heat is radiated away, the sun's radius must be half what it is now.
     
   • It is also to be remarked that the greatly diminished radiating surface, at a much lower temperature, would give out annually much less heat than the sun in his present condition gives.
     
   • that it is hardly likely that the sun can continue to give sufficient heat to support life on the earth (such life as we now are acquainted with, at least) for ten million years from the present time.
     
   • In all our calculations hitherto we have for simplicity taken the density as uniform throughout, and equal to the true mean density of the sun, being about 1.4 times the density of water, or about a quarter of the earth's mean density.
     
   • In reality the density in the upper parts of the sun's mass must be something less than this, and something considerably more than this in the central parts, because of the pressure in the interior increasing to something enormously great at the centre.
     
   • If we knew the distribution of interior density we could easily modify our calculations accordingly; but it does not seem probable that the correction could, with any probable assumption as to the greatness of the density throughout a considerable proportion of the sun's interior, add more than a few million years to the past of solar heat, and what could be added to the past must be taken from the future.
     
   • In the circumstances, and taking fully into account all possibilities of greater density in the sun's interior, and of greater or less activity of radiation in past ages, it would, I think, be exceedingly rash to assume as probable anything more than twenty million years of the sun's light in the past history of the earth, or to reckon on more than five or six million years of sunlight for time to come.
     
   • We have seen that the sun draws on no external source for the heat he radiates out from year to year, and that the whole energy of this heat is due to the mutual attraction between his parts acting in conformity with the Newtonian law of gravitation.
     
   • We have seen how an ideal mechanism, easily imagined and understood, though infinitely far from possibility of realisation, could direct the work done by mutual gravitation between all the parts of the shrinking mass, to actually generate its heat-equivalent in an ocean of white-hot liquid covering the sun's surface, and so keep it white-hot while constantly radiating out heat at the actual rate of the sun's heat-giving activity.
     
   • Let us now consider a little more in detail the real forces and movements actually concerned in the process of cooling by radiation from the uttermost region of the sun, the falling inwards of the fluid thus cooled, the consequent mixing up of the whole mass of the sun, the resulting diminished elastic resistance to pressure in equi-dense parts, and the consequent shrinkage of the whole mass under the influence of mutual gravitation.
     
   • Imagine, instead of the atoms and molecules of the various substances which constitute the sun's mass, a vast number of elastic globes, like schoolboys' marbles or billiard balls.
     
   • The second part of Thomson's lecture may be found here: Kelvin on the sun 2 .
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Kelvin_sun_1.html .
     

2. Kelvin on the sun, Part 2
   
   • Kelvin on the sun, Part 2 .
     
   • He addressed the audience on The Sun's Heat.
     
   • The first part of Thomson's lecture may be found here: Kelvin on the sun 1 .
     
   • The Sun's Heat, Part 2 .
     
   • This diminution of temperature upwards in our terrestrial atmosphere is most important and suggestive in respect to the constitution of the solar atmosphere, and not merely of the atmosphere or outer shell of the sun, but of the whole interior fluid mass with which it is continuous.
     
   • In the case of the terrestrial atmosphere the lowest parts receive by contact heat from the solid earth, warmed daily by the sun's radiation.
     
   • On the average of night and day, as the air does not become warmer on the whole, it must radiate out into space as much heat as all that it gets, both from the earth by contact, and by radiation of heat from the earth, and by intercepted radiation from the sun on its way to the earth.
     
   • In the case of the sun the heat radiated from the outer parts of the atmosphere is wholly derived from the interior.
     
   • Corresponding differences of temperature there certainly are throughout the fluid mass of the sun, but of very different magnitudes because of the twenty-seven fold greater gravity at the sun's surface, the vastness of the space through which there is free circulation of fluid, and last, though not least, the enormously higher temperature of the solar fluid than of the terrestrial atmosphere at points of equal density in the two.
     
   • Lane remarks that the density at the centre of the sun would be "nearly one-third greater than that of the metal platinum," if the gaseous law held up to so great a degree of condensation for the ingredients of the sun's mass; but he does not suggest this supposition as probable, and he no doubt agrees with the general opinion that in all probability the ingredients of the sun's mass, at the actual temperatures corresponding to their positions in his interior, obey the simple gaseous law through but a comparatively small space inwards from the surface; and that in the central regions they are much less condensed than according to that law.
     
   • According to the simple gaseous law, the sun's central density would be thirty-one times that of water; we may assume that it is in all probability much less than this, though considerably greater than the mean density, 1.4.
     
   • This is a wide range of uncertainty, but it would be unwise at present to narrow it, ignorant as we are of the main ingredients of the sun's whole mass, and of the laws of pressure, density, and temperature, even for known kinds of matter at very great pressures and very high temperatures.
     
   • The question, Is the sun becoming colder or hotter? is an exceedingly complicated one, and, in fact, either to put it or to answer it is a paradox, unless we define exactly where the temperature is to be reckoned.
     
   • If we ask, How does the temperature of equi-dense portions of the sun vary from age to age? the answer certainly is that the matter of the sun of which the density has any stated value, for example, the ordinary density of our atmosphere, becomes always less and less hot, whatever be its place in the fluid, and whatever be the law of compression of the fluid, whether the simple gaseous law or anything from that to absolute incompressibility.
     
   • This would certainly be the case if the gaseous law of condensation held throughout, but even then the effective radiational temperature, in virtue of which the sun sheds his heat outwards, might be becoming lower, because the temperatures of equi-dense portions are clearly becoming lower under all circumstances.
     
   • Leaving now these complicated and difficult questions to the scientific investigators who are devoting themselves to advancing the science of solar physics, consider the easily understood question, What is the temperature of the centre of the sun at any time, and does it rise or fall as time advances? If we go back a few million years to a time when we may believe the sun to have been wholly gaseous to the centre, then certainly the central temperature must have been augmenting; again, if, as is possible though not probable at the present time, but may probably be the case at some future time, there be a solid nucleus, then certainly the central temperature would be augmenting, because the conduction of heat outwards through the solid would be too slow to compensate the augmentation of pressure due to augmentation of gravity in the shrinking fluid around the solid.
     
   • Now we come to the most interesting part of our subject - the early history of the Sun.
     
   • We cannot, however, help asking the question, What was the condition of the sun's matter before it came together and became hot? It may have been two cool solid masses, which collided with the velocity due to their mutual gravitation; or, but with enormously less of probability, it may have been two masses colliding with velocities considerably greater than the velocities due to mutual gravitation.
     
   • This last supposition implies that, calling the two bodies A and B for brevity, the motion of the centre of inertia of B relatively to A, must, when the distances between them was great, have been directed with great exactness to pass through the centre of inertia of A; such great exactness that the rotational momentum, or "moment of momentum," after collision was no more than to let the sun have his present slow rotation when shrunk to his present dimensions.
     
   • In this connection it is most interesting to know from stellar astronomy, aided so splendidly as it has recently been by the spectroscope, that the relative motions of the visible stars and our sun are generally very small in comparison with the velocity (612 kilometres per second) which a body would acquire in falling into the sun, and are comparable with the moderate little velocity (29.5 kilometres per second) of the earth in her orbit round the sun.
     
   • To fix the ideas, think of two cool solid globes, each of the same mean density as the earth, and of half the sun's diameter; given at rest, or nearly at rest, at a distance asunder equal to twice the earth's distance from the sun.
     
   • It will again fall inwards, and after a rapidly subsiding series of quicker and quicker oscillations it will subside, probably in the course of two or three years, into a globular star of about the same dimensions, heat, and brightness as our present sun, but differing from him in this, that it will have no rotation.
     
