Transits of Venus explained
THE TRANSITS OF VENUS
by Nigel Foster
I shall start by explaining exactly what a transit of Venus is and why they are so rare. Venus orbits the Sun at a distance of about 67 million miles, and the Earth at about 93 million miles. Because Venus is considerably closer it has to move at a faster speed than the Earth to outrun the Sun’s enormous gravitational field. It orbits the Sun in 225 days, regularly overtaking us on the inside track in our 365 day orbit. That being the case one would expect to see transits of Venus on a very regular basis. However if we look at the Solar System in cross section rather than plan view we can see that the orbit of Venus is tilted at a slight angle to that of the Earth, vastly reducing the number of occasions when the Sun, Earth & Venus are all correctly aligned for us to see a transit.
Diagram 1: Orbits of Venus & Earth
Transits of Venus occur in fact in pairs eight years apart, with an interval of rather more than a century between each pair. During each event, the tiny disk of Venus takes approximately six hours to traverse the Sun. The geometry of planetary orbits is a fascinating subject in its own right, but I hope those of you fascinated by geometry will forgive me if I concentrate for the remainder of this article on the very human story of our attempts to observe this exceedingly rare astronomical event. It is a story of triumphs and tragedies, and of discoveries and disappointments, as well as some unexpected spin-offs in other completely unrelated fields of endeavour.
From the foregoing discussion I hope it will be apparent that in order for people to start observing the transits of Venus, two pre-conditions were necessary. Firstly, since the blinding light of the Sun renders the tiny disk of Venus completely invisible to the naked eye, the invention of suitable instrumentation was necessary. Secondly it was necessary to be able to predict exactly when the transits were going to occur. Both of these conditions were met in the first decade of the seventeenth century. Firstly the telescope was invented and secondly, the brilliant German mathematician, Johannes Kepler produced the first fundamentally correct model for planetary orbits. Kepler used this model to predict a transit of Venus in 1631 but did not live long enough to be able to observe it, dying in 1630. Pierre Gassendi in Paris did attempt to observe this transit but was unsuccessful. The reason for this was that the transit happened during the night for Western Europe.
Another thing that Kepler didn’t realise was that the transits occur in pairs and that there would be another one in 1639. The first person to work this out was a young Englishman, Jeremiah Horrocks. He was the tutor to the children of a wealthy family who lived in the small village of Much Hoole in Lancashire. Horrocks’ diary tells us that the weather was fairly cloudy on the day of the transit and also that he had other important business to attend to. Nevertheless about an hour before sunset he was rewarded with the sight of the transit he had predicted and made three careful drawings of the position of Venus as it crossed the Sun.
Horrocks had written to several other people to inform them of his prediction but as far as we know, his friend William Crabtree was the only other person who managed to see the 1639 transit. Horrocks’ description of the transit as “a most agreeable sight” must have been a considerable understatement compared with what he must have felt at his achievement and also compared with his description of Crabtree’s reaction. Horrocks informs us that “rapt in contemplation, he stood for some time, scarcely trusting his own senses, through excess of joy”. This is said to be why, unlike Horrocks, Crabtree made no record of the event. Possibly though there was a more prosaic reason. Crabtree didn’t see very much of the transit because it was cloudy in Manchester on the day concerned. Some things never change!
Horrocks’ achievement in performing the calculations and observations necessary to make his prediction was colossal, especially when one considers that he was largely self-taught in matters of astronomy, worked alone and was barely out of his teens. He was clearly in possession of a formidable intellect and it’s possible to conjecture that he might even have gone on to rival Sir Isaac Newton. Tragically though, he died only a couple of years after his transit observation.
One of the most significant aspects of Horrocks’ observation was that it was the first time anyone had been able to obtain an accurate measurement of the apparent size of any of the planets. Horrocks used his measurement of the size of Venus and Kepler’s theory to make an estimate of the distance from the Earth to the Sun. At the time, and until quite recently the only way of measuring the distance to the Sun or any other body in the Solar System was by use of triangulation in much the same way that a surveyor uses a theodolite to gauge distances on the Earth’s surface. Unfortunately in Space, the distances are huge and the angles are tiny.
