The Transit of Venus

On the 6th June 2012, at around 4am, I stood on top of a blustery Dorset hillside and waited for the sun to rise. You may wonder what would compel someone to get up at such a ridiculous hour; in this case, it was the chance to see something that would not be seen again until the year 2117 – the transit of Venus. I was up there with a pair of binoculars and a camera tripod that (as you can see from the pictures) were held together by a mix of random meccano pieces, rubber bands and a fair amount of stubbornness on my part. The aim was to project an image of the sun through the binoculars onto a piece of white card. When the sun finally rose, I adjusted my slightly dodgy equipment and hoped for a break in the omnipresent cloud cover of the british ‘summer’. Luckily for me, there was such a fortuitous break and there it was – the bright circle of the sun with a tiny black dot upon its surface. I was ecstatic – that tiny dot represented the planet Venus passing between the Earth and the Sun.

Transits
Observing the 2012 Transit of Venus

Again, you may wonder what all the fuss is about – what was it about this tiny speck that dragged millions of people out of their homes (or onto the web for livestreams) to observe it? Apart from the event’s extreme rarity, it also has a fascinating part to play in the history of science. Specifically, it had a role in the determination of the distance between the Earth and the Sun.

The size of the solar system

On looking up at the stars and planets in the sky, people have always wondered how far away these objects really are. But how do we put a value on the size of the solar system?

Johannes Kepler (1571-1630) was a German astronomer who studied the motion of the planets. His work is immortilised in Kepler’s Laws of Planetary Motion. For our purposes, the third law (that the squares of the times of revolution of any two planets about the sun are proportional to the cubes of their mean distances form the Sun) is of great interest.

As the time for a planet to orbit the sun can be related to its distance from it, this simple relationship allows us to calculate the relative distances of all the planets. If we define the mean distance of the Earth from the Sun as one Astronomical Unit (AU), then the distances to all other planets can be expressed in terms of AU.

This kind of work made it possible to know the relative distances to the various planets in the solar system, but not the absolute values. To achieve this, a method was required to measure the distance between the Earth and the Sun.

Transits and the distance to the Sun

Venus
Image of the 2012 transit of Venus (‘Transit of Venus Across the Sun 2012‘ by nate2b is licensed under CC BY-NC-ND 2.0)

One method of determining this distance relied on observation of events called ‘transits’.

A ‘transit’ is a time when a planet passes between the Earth and the Sun, such that we can observe it as a dark spot that moves across the Sun’s surface.

Transits therefore occur for the two planets that are closer to the Sun than the Earth – Mercury and Venus. Transits of Venus are far rarer than transits of Mercury, occurring in pairs (separated by about 8 years) every 100 years or so. Their rarity is a result of the orbit of Venus being at an angle to that of the Earth’s about the Sun. Therefore, transits can only occur when Venus is near one of its nodes (the points where its orbit crosses the plane of that of the Earth) at the right time to make it visible from the Earth against the Sun. This occurs very rarely indeed!

Oribts
Diagram showing the required alignment for a transit of Venus (none of this is to scale/the angles are exaggerated!) The orbit of Venus (green) is tilted at an angle to that of the Earth (blue). The line of nodes shows the line of intersection between these two orbital planes. A transit can only occur when both planets are near this line of nodes.

The first transit of Venus to be observed was in 1639 by Jeremiah Horrocks (1619-1641). He recognised that Kepler (in his prediction of various transits) had missed the possibility of another transit in 1639, and so made preparations to observe it with his friend William Crabtree. By projecting an image of the sun through a telescope onto a piece of paper, they become the first people in history to observe a transit of Venus.

As Horrocks described: ‘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 entered upon the Sun’s disc on the left, so that the limbs of the Sun and Venus precisely coincided, forming an angle of contact. Not doubting that this was really the shadow of the planet, I immediately applied myself sedulously to observe it’

M0004627 J. Horrock's first observing: transit of Venus
A 19th century painting of Horrocks observing the transit of Venus (‘M0004627’ from Wellcome Images is licensed under CC BY 4.0)

The Solar Parallax

Although the idea of using transits to determine the distance between the Earth and the Sun had arisen previously, Edmond Halley was key in developing and publicising this concept. Edmond Halley (1656-1742) was an English astronomer who, in 1676, undertook an expedition to the island of St. Helena. Among many other observations, he observed a transit of Mercury during his stay. In regards to this, he remarked, ‘On observing this I immediately concluded, that the Sun’s parallax might be… determined by such observations…’.

The ‘solar parallax’ (as shown in the diagram below) is the angle between the line of sight to the Sun from a position on the Earth’s surface, compared to its centre. Basically, parallax is the difference in the apparent position of an object when viewed from two different positions. E.g. if you hold your finger in front of your face and view it with just your left eye and then just your right, you will see it seems to shift from side to side. This change in apparent position is due to the different lines of sight of your left and right eyes.

In the same way, observing the sun from different positions on the Earth will give slightly different apparent positions for the Sun. The difference between these lines of sight from the surface of the Earth and its centre define the solar parallax.