   • The moment of momentum of these motions round an axis through the centre of gravity of the two globes perpendicular to their lines of motion is just equal to the moment of momentum of the sun's rotation round his axis.
     
   • The transverse velocity in the case we are now supposing is so small that none of the main features of the collision and of the wild oscillations following it, which we have been considering, or of the magnitude, heat, and brightness of the resulting star, will be sensibly altered; but now, instead of being rotationless, it will be revolving once round in twenty-five days and so in all respects like to our sun.
     
   • Suppose now, still choosing a particular case to fix the ideas, that twenty-nine million cold solid globes, each of about the same mass as the moon, and amounting in all to a total mass equal to the sun's, are scattered as uniformly as possible on a spherical surface of radius equal to one hundred times the radius of the earth's orbit, and that they are left absolutely at rest in that position.
     
   • The average density of the gaseous nebula thus formed would be (215 x 40)-3, or one six hundred and thirty-six thousand millionth of the sun's mean density; or one four hundred and fifty-four thousand millionth of the density of water; or one five hundred and seventy millionth of that of common air at an ordinary temperature of 10 degrees C.
     
   • The gaseous nebula thus constituted would in the course of a few million years, by constantly radiating out heat, shrink to the size of our present sun, when it would have exactly the same heating and lighting efficiency.
     
   • The moment of momentum of the whole solar system is about eighteen times that of the sun's rotation; seventeen-eighteenths being Jupiter's and one-eighteenth the Sun's, the other bodies being not worth taking into account in the reckoning of moment of momentum.
     
   • Thus there may in reality be nothing more of mystery or of difficulty in the automatic progress of the solar system from cold matter diffused through space, to its present manifest order and beauty, lighted and warmed by its brilliant sun, than there is in the winding up of a clock and letting it go till it stops.
     
   • I shall only say in conclusion: - Assuming the sun's mass to be composed of materials which were far asunder before it was hot, the immediate antecedent to its incandescence must have been either two bodies with details differing only in proportions and densities from the cases we have been now considering as examples; or it must have been some number more than two - some finite number - at the most the number of atoms in the sun's present mass, a finite number (which may probably enough be something between 4 x 1057 and 140 x 1057) as easily understood and imagined as number 4 or 140.
     
   • For the theory of the sun it is indifferent which of these varieties of configurations of matter may have been the immediate antecedent of his incandescence, but I can never think of these material antecedents without remembering a question put to me thirty years ago by the late Bishop Ewing, Bishop of Argyll and the Isles: "Do you imagine that piece of matter to have been as it is from the beginning; to have been created as it is, or to have been as it is through all time till it fell on the earth?" I had told him that I believed the sun to be built up of meteoric stones, but be would not be satisfied till he knew or could imagine, what kind of stones.
     
   • I could not but agree with him in feeling it impossible to imagine that any one of such meteorites as those just described has been as it is through all time, or that the materials of the sun were like this for all time before they came together and became hot.
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Kelvin_sun_2.html .
     

3. Kepler's Planetary Laws
   
   • Law I (the Ellipse Law) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.
     
   • Law II (the Area Law) - the time taken by a planet to reach a particular position is represented by the area swept out by the radius vector drawn from the fixed Sun.
     
   • Kepler followed the ancients in always starting to measure at the point furthest from the Sun.) Almost certainly Kepler was responsible for introducing the term 'orbit', in Astronomia Nova Ch.1, and on his behalf we shall precisely define an orbit as possessing a pair of independent constituents: the path or curve, together with a (geometrical) way of representing time.
     
   • it is an outer planet (and therefore it is seldom viewed close to the Sun); .
     
   • it is the nearest to the Sun of the outer planets (and therefore it makes more frequent circuits, producing more observations).
     
   • Since Greek times, the accepted description of the planetary system had been a geometrical one, known as the Ptolemaic theory (a geocentric configuration), which supposed that the Earth was fixed at the centre of the universe, with the Moon, the Sun, and the five known (naked-eye) planets revolving round it.
     
   • In fact, Kepler gave Copernican theory a new, mathematical precision by specifying two fundamental properties that were consistent with his conviction that the Sun was metaphorically the place of God: .
     
   • The Sun is the fixed hub of the universe.
     
   • The Sun is responsible for all celestial motion.
     
   • Thus Kepler's interpretation of heliocentricity provided him with an origin from which to determine the Sun-planet distances and so discover the actual path of the planet.
     
   • In order to transpose the observations from a geocentric to a heliocentric basis, he applied triangulation to ensure that each Mars-distance was measured as if from the fixed Sun.
     
   • Bearing in mind that the observations contained no distance-measurements (as explained in Section 2), this involved expressing all the Mars-Sun distances in terms of the Earth-Sun distance, regarded as a standard unit or 'baseline' (since the path of the Earth is very nearly circular, this approximation happened to be accurate enough for Kepler's purpose); .
     
   • He verified that the path of each planet lay in a plane that passed through the Sun; .
     
   • And because it was expressed geometrically, the solution would potentially be exact - the closed orbit of a single planet in a plane round the fixed Sun.
     
   • He began by assuming a fixed/known line of apsides CD, on which lies the fixed point A (the position of the Sun) at a known 'eccentric' distance AB (all previously determined from Tycho's observations), where B is the midpoint of CD.
     
   • However, he found that this placed the planet too far from the Sun in almost all positions.
     
   • Unless its focus coincides with the fixed Sun (the origin), the investigation would have been too complicated to manage by geometry.
     
   • From a heliocentric point of view, it is especially easy to be aware that planets move more slowly the further they are from the Sun (and faster when nearer).
     
   • Thus, as Kepler realized, a connection exists between a small (micro) interval of time and the corresponding distance of the planet from the Sun.
     
   • Initially, he suggested that this (macro) time (the sum of the micro intervals of time) could be represented geometrically by the sum of all the corresponding distances from the Sun.
     
   • Next, Kepler extended that proposition, and took the distance-sum from the eccentric point (A, the position of the Sun) to be (approximately) proportional to the area of the eccentric sector (the area QAC, shown in Figure (4)).
     
   • Firstly, between 1609 and 1618, he satisfied himself that the orbit of each of the six primary planets was an ellipse with the Sun at one focus.
     
   • radial motion which is measured by the linear variation in distance from the Sun; .
     
   • transradial motion which is measured by the variation in the area swept out: this motion is defined to be circular round the Sun, and thus precisely at right angles to the radial motion.
     
   • This pair of component motions, whose source is the Sun (see Section 3), is contrasted in Figure (6) with the single tangential velocity, shown dashed, which, in Newton's work, superseded and replaced the Keplerian components of motion.
     
   • Kepler could never have supposed that the Sun could exert an attractive force because that concept did not exist in Aristotelian terms.
     
   • Section 10 The Sun's rotation: the cause of transradial motion .
     Go directly to this paragraph
     
   • We will deal first with the cause of the transradial motion because the revolution of the planets round the Sun is the most outstanding feature of a heliocentric universe, and requires a universal cause.
     
   • Kepler accounted for that motion by inventing the rotation of the Sun on its axis.
     
   • Thus, Kepler envisaged that the rays emitted by the rotating Sun would 'hit' or impel each planet continuously round in a circle.
     
   • Naturally, he expected that this impulsion would be less when the planet was further from the Sun, so he reasonably supposed that the action of the rays would vary inverse-linearly (that is, weaken) with distance.
     