The Ancient Greeks made some valiant attempts to triangulate distances to the Sun and the Moon and in the second century BC Hipparchus was able to correctly measure the distance to the Moon with a precision of about 10%. This was one of the finest achievements of ancient astronomy but the Moon is much closer to us than the Sun and, before the seventeenth century, the distance to the Sun was little more than guesswork. Kepler’s theory gave the ratios of planetary distances very accurately but gave no clue about the actual size of the Solar System. At the time of Horrocks the best guess for the Sun-Earth distance (also known as the “Astronomical Unit”, or “A.U.”), made by Copernicus in the previous century was about six million miles. Horrocks advanced this figure to almost sixty million miles, so with his simple observation from the window of a house in Lancashire he at once increased the size of the Solar System by a factor of ten.
Horrocks’ estimate was still only really an inspired guess and throughout the seventeenth century, the size of the Astronomical Unit remained one of the most important unanswered questions in astronomy. A few decades after Horrocks, in 1672 on attempt was made to measure the A.U. by triangulating the position of Mars (the second closest planet to Earth) from different points on the Earth’s surface. This was a very difficult exercise at the time and gave rise to a wide spread of results between about 40 and 85 million miles. It is interesting to note however that Horrocks’ “guesstimate” lies well within this range.
In the late seventeenth and early eighteenth centuries various astronomers, notably England’s second Astronomer Royal, Edmund Halley (famous for determining the periodicity of the comet which bears his name), pointed out that transits of Venus presented a more promising opportunity for accurate determination of the A.U. by triangulation. By this time it had been established that the next pair of transits would occur in 1761 and 1769 and Halley realised that he would not live long enough to see them himself. Nevertheless in 1716 he implored future generations of astronomers to travel to widely separated places on the Earth’s surface in order to observe them and make the necessary measurements. Halley claimed that the A.U. could be calculated with an accuracy better than 1 part in 500, provided that the points of contact of the disk of Venus with the Sun’s limb, could be timed with an error of less than two seconds. Halley’s method involved recording the time for the whole transit from different points on the globe. In 1724 the French astronomer Joseph-Nicolas Delisle suggested an improvement to this method whereby it was only necessary to record the time of one of the contact points at each location.
The astronomers of the eighteenth century took Halley’s advice and no less than 120 expeditions set off, primarily from Britain and France, to observe the 1761 event. As well as the normal hazards faced by the seafarers of the time, such as scurvy, piracy and shipwreck, the intrepid astronomers of the 1761 expedition had to contend with the Seven Years War between Britain and France. The spirit of international collaboration that existed within the scientific community unfortunately did not extend to the navies of the two nations. Alexandre-Guy Pingre was attacked by British pirates on his way to Rodrigues in the Indian Ocean and by the British navy on the way back and was forced to return to Paris in an ox-cart. La Gentil de La Galaisiere set out for the French colony of Pondicherry in India only to find on his arrival that it had been captured by the British and so was forced to attempt his observations of the transit from the deck of a rolling ship with very unsatisfactory results. Jean Chappe d’Auteroche fared rather better, obtaining good measurements from Siberia.
On the British side, the expedition of Jeremiah Dixon and Charles Mason (famous for the Mason-Dixon Line separating the US & Canada), was attacked by the French navy, resulting in 11 dead and many more injured. Nevertheless they continued to the Cape where they obtained excellent results. Nevil Maskelyne’s expedition to St Helena was however ruined by bad weather.
Maskelyne, the fifth Astronomer Royal is remembered famously as the anti-hero of the saga of the first reliable determinations of longitude at sea by Harrison’s Chronometer, recently made into a TV documentary. .
The biggest problem though was an entirely unexpected one: the infamous “black drop” effect. The image of Venus was seen to smear out as it contacted the Sun’s limb, making it impossible to obtain precise timings of the contact points. This effect was due in large part to the primitive nature of the telescopes that were used.
Diagram 3: The “Black Drop” Effect
Estimates of the A.U. from the 1761 transit ranged between 77 and 99 million miles. The 1761 campaign was certainly a failure judged against Halley’s rather exacting requirement. However this seems a harsh judgment given the considerable difficulties faced by the travelling astronomers and the fact that the results obtained, although imprecise, gave the best estimate to date of the size of the A.U. The 1761 effort was also unprecedented as an example of international collaboration on a scientific project of this scale and has to be regarded as a success in that respect.
