I [EFR] am sitting at my desk in St Andrews beginning to write this article just after 10 am on Tuesday 8 June 2004. 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. Sadly I am unable to view it since the sky is covered with heavy cloud. Previous such transits have been significant in determining the distance between the Earth and the Sun. Halley, in 1679, pointed out that viewing such a transit from two points on the Earth a known distance apart could be used to determine the size of the solar system. 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. We shall return to this event later in the article, but we should begin with the earliest attempts to measure the size of the universe.
Perhaps the first thing to mention is that the concept of the "universe" has changed over time. In the earliest times the universe was considered to consist of the Earth with the Moon, Sun, and planets revolving round it. The outer limit of this universe was the sphere of the fixed stars. 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. Although no means to estimate distances to these bodies was available, it was taken as "obvious" that the objects closer to the Earth would return to the same position relative to the fixed stars more quickly than the more distant objects. Knowing that the Moon took 27 days, Mercury 88 days, Venus 225 days, Mars 2 years, Jupiter 12 years, and Saturn 29 years, this was taken as a measure of their distances from Earth.
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. See our biography of Aristarchus for details of his method. The way he determined the distances was theoretically correct, although he had problems measuring of small angles accurate and also with knowing the moment when the Moon was exactly half illuminated. These difficulties led to considerable errors. He estimated the diameter of the Moon by observing the shape of the shadow of the Earth on it during an eclipse.
Hipparchus in the 2nd century BC used the same methods as Aristarchus but with improved accuracy. 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. Ptolemy, in the 2nd century AD, calculated the distance to the Moon using a parallax method. Observing the position of the Moon against the fixed stars from two points on the Earth a known distance apart at the same time led him to obtain the same result as Hipparchus, namely that he distance from the Earth to the Moon was 59 times the radius of the Earth. Using the same method as Hipparchus to determine the distance to the Sun led Ptolemy to the same serious underestimate in its distance. No further progress occurred until Copernicus in the 16th century.
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. In February 1632 Galileo published Dialogue Concerning the Two Chief Systems of the World - Ptolemaic and Copernican. It takes the form of a dialogue between Salviati, who argues for the Copernican system, and Simplicio who is an Aristotelian philosopher. 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. For this not to be observed meant that the stars must be very distant indeed. But most claimed that the stars were not points of light but actually small disks, so must be extremely large. Salviati counters these arguments by claiming (correctly) that the stars are only points of light and the appearance of a disk is an illusion. If Galileo was correct, however, the argument did show that the universe was huge and the distances to the stars was immense.
Kepler's Third Law, published in 1619, made the relative distances within the solar system known, but until one distance was known accurately the size was still unknown. 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. This meant that Mars should exhibit a parallax which was well within the accuracy of his observations. However, he did not observe any parallax so deduced that the accepted distance to the Sun was an underestimate. Having no data on which to base a more accurate estimate he resorted to his ideas of harmony. However, all that was now needed, as Kepler had pointed out, was an accurate measurement of the distance to Mars and the scale was fixed.
In 1671 the French planned an expedition, one aim of which was to find an accurate distance to Mars. The expedition was to go to Cayenne and observations of Mars made from there and from Paris would provide an accurate value for its distance. The time was chosen to coincide with the closest approach of Mars to the Earth to maximise the accuracy of the observations. 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. One could argue that this is still relatively far from the true value of 93 million miles, but it was a vast improvement over Ptolemy's value which was of the order of 4 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. Sirius had even moved from the position given by Tycho Brache. Certainly it was not due to the ecliptic moving as Halley determined from the positions of other stars. Of course Halley had no means of knowing whether this was due to observational errors by Hipparchus, but he was confident enough in the ancient data to state clearly that he believed that it was due to these stars moving their actual positions, called the proper motion of a star. Many attempts to measure the parallax of a star were made, but none were successful. Bradley, in 1728, did discover the aberration of light while trying to determine a stellar parallax.
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. There was considerable interest in using the transits of June 1761 and June 1769 for this purpose and many astronomers set out to observe them from a variety of places such as St Helena, the Cape of Good Hope, and India. 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.