   • Because of his Copernican convictions, Kepler extended this idea to suppose that every planet possessed magnetism, and contained a set of 'fibres' fixed within its body which could be activated by the Sun's magnetism; and he further supposed that each set of fibres possessed a unique potential magnetic 'strength' that could be associated with the individual eccentricity of the particular planetary path.
     
   • The radial motion itself was evaluated by taking a small variation (an increment) of the distance from the Sun with respect to a small change in the auxiliary angle: see Summary Table at the end, confirmed by the modern treatment in Planetary motion tackled kinematically.
     
   • Kepler was the first to introduce the concept of causation into astronomy, and in accordance with his Copernican convictions, he naturally believed that the Sun was the generator of all causes.
     
   • Moreover, it seemed common sense to suppose that the Sun could only act (or activate) continuously either in a radial direction or circularly round itself, and this consideration, for Kepler, determined the direction of the causes available and limited their number to two.
     
   • The precedent cause was the action of the Sun's rays, due to its rotation, which produced transradial motion.
     
   • The lesser cause was magnetism, generated by the Sun, which activated the planetary fibres.
     
   • The Sun appeared to function merely as a catalyst to facilitate radial motion - on no account can it be regarded as a Newtonian force (nor as an Aristotelian 'force').
     
   • Therefore, from a modern viewpoint, Kepler's work was purely kinematical, and he was entirely correct to treat each individual planet as if it were the only particle in the universe apart from the fixed Sun.
     
   • Action circularly round Sun:perpendicular to Sun's raysDirectionof componentsActivation in direction of Sun, thoughfibres are supposed fixed in direction .
     
   • 'Impulsion' of Sun's rays proportional 1/r Kepleriancauses[Strength of planet's fibres proportional e] .
     

4. Kepler's Planetary Laws
   
   • Law I (the Ellipse Law) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.
     
   • Law II (the Area Law) - the time taken by a planet to reach a particular position is represented by the area swept out by the radius vector drawn from the fixed Sun.
     
   • Kepler followed the ancients in always starting to measure at the point furthest from the Sun.) Almost certainly Kepler was responsible for introducing the term 'orbit', in Astronomia Nova Ch.1, and on his behalf we shall precisely define an orbit as possessing a pair of independent constituents: the path or curve, together with a (geometrical) way of representing time.
     
   • it is an outer planet (and therefore it is seldom viewed close to the Sun); .
     
   • it is the nearest to the Sun of the outer planets (and therefore it makes more frequent circuits, producing more observations).
     
   • Since Greek times, the accepted description of the planetary system had been a geometrical one, known as the Ptolemaic theory (a geocentric configuration), which supposed that the Earth was fixed at the centre of the universe, with the Moon, the Sun, and the five known (naked-eye) planets revolving round it.
     
   • In fact, Kepler gave Copernican theory a new, mathematical precision by specifying two fundamental tenets that were consistent with his conviction that the Sun was metaphorically the place of God: .
     
   • The Sun is the fixed hub of the universe.
     
   • The Sun is responsible for all celestial motion.
     
   • Thus Kepler's interpretation of heliocentricity provided him with an origin from which to determine the Sun-planet distances and so discover the actual path of the planet.
     
   • In order to transpose the observations from a geocentric to a heliocentric basis, he applied triangulation to ensure that each Mars-distance was measured as if from the fixed Sun.
     
   • Bearing in mind that the observations contained no distance-measurements (as explained in Section 2), this involved expressing all the Mars-Sun distances in terms of the Earth-Sun distance, regarded as a standard unit or 'baseline' (since the path of the Earth is very nearly circular, this approximation happened to be accurate enough for Kepler's purpose); .
     
   • He verified that the path of each planet lay in a plane that passed through the Sun; .
     
   • And because it was expressed geometrically, the solution would potentially be exact - the closed orbit of a single planet in a plane round the fixed Sun.
     
   • He began by assuming a fixed/known line of apsides CD, on which lies the fixed point A (the position of the Sun) at a known 'eccentric' distance AB (all previously determined from Tycho's observations), where B is the midpoint of CD.
     
   • However, he found that this placed the planet too far from the Sun in almost all positions.
     
   • Unless its focus coincides with the fixed Sun (the origin), the investigation would have been too complicated to manage by geometry.
     
   • From a heliocentric point of view, it is especially easy to be aware that planets move more slowly the further they are from the Sun (and faster when nearer).
     
   • Thus, as Kepler realized, a connection exists between a small (micro) interval of time and the corresponding distance of the planet from the Sun.
     
   • Initially, he suggested that this (macro) time (the sum of the micro intervals of time) could be represented geometrically by the sum of all the corresponding distances from the Sun.
     
   • Next, Kepler extended that proposition, and took the distance-sum from the eccentric point (A, the position of the Sun) to be (approximately) proportional to the area of the eccentric sector (the area QAC, shown in Figure (4)).
     
   • Firstly, between 1609 and 1618, he satisfied himself that the orbit of each of the six primary planets was an ellipse with the Sun at one focus.
     
   • radial motion which is measured by the linear variation in distance from the Sun; .
     
   • transradial motion which is measured by the variation in the area swept out: this motion is defined to be circular round the Sun, and thus precisely at right angles to the radial motion.
     
   • This pair of component motions, whose source is the Sun (see Section 3), is contrasted in Figure (6) with the single tangential velocity, shown dashed, which, in Newton's work, superseded and replaced the Keplerian components of motion.
     
   • Kepler could never have supposed that the Sun could exert an attractive force because that concept did not exist in Aristotelian terms.
     
   • 10.nnThe Sun's rotation: the cause of transradial motion .
     Go directly to this paragraph
     
   • We will deal first with the cause of the transradial motion because the revolution of the planets round the Sun is the most outstanding feature of a heliocentric universe, and requires a universal cause.
     
   • Kepler accounted for that motion by inventing the rotation of the Sun on its axis.
     
   • Thus, Kepler envisaged that the rays emitted by the rotating Sun would 'hit' or impel each planet continuously round in a circle.
     
   • Naturally, he expected that this impulsion would be less when the planet was further from the Sun, so he reasonably supposed that the action of the rays would vary inverse-linearly (that is, weaken) with distance.
     
   • Because of his Copernican convictions, Kepler extended this idea to suppose that every planet possessed magnetism, and contained a set of 'fibres' fixed within its body which could be activated by the Sun's magnetism; and he further supposed that each set of fibres possessed a unique potential magnetic 'strength' that could be associated with the individual eccentricity of the particular planetary path.
     
   • The radial motion itself was evaluated by taking a small variation (an increment) of the distance from the Sun with respect to a small change in the auxiliary angle: see Summary Table at the end, confirmed by the modern treatment in Planetary motion tackled kinematically.
     
   • Kepler was the first to introduce the concept of causation into astronomy, and in accordance with his Copernican convictions, he naturally believed that the Sun was the generator of all causes.
     
   • Moreover, it seemed common sense to suppose that the Sun could only act (or activate) continuously either in a radial direction or circularly round itself, and this consideration, for Kepler, determined the direction of the causes available and limited their number to two.
     
   • The precedent cause was the action of the Sun's rays, due to its rotation, which produced transradial motion.
     
   • The lesser cause was magnetism, generated by the Sun, which activated the planetary fibres.
     
   • The Sun appeared to function merely as a catalyst to facilitate radial motion - on no account can it be regarded as a Newtonian force (nor as an Aristotelian 'force').
     
   • Hence we can now recognize that Kepler's work was entirely kinematical, and acknowledge that he was, then, absolutely justified in treating each individual planet as if it were the only particle in the universe apart from the fixed Sun.
     