The 1761 campaign can also be regarded as a trial run for the 1769 transit expeditions. Astronomers were able to learn from the problems that had been encountered in 1761, particularly the black drop effect, and the 150 or so expeditions that set off to view the 1769 transit took with them generally much better quality telescopes than in 1761. The Seven Years War had also ended by this time which made the high seas a somewhat safer place. Despite this however, there were just as many tales of hardship and misfortune from 1769 as from the earlier expeditions. Chappe d’Auteroche for example, veteran of the 1761 expedition to Siberia, went this time to Baja California, where his team succumbed to a lethal epidemic. The sole survivor reported that Chappe d’Auteroche himself observed to the end despite being in agony and died in the knowledge that his mission had been successful. Pingre who had been hounded by the British navy in 1761 achieved poor results in Haiti. La Gentil who had also been foiled by the British in his attempt to observe from Pondicherry in 1761 finally got there in 1769 having decided to remain in the Indian Ocean for the intervening eight years. As the time of the transit approached however the clouds rolled over Pondicherry, foiling him yet again. His woes didn’t end there. He was shipwrecked no less than twice on the return voyage and got back to France only to find that his family had assumed him dead and were in the process of dividing his estate!
Amongst the British, Dixon was the only 1761 veteran to travel again. He led a successful expedition to Hammerfest in northern Norway. William Wales in Hudson Bay was plagued by horse flies and mosquitoes and did not get a good view of the transit. The most famous of the 1769 and indeed all of the eighteenth century expeditions however was that led by Captain James Cook to Tahiti. Cook carried a top secret envelope on this voyage which he was not allowed to open until he had completed his successful observation of the transit. This envelope contained instructions to investigate rumours of a large new southern continent. Nowadays Cook’s voyage is more famous for his discovery of Australia, but at the time the observation of the transit was his primary objective.
The measurements from the 1769 transit expeditions resulted in a range of values for the A.U. of between 92 and 96 million miles. Again this fell well short of Halley’s hoped for precision of 1 part in 500 and as a result the 1769 campaign still tended to be regarded as a failure. It did however represent a considerable improvement on the 1761 result, and was improved on still further in the early nineteenth century when improved values for the longitudes of some of the places visited were obtained (doubtless with the assistance of Harrison’s chronometer).
By the time of the two nineteenth century transits in 1874 and 1882, other methods of determining the A.U. had emerged. However because of the rarity of these events, campaigns to observe them were mounted on no less a scale than in the previous century. By 1874 photography had been invented and it was hoped that this would be the key to success. Pierre Jules-Janssen invented a “photographic revolver” based on the Colt revolver. It was hoped that this device would enable timings of the contact points to be made with split-second accuracy. In the event the photographs obtained were too blurred to be of use. Jules-Janssen’s device did however prove very useful in the development of cinema.
The 1874 campaign, like its predecessors, came to be regarded as something of a failure and the wisdom of using further public funds to observe the 1882 transit was called into question. Because there would not be another opportunity until the twenty-first century however, the astronomers had their way and in 1891 data from the 1882 transit was reduced independently by William Harkness and Simon Newcomb to finally give a result that met (and indeed exceeded) Halley’s requirement. The two men agreed on the size of the A.U. to within a hundred thousand miles, virtually “spot on” in cosmic terms.
There were no transits of Venus during the twentieth century and by the time of this year’s transit, radar techniques had enabled us to measure distances within the Solar System to within a few metres. As a result the 2004 transit was more notable in terms of its rarity value than its scientific importance. Nevertheless the intrepid astronomers of Knowle attempted to replicate the efforts of eighteenth and nineteenth century astronomers by making timings of the contact points and calculating the size of the A.U. I am pleased to report that we managed to achieve the 1769 standard, although we did not have to send our members half way round the World, risking piracy, shipwreck and scurvy to do so. Nor did we have to tackle the daunting mathematics required to reduce the results. In true twenty-first century style we simply input our timings into a computer programme provided for the purpose on the Internet.
From the UK the whole of the 2004 event took place well above the horizon and we were very fortunate to have good clear weather to see it. However we are poorly placed for the next transit in 2012, for which the best view is going to be from Australia or the Pacific. For those prepared to wait until the twenty-second century, the 2125 event will be better observed from the UK than the 2117 event!
Nigel Foster, October 2004.
APPENDIX: ESTIMATES OF THE ASTRONOMICAL UNIT (millions of miles)