William Herschel believed that the brightness of a star could be taken as a measure of its distance. He studied nebulas, some of which had been catalogued by Charles Messier, which could not be resolved into stars. At first he thought these were new "island universes" - star systems like the Milky Way but far more distant. However when he studied large numbers of these he discovered that their distribution was connected to the plane of the Milky Way, so this seemed to prove that these were not "island universes" but rather star clusters in the Milky Way which could not be resolved into stars. Further evidence for this latter theory occurred when more powerful telescopes were able to resolve some into stars. However, Herschel seems to have continued to believe that some of the nebulas that he was observing were indeed island universes. He was right!
The first person to measure a stellar parallax was Bessel. He determined the distance to 61 Cygni, announcing his result in 1838. Clearly to succeed it was important to choose a star which was close to the Sun. His method for selecting such a star was based on selecting one which had the greatest proper motion of all the stars he had studied. He correctly deduced that this would mean that the star was close. Since 61 Cygni is a relatively dim star it was a bold choice based on his correct understanding of the cause of the proper motions. Bessel, using a Fraunhofer heliometer to make the measurements, announced his value of 0.314" which, given the diameter of the Earth's orbit, gave a distance of about 10 light years. The correct value of the parallax of 61 Cygni is 0.292". Although there had been many years of failed attempts to measure a stellar parallax, once Bessel made his announcement distances to several others were measured. Thomas Henderson measured the parallax of Alpha Centuari in 1839, showing it had a parallax around three times greater that 61 Cygni, so was much closer. Henderson had indeed measured the distance to the nearest star. Over the next years the distances to many other stars were found using the parallax method but it was a method which would never be able to find distances to any but the closest stars.
A major advance in calculating distances came about in 1908 when Henrietta Swan Leavitt observed variable stars in the Large and Small Magellanic Clouds. These are two small companion galaxies of the Milky Way and since the distance to these small galaxies is much greater than their diameters, all the stars in them are approximately the same distance away. Leavitt observed that there was a relationship between the period of variability of the stars she was studying, namely stars called Cepheids, and their absolute brightness. By 1912 this had been refined so that it was a reliable measure of the distance of a Cepheid variable star, for one only needed to determine the period, which is the time between two occurrences of maximum brightness, to obtain a value for the absolute brightness of the star. Once the absolute brightness of a star is known, then it is easy to determine its distance by measuring its apparent brightness.
Harlow Shapley, working at the Mount Wilson Observatory in the United States, began to try to work out the shape and size of the Milky Way using Cepheids as a measure of distance. By 1919 he had worked out that it was a disk which had a huge bulge at the centre. The Sun, he estimated, was situated at about 2/3 of the distance from the centre to the outer edge of the galaxy. In this he was absolutely correct, but in his estimate of the size of the Milky Way galaxy he overestimated by a factor of about 3 (it is actually about 100,000 light years in diameter). This came about since distant stars are faint not only because of their distance, but also because their light has had to pass through dust and gas on its journey. Failing to take this into account meant that Shapley thought that distant stars were further away than they actually were. However, at this stage Shapley and other astronomers thought that at last we had an accurate estimate for the size of the universe which, despite William Herschel's belief in island universes beyond the Milky Way, was thought to consist of only the Milky Way galaxy and some small companion galaxies such as the Large and Small Magellanic Clouds.
In 1920 there was a debate between Shapley and Heber Curtis on the distance scale of the universe and on the spiral nebulas. Shapley was totally committed to the view that the Milky Way was essentially the whole universe and that the spiral nebulas were local to that system. Vesto Slipher, who had worked at the Lowell Observatory with the 24-inch telescope there since 1901, had been asked to investigate the spiral nebulas by Percival Lowell. By 1912 Slipher had made a major breakthrough when he had obtained a spectrograph of the Andromeda Nebula and found its light shifted towards the blue. This, he realised, was as a result of the Doppler effect, and meant that the Andromeda Nebula was approaching at 300 km per second. This was at the time the greatest velocity measured for an astronomical object. Slipher continued his work and by 1914 had obtained spectrographs of 15 spiral nebulas. Of these 13 exhibited redshifts, so were receding, and he discovered that two were receding at over 1000 km per second. In a paper of 1917 he wrote:
It has for a long time been suggested that the spiral nebulae are stellar systems seen at great distances. This is the so-called "island universe" theory, which regards our stellar system and the Milky Way as a great spiral nebula which we see from within.Another person who believed that they had discovered another galaxy comparable to the Milky Way was Milton Humason. He was employed as a janitor at the Mount Wilson observatory but had been taught to operate the telescopes. In the winter of 1920-21 Shapley had asked him to take photographs of the Andromeda Nebula with the 100-inch telescope at Mount Wilson which had been in operation for about 2 years. Humason thought that the photographs had just resolved the Andromeda Nebula into individual stars but when he pointed this out to Shapley he was told not to be silly! Shapley had staked his reputation on the belief that the Milky Way comprised the whole universe and he wasn't going to change his mind because of evidence coming from a former janitor who had just been promoted onto the scientific staff.