   • Action circularly round Sun:perpendicular to Sun's raysDirectionof componentsActivation in direction of Sun, thoughfibres are supposed fixed in direction .
     
   • 'Impulsion' of Sun's rays proportional 1/r Kepleriancauses[Strength of planet's fibres proportional e] .
     

5. Planetary motion tackled kinematically
   
   • Law I (the Ellipse Law) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.
     
   • Law II (the Area Law) - the time taken by a planet to reach a particular position is measured by the area swept out by the radius vector drawn from the fixed Sun.
     
   • This composite solution represents what is in fact the earliest instance of a planetary orbit: it will be succinctly referred to in what follows as 'the Sun-focused ellipse'.
     
   • Unexpectedly, this analysis is carried through in terms of the auxiliary angle, rather than the polar angle (at the Sun) that is invariably used nowadays: this came about for historical reasons [4].
     
   • It is essential to appreciate here that e not only denotes the focal eccentricity (the 'ellipticity') but the polar eccentricity as well, since A is both the focus and the origin or pole of coordinates (which here coincides with the position of the Sun).
     
   • Further, this argument could be generalized by carrying out a similar brief calculation to find the radius vector of any ellipse belonging to the system of conics whose origin is at the Sun (again setting polar distance AB = ae) that has CQD as its auxiliary circle and its typical point lying on QH (still defined by auxiliary angle beta ).
     
   • This identity acts as the bridging relation (inverse or direct) between the modern treatment by polar angle and the present treatment by auxiliary angle (which will only work effectively in the case of the unique Sun-focused ellipse alone).
     
   • Whatever we call it, this motion is defined to take place round the Sun instantaneously in a circle.
     
   • The constant of proportionality involved (1/2h is standard usage) is expressed mathematically by the following relationship, in which r represents the radius vector measured from the source of motion at the Sun, still taken as the origin of coordinates, again with reference to the figure: .
     
   • We now apply this to the special case of the Sun-focused ellipse, whose total area is πab and periodic time T, in order to evaluate its particular constant.
     
   • Thus for the Sun-focused ellipse alone, we deduce from (10) and (11): .
     
   • This is Law II: the time expressed in angular measure, discovered by Kepler in 1609, where he established that (when the dimensional constant is specified, for the Sun-focused ellipse alone) time is proportional to area.
     
   • This motion takes place linearly in the direction of the radius vector -- towards or away from the Sun.
     
   • Radial acceleration directed towards the Sun.nnnnnnnnnnnn(15) .
     
   • Radial acceleration = (2π)2a3/T2.(1/r2) towards the Sun.
     
   • Acceleration = mu 0/r2 towards the Sun.
     
   • From ancient times, astronomy had involved circles whose centres were eccentrically placed with respect to the Sun - which itself did not, until the arrival of the heliocentric view, play an explicit part in planetary theory.
     

6. Airy on Thales' eclipse
   
   • In explanation of this, the Lecturer pointed out that the force which acts upon the moon tending to draw it towards the earth is not simply the attraction of the earth, but consists of that attraction diminished by a disturbing force which is produced by the sun's attraction.
     
   • The sun sometimes attracts the moon towards the earth or the earth towards the moon, sometimes it produces the opposite effect; but on the whole it tends to pull the moon away from the earth.
     
   • And this diminution of the earth's attraction is greater as the sun is nearer; and therefore, in an elliptic orbit such as the earth describes about the sun (or such as the sun appears to describe about the earth), the diminution of the earth's attraction is greater when the earth is nearest to the sun than when the earth is farthest from the sun.
     
   • It might be supposed that one of these effects exceeds that which would happen when the earth is at its mean distance from the sun, as much as the other falls short of it; but in reality the excess is greater than the deficiency, and therefore the more eccentric the earth's orbit is, the greater is this disturbing force.
     
   • But the fact is, that, in consequence of the perturbations produced by the planets, though the earth's mean distance from the sun remains unaltered from age to age, yet the eccentricity of its orbit is diminishing from age to age; the sun's disturbing force is therefore diminishing from age to age: and the real force which acts upon the moon as tending to draw it towards the earth is therefore increasing from age to age; and, from age to age, the moon approaches a little nearer to the earth and performs her revolutions a little quicker.
     
   • He explained that the moon's orbit is inclined to the sun's apparent orbit round the earth, but not always in the same direction, the line of nodes (or the intersection of the planes of the two orbits) revolving so as to complete a revolution in about 191 years; and that an eclipse of the sun can happen only when the line of nodes is turned nearly towards the sun (as, in other cases.
     
   • If for a given day of the year, (when the sun is in one certain position), the moon is in that part of its orbit most nearly in the direction of the sun, the shadow of the moon will fall upon a certain point of the earth; but now if the place of the node be changed, the effect will be that of driving a wedge under the moon, and she will be thrown further north or south, and the shadow upon the earth will be thrown further north or south.
     
   • The next morning there was an eclipse of the sun which was evidently total.
     
   • Sir John Malcolm considered, and it appears most probable, that this is the record of a total eclipse of the sun; but no total eclipse near this time passed over Mazenderam.
     

7. Finlay Freundlich's Inaugural Address
   
   • He asserts in the third of his laws describing the motion of the planets that for all members of the solar system the ratio of the squares of their periods of revolution around the Sun over the cubes of their mean distances from the Sun has the same constant value.
     
   • Newton's law of gravitation revealed the nature of this constant; it is mainly the mass of the Sun.
     
   • In truth, the sum of the Sun's and the planet's mass enter in each case.
     
   • Applying Kepler's law the mass of the Sun can be determined, when we know the mean distance of the planet from the Sun and the period of its revolution around the Sun.
     
   • In this way the mass of the Sun and also that of the other members of the Solar system became known.
     
   • The planet nearest to the Sun is Mercury, revolving in 88 days around the Sun.
     
   • Accurate observations extending at present over more than a century, disclose that the orbit, which if the Sun's gravitation were alone acting, should be a closed ellipse - remaining as a whole fixed relative to the stellar system, each revolution being completed in a time strictly prescribed by Kepler's third law - that this orbit appears actually to be closed about one-half of a second of time later than predicted by Kepler's law.
     
   • For the other planets, more distant from the Sun, this additional effect becomes insignificant.
     
   • We have today justifiable hopes that we shall reach an understanding of the problem how were the chemical elements formed, and when were the stars built up? We have already very definite knowledge that the radiation of the stars, in particular that of the Sun, depends on the building up of heavier chemical elements from hydrogen.
     
   • For, the stellar matter near to the centre of the Sun must be able to support the weight of the overlying matter, and can only do this, unless the structure of the atoms be crushed, if the temperature rises to a sufficient height towards the centre.
     
   • Inside the Sun the temperature of its matter must rise to values of at least 10 to 20 million degrees.
     
   • This mass defect, released in the form of energy, yields the huge amount of radiation breaking out of the surface of a star like the Sun.
     

8. D'Arcy Thompson on Plato and Planets
   
   • The Sun.
     
   • According to some old writers Plato had set Venus to the farther side of Mercury; others, if I mistake not, put the Sun beyond both of these planets.
     
   • The Sun.
     
   • To account for the apparent movements of the Sun and Moon Eudoxus postulates three concentric spheres in each case, and four spheres for each of the other planetary bodies.
     
   • The two outermost spheres are alike in all, Sun and Moon included.
     
   • The second sphere, sharing in the revolution of the first but with its own proper motion superadded, revolves about the axis of the ecliptic; its poles are fixed within the former sphere at points corresponding with the poles of the ecliptic, and its rotation carries Sun or Moon or planet along its oblique pathway, through the circle of the zodiacal signs.
     
