In a previous article we looked at the role that Edmund Halley played in determining that a transit of Venus could be used to determine the distance from the Earth to the Sun. This distance was important for astronomers to know as it would enable them to understand the scale of the universe. Up until that point relative masses and distances only were determined by using Kepler’s and Newton’s laws. The distance scale most commonly used was the distance from the Earth to the Sun, this was measured as 1 Astronomical Unit (AU). By knowing the orbital periods of the other planets, then their orbits and distances could be worked out in terms of AU. The problem was that the AU itself was not known in a more useful measure such as miles or kilometres. This article is not going to look at the maths, we’ll do that at some other time, but more at the concepts and the challenges associated with obtaining the data. We are doing this series of articles because the transit of Venus was the reason that James Cook came to the South Pacific and this year marks the 250th anniversary of that 1769 voyage. Leaving the rights and wrongs of his voyage and subsequent trips to be commented on in other forums, we want to cover the space science aspects of how important that trip was and what it contributed to.
It was Jeremiah Horrocks that first observed a transit of Venus after accurately predicting the 1639 transit. This, and the transit of Mercury observed from St Helena, were the two events that inspired Edmund Halley to realise that the distance between the Earth and the Sun could be calculated if careful measurements of observations were taken from different locations around the world. This lead to a huge campaign to measure the transit in 1761. The problem was that this was a period of significant turmoil with the French and English locked in war. Despite the war, the expeditions went ahead but were ultimately inconclusive and didn’t provide the accuracy that was hoped for. James Short conducted an analysis of the results and published in the Philosophical Transactions of the Royal Society of 1763 that the distance from the Earth to the Sun was “very nearly 94,380,685 English miles”. Following the 1769 observations this was refined further by Thomas Hornsby in the same journal in 1771, that the “mean distance of the Earth from the Sun will be 93,726,900 English miles”. It is now known that this distance is 92,955,807 miles (149,597,870.7 kms) so Hornsby was still a little under 800,000 miles out, but not bad considering they were measuring the Solar System from the surface of the Earth using nothing other than maths and some basic observations.
To measure the distance from the Earth to the Sun using the transit of Venus there needs to be a comparison of observations from different parts of the Earth to obtain the parallax of how Venus appears on the Sun’s surface. Simply put, an observer at a higher latitude than another observer will observe Venus cross at a slightly lower position on the Sun’s disk. The distance between the two different observed paths can be used to work out the parallax between the Sun and the Earth and the distance, relative to a known baseline of the distance between the observers. If only it was that simple! The problem is that even with observers 7000km apart the difference in the paths across the Sun will be significantly less than the diameter of Venus, so extremely hard to measure. Especially without the aid of photographic equipment as in 1769. Halley figured out that the time taken for transits could be a better comparison and that could be used to derive the distance between the two path lines. The reason for this is because the sun is huge and the transit takes a long time and the paths traced by the transit across the Sun’s face observed from different places will have different chord lengths, and hence different amount of times to cross the face. The observed difference in time could be around 5 minutes for observers 7000km apart for example. This time difference was immensely more simple to measure than the observed difference between the paths across the Sun. All astronomers had to agree on, was when to time from. Again, not as simple as it seems because clocks were not all that accurate back in the late 1700s and had to be backed up by meticulous observations.
The other challenge that observers of the transit had that related to the timing was when to start the clock and when to finish. They chose what is known as the second and third contact. This is the point when the disk of Venus is immediately just fully inside the disk of the Sun and the corresponding internal point on the way out, at the other end of the transit. This resulted in another unexpected problem known as the black-drop effect. This is where Venus’ disk seems to draw the darkness from outside of the Sun’s disk into the Sun and makes it quite tricky to determine when to measure from. Cook and Green during the South Pacific observations in Tahiti also noticed this and so did William Wales in Hudson Bay. Getting an accurate time proved to be difficult.
The other challenge in getting an accurate result in time measurement is factoring in the difference in observations from the difference in longitudes. This is because Venus will appear to travel at different speeds across the Sun’s disk depending where it is observed from on the Earth’s surface, with respect to longitude, so the times have to be adjusted to take into account this difference. For example, observer on the side of the Earth approaching Venus (Venus rising in the sky) will see the planet move slower across the Sun’s disk than an observer who is past Venus (Venus past it’s maximum altitude in the sky, which would have been noon on the day of the transit). This problem doesn’t balance out because depending where you are observing from, it could have a huge influence on the measured time of the transit compared to other longitudes.
Longitude was quite a problem in the late 1700s, as determining it accurately was not easy. Nevil Maskelyne, the Astronomer Royal, had been instrumental in getting the Nautical Almanac published, which helped seafarers determine longitude from observations of Jupiter’s moons and the Moon as this was the main way to measure longitude. Carrying accurate clocks that allowed observers to compare local times with Greenwich Mean Time was not possible because clocks could not keep their times very accurately through the long voyages to get to the various sites where the transit was observed from.
Other observations that were required were the angular size of Venus and the Sun and detailed observations of the path that the planet took across the face of the Sun so that the angle between the centre of the Sun and the ingress point could be measured as this would give the position of the path across the disk in relation to the Sun’s diameter. All of these measurements required precise observations and the people doing them had to be skilled and well practised. In the case of William Wales, he and his team arrived in location nearly a year before the transit so had ample time to hone in their skills. Wales took daily measurements of the Sun and other astronomical observations at night so by the time the transit happened he was ready to make the required measurements as accurately as possible. Cook arrived in Tahiti a month earlier and was already an accomplished astronomer with published work on observations of an eclipse. Cook also had Green and Solander taking observations as well as two other seperate sites away from the main camp at Point Venus.
The final error that had to be corrected for was the parallax of the Sun. This was where the Sun would appear in a slightly different place depending on where the observer was standing on Earth. This apparent movement is big enough to have an affect on the final result, so had to be calculated and applied to the distance between the two paths of Venus across the Sun’s face. With all of these corrections applied then a factor that is multiplied by the reference distance would ultimately give the distance between the Earth and the Sun. The reference distance was the distance between the two observers in latitude calculated in a straight line that takes into account the Earth axis tilt. The maths, though not difficult, would have been laborious in the late 1700s without the benefit of a calculator, hence it took some time before the calculations produced a result.