The first observations of the Andromeda Nebula which led to its distance being calculated were made in 1923 by Edwin Hubble, also using the 100-inch telescope at Mount Wilson. He hoped to show that it was a star system outside the Milky Way and took photographs to see if he might be lucky and spot a nova, a star which dramatically brightens then slowly fades back to its original brightness. In October 1923 he did identify three objects which he thought were novas, but he checked older photographs taken by Humason and realised that one of these wasn't a nova but rather it was a Cepheid variable star. He was now in a position to actively search for further Cepheid variables in the Andromeda Nebula and found several others, and identified Cepheid variables in a number of other spiral nebulas too. He reported his findings to the January meeting of the American Astronomical Society. He estimated that the Andromeda Nebula was one million light years away (about 1019 km). Actually it is about twice that distance.
Now that he knew that the spiral nebulas were external galaxies, Hubble was able to see from Slipher's results on the redshifts of the spiral nebulas that most were receding and, it looked as though those further away were receding more rapidly. Hubble then asked Humason to use the 100-inch at Mount Wilson to find more spectrographs of spiral galaxies than had been within range of Slipher with his 24-inch telescope. Hubble himself tried to use a variety of techniques to estimate the distances of these galaxies. In 1919 Hubble announced that there was a linear relation between the distance to a spiral galaxy and its speed of recession. In a paper written jointly by Hubble and Humason in 1931 they gave data for more spiral galaxies and estimated the constant in the linear relation to be 558. Now to measure distance to a distant galaxy one only had to find its redshift and use Hubble's Law to find its distance.
Eddington soon pointed out what he considered a flaw in Hubble's theory. We now knew the distances to galaxies, could measure their brightness, so could find their size. It turned out that the two largest galaxies in the whole universe seemed to be the Milky Way and the Andromeda galaxy. Eddington wrote in 1933:-
Frankly I do not believe it; it would be too much of a coincidence. I think that ... ultimately we shall find that there are many galaxies of a size equal to and surpassing our own.One could of course play the game the other way round and ask what value of Hubble's constant had to be so that distant galaxies were comparable in size to the Milky Way. The answer came out to somewhere between 55 and 60 so it this argument was right then Hubble's measurements gave a constant 10 times too large. There was a second problem. If one asked what had happened in the past then at one time all the galaxies must have been very close together. This fitted with the big bang theory of the creation of the universe but taking Hubble's constant as 558 gave an age for the universe which was less than the ages of the oldest rocks on Earth. How could this be?
Walter Baade made observations with the 100-inch telescope in 1944 which led to the discovery that there were two type of stars, Population I and Population II stars. Moreover there were two different types of Cepheid variables, one for each Population. In 1948 the 200-inch telescope at Mount Palomar became operational and more data could be obtained. By 1952 Baade could announce that the distance scale was wrong by a factor of 2, the Andromeda galaxy was twice as far away as Hubble had estimated, and the Hubble constant was about 250. He had measured the distance to the Andromeda galaxy pretty accurately but his value for the Hubble constant still left it open to Eddington's objection.
It was Allan Sandage, who was just completing his doctorate in 1952, who carried on refining the distance scale using the 200-inch telescope. He found many errors in the earlier work which had led to incorrect results. In 1956, in a joint paper with Humason and Nick Mayall, he gave 180 as his estimate of the Hubble constant. This meant that the universe was, by Sandage's calculations, three times bigger than Hubble had believed in the sense that distances to distant galaxies were three times their previous value. By the early 1960s Sandage was claiming that his best estimate for the Hubble constant was 75. Most didn't accept this value at the time but data from the Hubble space telescope in the 1990s has confirmed that the Hubble constant is between 65 and 77. Distances are nearly ten times greater than Hubble had calculated.
Article by: J J O'Connor and E F Robertson
MacTutor History of Mathematics