   • The second spheres, then, are all alike in configuration and orientation, but differ in their speed of rotation: that of the Moon revolving in a month, that of the Sun in a year, and those of the planets according to their own proper orbital periods.
     
   • Without recapitulating further details for Sun and Moon, we come to a very great difficulty in the case of the planets, namely to explain, by any simple imaginary mechanism, what are known as their stations and retrogradations.
     
   • Now these numbers place the planets, other than the Sun and Moon, in the precise order of Plato's text.
     
   • Moreover, though not identical with these motions of the planets properly so called, the excursions of the Sun and Moon to either side of the equator, across the intertropic belt, are in a way comparable to them: so far at least, that they might with equal truth be described as [ motions in breadth], or ascribed to a range of freedom on either side of a theoretic orbit; and the analogy is all the better seen when we think of the identical mechanism of axial obliquities to which in each case, according to Eudoxus, the phenomenon is due.
     
   • We may be justified in including in our series the angle of the ecliptic for the Sun, that is to say about 23 degrees 28', or rather, if we assume the epoch of Eudoxus (as Dr Copeland suggested to me long ago) about 23 degrees 45': which angle, in the [ artificial sphere] of Eudoxus, is the angle which the axis of the Sun's second sphere makes with that of his first; and in including for the Moon an angle which, as Eudoxus tells us, is in her case somewhat greater than the Sun's, in fact about 5 degrees more.
     
   • The Sun .
     

9. Finlay Freundlich's Inaugural Address, Part 2
   
   • Earth and Moon together are similarly enchained by the gravitation of the Sun, and so on.
     
   • The theory of relativity teaches us that the Earth, placed at a certain distance from the Sun and given an initial speed, will be guided, due to the Sun's gravitation - as if an invisible surface connected the two subsequent orbital positions - along the shortest path which connects these two positions.
     
   • But due to the changed geometrical conditions of space, arising from the gravitational field produced by the Sun, this shortest connection is no longer a straight line of Euclid's geometry, but the arc of a Kepler orbit.
     
   • It is no longer appropriate to talk of a force exerted by the Sun upon the Earth, as Newton's law implies; for, as there is no bodily connection between Sun and the planets, or between the Earth and the Moon, it is impossible to envisage how a gravitational attraction should act.
     
   • When a ray of light passes near to the Sun, the gravitational field of the Sun must affect the propagation of the light.
     
   • This assumption leads to an observable effect; it is a measurable deflection of the light of a star passing near to the Sun.
     
   • This deflection depends on the solar mass and on the distance at which the light beam passes the Sun, and is large enough to be accurately measured.
     

10. Eulogy to Euler by Fuss
    
    • Euler's is especially remarkable by its clarity and the way in which he explains the effects of the action of the sun and the moon to the exclusion of all other forces on the sea which occurs due to the shape of the earth and how she is altered by the action of these two forces.
      
    • Newton's vacuum hypothesis is contrary to the material diffusions of the sun and the fixed stars.
      
    • During the same time that the Academy was publishing this work its presses were occupied in printing the Letters to a Princess of Germany, Integral Calculus, Elements of Algebra, the calculation concerning the comet of 1769, the sun's eclipse and the passage of Venus, all in the same year, the new lunar theory and that of navigation, not withstanding the huge number of memoires which are found in the Commentarii of this period.
      
    • The year 1769 will forever be distinguished in the history of the progress of the sciences by the felicitous competition of those on earth who encouraged the astronomers to be in a position to take advantage of the passage of Venus across the sun's disk.
      
    • Euler thought of new ways to interpret the various parts of their observations to determine the true parallax of the sun, and consequentially the distances from all the planets.
      
    • He found a particularly elegant one to calculate, not only the observations of passage, but also those of the eclipse of the sun which followed soon after the first phenomenon and from which it was able to determine the geographic location from where the best observations could be taken.
      
    • Euler that astronomy is grateful due to the perfection that she evinced from the exact determination of the sun's parallax.
      
    • Instead of being stopped in his tracks as in the past due to the inability to integrate the three differential equations of the second degree that the mechanical principles furnish, he regrouped them at first into the three coordinates which determine the location of the moon, he then distributed all the inequalities of the moon into separate classes based on whether they depended either on the mean length of the sun from the moon or concerning the eccentricity or the parallax or the inclination of the lunar orbit.
      

11. Eulogy to Euler by Fuss
    
    • Euler's is especially remarkable by its clarity and the way in which he explains the effects of the action of the sun and the moon to the exclusion of all other forces on the sea which occurs due to the shape of the earth and how she is altered by the action of these two forces.
      
    • Newton's vacuum hypothesis is contrary to the material diffusions of the sun and the fixed stars.
      
    • During the same time that the Academy was publishing this work its presses were occupied in printing the Letters to a Princess of Germany, Integral Calculus, Elements of Algebra, the calculation concerning the comet of 1769, the sun's eclipse and the passage of Venus, all in the same year, the new lunar theory and that of navigation, not withstanding the huge number of memoires which are found in the Commentarii of this period.
      
    • The year 1769 will forever be distinguished in the history of the progress of the sciences by the felicitous competition of those on earth who encouraged the astronomers to be in a position to take advantage of the passage of Venus across the sun's disk.
      
    • Euler thought of new ways to interpret the various parts of their observations to determine the true parallax of the sun, and consequentially the distances from all the planets.
      
    • He found a particularly elegant one to calculate, not only the observations of passage, but also those of the eclipse of the sun which followed soon after the first phenomenon and from which it was able to determine the geographic location from where the best observations could be taken.
      
    • Euler that astronomy is grateful due to the perfection that she evinced from the exact determination of the sun's parallax.
      
    • Instead of being stopped in his tracks as in the past due to the inability to integrate the three differential equations of the second degree that the mechanical principles furnish, he regrouped them at first into the three coordinates which determine the location of the moon, he then distributed all the inequalities of the moon into separate classes based on whether they depended either on the mean length of the sun from the moon or concerning the eccentricity or the parallax or the inclination of the lunar orbit.
      

12. Lucretius: 'On the Nature of Things
    
    • Of the rest which wander through the great void, a few leap far apart, and recoil afar with great spaces between; these supply for us thin air and the bright light of the sun.
      
    • For look closely, whenever rays are let in and pour the sun's light through the dark places in houses: for you will see many tiny bodies mingle in many ways all through the empty space right in the light of the rays, and as though in some everlasting strife wage war and battle, struggling troop against troop, nor ever crying a halt, harried with constant meetings and partings; so that you may guess from this what it means that the first-beginnings of things are for ever tossing in the great void.
      
    • And for this reason it is the more right for you to give heed to these bodies, which you see jostling in the sun's rays, because such jostlings hint that there are movements of matter too beneath them, secret and unseen.
      
    • And so the movement passes upwards from the first-beginnings, and little by little comes forth to our senses, so that those bodies move too, which we can descry in the sun's light; yet it is not clearly seen by what blows they do it.
      
    • First, when dawn strews the land with new light, and the diverse birds flitting through the distant woods across the soft air fill the place with their clear cries, we see that it is plain and evident for all to behold how suddenly the sun is wont at such a time to rise and clothe all things, bathing them in his light.
      
    • And yet that heat which the sun sends out, and that calm light of his, is not passing through empty space; therefore, it is constrained to go more slowly, while it dashes asunder, as it were, the waves of air.
      
    • But the first-beginnings, which are of solid singleness, when they pass through the empty void, and nothing checks them without, and they themselves, single wholes with all their parts, are borne, as they press on, towards the one spot which they first began to seek, must needs, we may be sure, surpass in speed of motion, and be carried far more quickly than the light of the sun, and rush through many times the distance of space in the same time in which the flashing light of the sun crowds the sky.
      

13. James Jeans: 'Physics and Philosophy' I
    
    • Thus to primitive man the sun was a life-giving god - to the Greeks the horse-drawn chariot of a god - while a later and less pagan age supposed that angels had been entrusted with the task of pushing along the sun, moon and planets, and of maintaining the motion of the celestial spheres to which the more distant stars were supposed to be affixed.
      
    • To be more explicit, it ended when Copernicus, in accordance with the earlier teaching of Pythagoras, Aristarchus and others, showed how the apparent motion of the sun, moon and stars across the sky resulted from a daily rotation of the earth, while the motions of the planets through the stars could be explained by their revolutions round a fixed sun.
      
    • Even when Kepler discovered the true shapes of these planetary orbits sixty years later, he still postulated a 'power' or influence to keep the planets moving; he thought they would all stop dead if a material emanation from the sun did not continually urge them on.
      

14. Simplicius on astronomy and physics
    
    • It is the business of physical inquiry to consider the substance of the heaven and the stars, their force and quality, their coming into being and their destruction, nay, it is in a position even to prove the facts about their size, shape, and arrangement; astronomy, on the other hand, does not attempt to speak of anything of this kind, but proves the arrangement of the heavenly bodies by considerations based on the view that the heaven is a real cosmos, and further, it tells us of the shapes and sizes and distances of the earth, sun, and moon, and of eclipses and conjunctions of the stars, as well as of the quality and extent of their movements.
      
    • Now in many cases the astronomer and the physicist will propose to prove the same point, e.g., that the sun is of great size or that the earth is spherical, but they will not proceed by the same road.
      
    • For example, why do the sun, the moon, and the planets appear to move irregularly? We may answer that, if we assume that their orbits are eccentric circles or that the stars describe an epicycle, their apparent irregularity will be saved; and it will be necessary to go further and examine in how many different ways it is possible for these phenomena to be brought about, so that we may bring our theory concerning the planets into agreement with that explanation of the causes which follows an admissible method.
      
    • Hence we actually find a certain person, Heraclides of Pontus [the comment here indicates that Heraclides anticipated Copernicus], coming forward and saying that, even on the assumption that the earth moves in a certain way, while the sun is in a certain way at rest, the apparent irregularity with reference to the sun can be saved.
      

15. John Couch Adams' account of the discovery of Neptune
    
    • Some had even supposed that, at the great distance of Uranus from the sun, the law of attraction becomes different from that of the inverse square of the distance.
      
    • I find among my papers the following memorandum, dated July 3, 1841: "Formed a design, in the beginning of this week, of investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus, which are yet unaccounted for, in order to find whether they may be attributed to the action of an undiscovered planet beyond it, and, if possible, thence to determine approximately the elements of its orbit, etc., which would probably lead to its discovery." Accordingly, in 1843, I attempted a first solution of the problem, assuming the orbit to be a circle, with a radius equal to twice the mean distance of Uranus from the sun.
      
    • In November 1845, M Le Verrier presented to the Royal Academy of Sciences, at Paris, a very complete and elaborate investigation of the theory of Uranus, as disturbed by the action of Jupiter and Saturn, in which he pointed out several small inequalities which had previously been neglected; and in June, of the present year, he followed up this investigation by a memoir, in which he attributed the residual disturbances to the action of another planet at a distance from the sun equal to twice that of Uranus, and found a longitude for the new planet agreeing very nearly with the result which I had obtained on the same hypothesis.
      

16. Christiaan Huygens' article on Saturn's Ring
    
    • For even before this I had always believed that the other primary planets were like our Earth in this respect that each rotated on its own axis, and so the entire surface rejoiced in the light of the Sun, a part at a time; and, more than this, I believe that in general the arrangement with the large bodies of the world was such that those around which smaller bodies revolved, having themselves a central position, had also a shorter period of rotation.
      
    • Thus the Sun, its spots declare, rotates on its own axis in about twenty-six days; but around the Sun the various planets, among which the Earth is also to be reckoned, complete their courses in times varying as their distances.
      

17. John Couch Adams' account of the discovery of Neptune
    
    • Some had even supposed that, at the great distance of Uranus from the sun, the law of attraction becomes different from that of the inverse square of the distance.
      
    • I find among my papers the following memorandum, dated July 3, 1841: "Formed a design, in the beginning of this week, of investigating, as soon as possible after taking my degree, the irregularities in the motion of Uranus, which are yet unaccounted for, in order to find whether they may be attributed to the action of an undiscovered planet beyond it, and, if possible, thence to determine approximately the elements of its orbit, etc., which would probably lead to its discovery." Accordingly, in 1843, I attempted a first solution of the problem, assuming the orbit to be a circle, with a radius equal to twice the mean distance of Uranus from the sun.
      
    • In November 1845, M Le Verrier presented to the Royal Academy of Sciences, at Paris, a very complete and elaborate investigation of the theory of Uranus, as disturbed by the action of Jupiter and Saturn, in which he pointed out several small inequalities which had previously been neglected; and in June, of the present year, he followed up this investigation by a memoir, in which he attributed the residual disturbances to the action of another planet at a distance from the sun equal to twice that of Uranus, and found a longitude for the new planet agreeing very nearly with the result which I had obtained on the same hypothesis.
      

18. Galileo: 'Confession
    
    • When I ask: whose work is the Sun, the Moon, the Earth, the Stars, their motions and dispositions, I shall probably be told that they are God's work.
      
    • Therefore I must ask why it is that we insist that whenever it speaks of the Sun or of the Earth, Holy Scripture be considered as quite infallible? .
      
    • But because I have been enjoined, by this Holy Office, altogether to abandon the false opinion which maintains that the Sun is the centre and immovable, and forbidden to hold, defend, or teach, the said false doctrine in any manner ..
      

19. Christiaan Huygens' article on Saturn's Ring
    
    • For even before this I had always believed that the other primary planets were like our Earth in this respect that each rotated on its own axis, and so the entire surface rejoiced in the light of the Sun, a part at a time; and, more than this, I believe that in general the arrangement with the large bodies of the world was such that those around which smaller bodies revolved, having themselves a central position, had also a shorter period of rotation.
      
    • Thus the Sun, its spots declare, rotates on its own axis in about twenty-six days; but around the Sun the various planets, among which the Earth is also to be reckoned, complete their courses in times varying as their distances.
      

20. Thomson on 'ether
    
    • The sun warms and lights the earth by wave motion, excited in virtue of his white-hot temperature, and transmitted through a material commonly called the luminiferous ether, which fills all space as far as the remotest star, and has the property of transmitting radiant heat (or light) without itself becoming heated.
      
    • I feel that I have a right to drop the adjective luminiferous, because the medium, far above the earth's surface, through which we receive sun-heat (or light), and through which the planets move, was called ether 2000 years before chemists usurped the name for "sulphuric ether," "muriatic ether," and other compounds, fancifully supposed to be peculiarly ethereal; and I trust that chemists of the present day will not be angry with me if I use the word ether, pure and simple, to denote the medium whose undulatory motions constitute radiant heat (or light).
      

21. The Tercentenary of the birth of James Gregory
    
    • "Let in the sun's light," he says, "by a small hole to a darkened house, and at the hole place a feather (the more delicate and white the better for this purpose), and it shall direct to a white wall or paper opposite to it a number of small circles and ovals (if I mistake them not) whereof one is somewhat white (to wit, the middle which is opposite the sun) and all the rest severally coloured.
      

22. Proclus on pure and applied mathematics
    
    • Geodesy deals, then, with straight lines, not as conceived by the mind, but as perceived by the senses, sometimes more sharply defined, as in the case of the rays of the sun, sometimes less sharply defined, as in the case of cords or a plumb-line.
      
    • Its branches are: (a) gnomonics, which is concerned with the measuring of the hours by the proper placing of gnomons; (b) meteoroscopy, which investigates the different elevations and distances of stars, and sets forth numerous other theorems of various sorts in the field of astronomy; (c) the science of dioptrics, which, with the use of the proper instruments, investigates the positions of the sun, moon, and the other stars.
      

23. Horace Lamb addresses the British Association in 1904, Part 2
    
    • Everyone will grant, however, that the distance between two clouds, for instance, is not a definable magnitude; and the distance of the earth from the sun, and even the length of a wave of light, are in precisely the same case.
      
    • We have been led to recognise that the formal and mathematical element is of our own introduction; that it is merely the apparatus by which we map out our knowledge, and has no more objective reality than the circles of latitude and longitude on the sun.
      

24. Ptolemy's hypotheses of astronomy
    
    • The second part gives an account of the motion of the sun and the moon and of the phenomena that depend on these motions.
      
    • They saw the sun and the moon and the other stars moving from east to west in circles always parallel to each other; they saw the bodies begin to rise from below, as if from the earth itself, and gradually to rise to their highest point, and then, with a correspondingly gradual decline, to trace a downward course until they finally disappeared, apparently sinking into the earth.
      

25. Cassini and the Division in Saturn's Ring
    
    • After the emergence of Saturn from the rays of the Sun as a morning star in the year 1675, the globe of the planet appeared with a dark band, similar to those of Jupiter, extending the length of the ring from East to West, as it is nearly always shown by the 34-foot telescope, and the breadth of the ring was divided by a dark line into two equal parts, of which the interior and nearer one to the globe was very bright, and the exterior part slightly dark.
      
    • In the same year, 1671, the shorter diameter of the ring was still less than the diameter of the globe which extended outside the ring on the North and South sides, and this phase lasted until the immersion of Saturn in the rays of the Sun in the year 1676.
      

26. University of Glasgow Examinations
    
    • What is the lowest latitude at which the phenomenon of a non-setting sun may be observed.
      
    • Show how the distance of Mercury from the sun may be obtained from observation of his greatest and least apparent diameters.
      

27. Letters from Galileo' Preface
    
    • We present Galileo's last Copernican writings before the decree of March 5, 1616, in which the Inquisition denounced as "false and against the Holy Scriptures the Pythagorean doctrine of the motion of the Earth and the immobility of the Sun, which is also taught by Nicolas Copernicus in De revolutionibus orbium coelestium ..
      
    • A few days earlier, by order of His Holiness Pope Paul V, Galileo had been summoned before Cardinal Roberto Bellarmino, in order "that he be warned to abandon that opinion (that the Sun is immobile at the centre of the world and that the Earth moves); and, if he refuses to obey, that he be ordered to stop teaching, defending and even discussing this doctrine".
      

28. Association 1904 Part 2.html
    

29. Mathematicians and Music 2.1
    
    • Pythagoras proposed to find in the order of the universe, where whole numbers and simple ratios prevail, an answer to the question: Why is consonance (the beautiful in sound) determined by the ratio of small whole numbers? The correct numerical ratios existing between the seven tones of the diatonic scale corresponded, according to Pythagoras, to the sun, moon and five planets, and the distances of the celestial bodies from the central fire, etc.
      
    • It was the elaboration of these figments of philosophy, and because the fifth as the central tone of the octave corresponded to the astronomical order in which the Samian sage ranged the sun and planets, that he laid such a deep stress upon the c scale obtained from fifths only.
      

30. Born Inaugural
    
    • The orbit of the earth round the sun is an ellipse only for an observer standing just at the centre of mass of the two bodies.
      
    • We have not only the fact of the finite velocity of light, but another most important fact, disclosed by Michelson's celebrated experiment: that light on this earth travels with the same speed in all directions, independently of the motion of the earth round the sun.
      

31. Laplace: 'Essay on probabilities
    
    • All events, even those which on account of their insignificance do not seem to follow the great laws of nature, are a result of it just as necessarily as the revolutions of the sun.
      
    • No one prayed to have the planets and the sun arrested in their courses; observations had soon made apparent the futility of such prayers.
      

32. Thomson on British units
    
    • The context was an article on the sun and he is explaining why he is not going to use British units.
      
    • The awful and unnecessary toil and waste of brain power involved in the use of the British system of inches, feet, yards, perches, or rods, or poles, "chains," furlongs, British statute miles, nautical miles, square rod (30 1/4 square yards)! rood (1210 square yards)! acre (4 roods), may be my apology, but it is only a part of my reason, for not reckoning the sun's area in acres, his activity in horse-power per square inch or per square foot, and his radius, and the earth's distance from him in British statute miles, and for using exclusively the one-denominational system introduced by the French ninety years ago, and now in common use in every civilised country of the world, except England and the United States of North America.
      

33. Cassini and the Division in Saturn's Ring
    
    • After the emergence of Saturn from the rays of the Sun as a morning star in the year 1675, the globe of the planet appeared with a dark band, similar to those of Jupiter, extending the length of the ring from East to West, as it is nearly always shown by the 34-foot telescope, and the breadth of the ring was divided by a dark line into two equal parts, of which the interior and nearer one to the globe was very bright, and the exterior part slightly dark.
      
    • In the same year, 1671, the shorter diameter of the ring was still less than the diameter of the globe which extended outside the ring on the North and South sides, and this phase lasted until the immersion of Saturn in the rays of the Sun in the year 1676.
      

34. Edmund Whittaker: 'Physics and Philosophy
    
    • This is illustrated by the predictions as a result of mathematical reasoning of conical refraction by Hamilton and of the bending of light rays in the sun's gravitational field by Einstein.
      
    • Hipparchus described the motion of the sun relative to the earth in two ways: firstly, as a circular motion with the earth not quite at the centre; secondly, as a circular motion with the centre of the circle describing a circle about the earth as centre.
      

35. Plato describes the planets
    
    • One has to understand that he thought the Earth was in the centre, the fixed stars on a sphere surrounding the whole system, and that the sun, moon and planets were on the rims of whorls between the fixed stars and the earth.
      
    • The largest (of fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) coloured by the reflected light of the seventh; the second and fifth (Saturn and Mercury) are in colour like one another, and yellower than the preceding; the third (Venus) has the whitest light; the fourth (Mars) is reddish; the sixth (Jupiter) is in whiteness second.
      

36. Pappus on mechanics
    
    • Sometimes they employ air pressure, as does Hero in his Pneumatica; sometimes ropes and cables to simulate the motions of living things, e.g., Hero in his works on Automata and Balances; and sometimes they use objects floating on water, e.g., Archimedes in his work On Floating Bodies, or water clocks, e.g., Hero in his treatise on that subject, which is evidently connected with the theory of the sun dial.
      

37. Al-Biruni: 'Coordinates of Cities
    
    • Each party observed the meridian altitude of the sun until they found that the change in its meridian altitude had amounted to one degree, apart from the change due to variation in the declination.
      

38. The Samarkand Observatory
    
    • describes and illustrates an ancient concept of a sun-centered solar system.
      

39. Mathematicians and Music 2.2
    
    • It is in the fifth book of this work that one first finds the third fundamental law of modern astronomy, "The squares of the periodic times of the several planets are proportional to the cubes of their mean distances from the sun," demonstration of which furnished Newton with the basis for his theory of gravitation.
      

40. James Jeans addresses the British Association in 1934, Part 2
    
    • If the nature we study consists so largely of our own mental constructs, why do our many minds all construct one and the same nature? Why, in brief, do we all see the same sun, moon and stars? .
      

41. Al-Kashi's letter
    
    • From these very given data, by mental computation, and from horseback, he determined the true longitude of the sun (correct) to degrees and minutes.
      

42. Max Planck: 'The Nature of Light
    
    • These electrons circle about the nucleus in a greater or smaller number and at different distances, in certain definite paths and obey the same laws as those governing the motions of the planets about the sun.
      

43. The Works of Sir John Leslie
    
    • In the next volume he purposes to discourse on Frictional Heat, the Sun as source of Heat, Climate, Humidity, Hygrometry, and hopes "to prepare a solid foundation for erecting a system of meteorology." His death occurred before this volume was completed.
      

44. Euclid on elementary astronomy
    
    • He does not attempt to give any theory to describe the motions of the sun, moon and planets.
      

45. Edward Sang on his tables
    
    • Every page in it cries out aloud in distress, 'Give us decimals.' For the sun's meridian passage, the usual difference columns are suppressed, and those titled 'var.
      

46. W H Young addresses ICM 1928 Part 2
    
    • And although these have put in the shade for the moment the still more striking progress in Astronomy of an earlier age, we are expecting equally momentous consequences to the human race to emerge from the mathematical discussion of the electro-magnetic field of the sun, based on the joint work of astronomer and physicist.
      

47. Charles Bossut on Leibniz and Newton
    
    • In one of his letters to Oldenburg, written even while he was in London, Leibniz says that having discovered a method of summing up certain series by means of their differences, this method was shown to him already published in a book by Mouton, canon of St Paul's at Lyon, 'On the Diameters of the Sun and Moon:' that he then invented another method, which he explains, of forming the differences and thence deducing the sums of the series: that he is capable of summing up a series of fractions of which the numerators are unity and the denominators either the terms of the series of natural numbers, those of the series of triangular numbers, or those of the series of pyramidal numbers, etc.
      

48. Bessel and the Royal Astronomical Society
    
    • this was, of course, because he had measured the distance to the nearest star to the sun, as was later confirmed.
      

49. Hardy in the USA
    
    • But American football knocks other spectacles absolutely flat; the sun shines more or less continuously; and for quietness and the opportunity to be your own master I've never come across anything like it.
      

50. De Coste on Mersenne
    
    • The souls of such people have the same quality as that fountain admired by the great Alexander in Babylon, whose waters immediately became illuminated by the rays of the sun, or as soon as they were shown fire; for these good people are so fine and purified and have a vision so clear and brilliant that they are enflamed by the smallest spark to meditate on the things of Heaven and the love of God.
      

51. EMS obituary
    
    • Amongst other Greenwich programmes in which he took an energetic interest was that on geomagnetic effects produced by the sun and he shared in important discoveries about solar conditions associated with various types of magnetic "storms." His second presidential address gave: him occasion to survey this subject.
      

52. Mathematics at Aberdeen 1
    
    • The list includes globes, sea chart, compasses, lodestone, quadrants, astrolabes, nocturnlabes, planisphere, theodolite, surveying table, Gunter's Cross staff (an ancestor of the modern sextant), graphometer and analemma (an instrument on which a projection of a sphere on the plane of the meridian is drawn, or a graduated scale on a terrestrial globe showing the daily declination of the sun).
      

53. Aristotle on physics and mathematics
    
    • Further, is astronomy different from physics or a department of it? It seems absurd that the physicist should be supposed to know the nature of sun or moon, but not to know any of their essential attributes, particularly as the writers on physics obviously do discuss their shape also and whether the earth and the world are spherical or not.
      

54. James Jeans addresses the British Association in 1934, Part 3
    
    • If the nature we study consists so largely of our own mental constructs, why do our many minds all construct one and the same nature? Why, in brief, do we all see the same sun, moon and stars? .
      

55. J Ruska on Heinrich Suter
    
    • But from time to time he went to Italy, so that he could become acquainted with that country and its people, and to enjoy the sun and wine.
      

56. Coulson: 'Electricity
    
    • The positive charge rests on the heavy part, or nucleus, of each atom, and the negative charge is in the form of electrons that move round the nucleus in much the same way as planets round the sun.
      

57. De Coste on Mersenne 1.html
    

58. Oliver Heaviside and Newton Abbott
    
    • knowledge of the relationship between the sun and the Earth.
      

Quotations

1. Quotations by Kepler
   
   • repudiating the sensible world, which he neither sees himself nor believes from those who have, the Peripatetic [follower of Aristotle] joins combat by childish quibbling in a world on paper, and denies the Sun shines because he himself is blind.
     
   • and thus it comes about gradually by the linking and accumulation of a great many revolutions that a kind of concave sphere is displayed, having the same center as the Sun, just as by a great many circles of silken thread, linked with each other and wound together, the dwelling of a silkworm is made.
     
   • Now, eighteen months after the first light, three months after the true day, but a very few days after the pure Sun of that most wonderful study began to shine, nothing restrains me; it is my pleasure to yield to the inspired frenzy, it is my pleasure to taunt mortal men with the candid acknowledgement that I am stealing the golden vessels of the Egyptians to build a tabernacle to my God from them, far, far away from the boundaries of Egypt.
     

2. Quotations by Galileo
   
   • Take note, theologians, that in your desire to make matters of faith out of propositions relating to the fixity of sun and earth you run the risk of eventually having to condemn as heretics those who would declare the earth to stand still and the sun to change position -- eventually, I say, at such a time as it might be proved that the earth moves and the sun stands still.
     

3. Quotations by Leonardo
   
   • The sun does not move.
     

4. Quotations by Khayyam
   
   • Played in a Box whose Candle is the Sun, .
     

5. Quotations by Ulam
   
   • there's nothing new under the sun - everything can be traced .
     

6. Quotations by Turing
   
   • In the time of Galileo it was argued that the texts, 'And the sun stood still ..
     

7. A quotation by Eudoxus
   
   • Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance.
     

8. Quotations by Copernicus
   
   • Finally we shall place the Sun himself at the center of the Universe.
     

9. Quotations by Brahmagupta
   
   • As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.
     

Chronology

1. Mathematical Chronology
   
   • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets.
     
   • Aristarchus of Samos uses a geometric method to calculate the distance of the Sun and the Moon from Earth.
     
   • He also proposes that the Earth orbits the Sun.
     
   • He uses Ptolemy's epicycle theory of the planets but believes they are controlled by the sun.
     
   • It gives a full account of the Copernican theory, namely that the Sun (not the Earth) is at rest in the centre of the Universe.
     

2. Chronology for 500BC to 1AD
   
   • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets.
     
   • Aristarchus of Samos uses a geometric method to calculate the distance of the Sun and the Moon from Earth.
     
   • He also proposes that the Earth orbits the Sun.
     

3. Chronology for 1300 to 1500
   
   • He uses Ptolemy's epicycle theory of the planets but believes they are controlled by the sun.
     

4. Chronology for 30000BC to 500BC
   
   • The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets.
     

5. Chronology for 1500 to 1600
   
   • It gives a full account of the Copernican theory, namely that the Sun (not the Earth) is at rest in the centre of the Universe.