Parallax
Diagram showing the definition of the solar parallax (not to scale!)

If this angle is known (and also the radius of the Earth) then by simple trigonometry the distance between the Earth and the Sun can be calculated. The difficulty comes in measuring the value of the solar parallax – this extremely small angle is very difficult to measure!

Observation of the transit of Venus can provide an indirect way of determining the solar parallax and therefore the distance between the Earth and the Sun.

This again relies on the idea of parallax – if a transit is observed from various different locations on the Earth then, because of their slightly different lines of sight, they will observe slightly different paths of the planet across the Sun. The timings of the start and end of the transit will also be slightly different.

Paths
Diagram illustrating the idea that observing from different points on the Earth (e.g. point A vs point B) results in observation of differing paths of Venus across the Sun. (not to scale!)

Through these differences in the timings of the transit seen from many sites, the differences between the parallaxes of the planet and the Sun can be obtained. Then, using Kepler’s third law, the parallax of the Sun can be calculated.

Although Halley hoped that observations of the transit of Mercury could be used to this end, its parallax was too small to be measured accurately. Venus, as it is closer to the Earth, shows a greater effect of parallax on the timings of its transit. This can again be understood by comparing, for example, placing your finger very close to your face and closing one eye then the other, compared to holding it further away. The apparent shift is much greater when it is held close to your face. In the same way, Venus being closer to the Earth gives a greater parallax and therefore greater differences in timing that make it easier to measure accurately.

In 1691, Halley wrote a detailed account of how the transit of Venus could be used to assess the solar parallax. Knowing that he would not live long enough to observe the transit himself he stated, ‘I recommend it, therefore, again and again, to those curious Astronomers, who (when I am dead) will have an opportunity of observing these things, that they would remember this my admonition, and diligently apply themselves with all their might to the making of this observation’.

1761 and 1769 transits

After Halley’s work, there were great preparations to send astronomers to various locations across the globe to observe the next transits – those of 1761 and 1769.

For the 1761 transit, it is estimated that more than 120 astronomers from at least eight different nations observed the transit of Venus from various locations about the globe. These numbers were even higher for the that of 1769. This sort of wide-scale international collaboration was unprecedented for the time. Also, considering the difficulties of travelling by sea, the journeys undertaken by these astronomers to reach their observing sites are remarkable.

As an example, take the expedition of Mason and Dixon to Bencoolen (Sumatra) for the 1761 transit. During this time the Seven Years’ War was ongoing and, after setting out from Portsmouth, their ship was promptly attacked by a French frigate. After extensive damage they were forced to return to England for repairs. They wrote to the Royal Society to state that they would no longer go to Sumatra (understandably, given their rather traumatic experience). Yet there was no sympathy and they were sent out again. As you may expect, they never made it to Bencoolen – instead they stopped at the Dutch colony of Cape Town where they successfully viewed the second half of the transit (after poor weather obscuring the first portion!).

Apart from the difficulties of the international travel required for this endeavour, observations of the transit also suffered timing inaccuracies. It is vital to be able to very accurately measure the time of the start and the end of the transit (i.e. the time at which Venus touches the edge of the Sun’s disc)

Black drop
Sketches of the appearance of Venus in the 1769 transit, drawn by Captain James Cook (top) and Charles Green (bottom). Note their observation of the Black Drop effect as an extension connecting the black circle of Venus to the outer edge of the Sun’s disc. They also illustrate the ‘luminous ring’ that some saw around Venus. (via Wikimedia Commons)

This was made difficult by a phenomenon known as the ‘black drop’ effect. When Venus approached the edge of the Sun’s disc, many saw a teardrop like extension from the planet to the Sun’s edge. This has been attributed to many factors including deficiencies in the instruments, atmospheric disturbance etc. The main point though is that this ‘black drop’ meant that determining the precise times of contact were made extremely difficult, causing a much greater inaccuracy in timing than anticipated.

Also, some observed a sort of ‘luminous ring’ around Venus which also complicated this measurement. This is actually quite fascinating as it was evidence for the presence of an atmosphere on Venus.

The problems brought about mainly by the black drop effect resulted in a range of values for the solar parallax. After observations of the 1769 transit, results ranged from around 8.43 seconds to 8.80 seconds, giving a distance to the sun of 90-94 million miles.

Although the results from the transit were not as accurate as Halley had hoped back in 1691, they still represented a significant advance in how accurately the value of the distance between the Earth and the Sun was known.

Beyond Venus: the AU

Transits since this time have continued to be observed avidly, but it was soon clear that the inaccuracies faced in timing the transit would never allow the desired level of accuracy. Increasingly, scientists looked to other methods to narrow down the Earth-Sun distance.

Mosaic of Eros' Northern Hemisphere
The asteroid Eros (‘Mosaic of Eros Northern Hemisphere‘ by NASA/JPL/JHUAPL)

For example, between 1930-31 an attempt was made relying on the asteroid Eros. The orbit of Eros brings it much closer than either Mars or Venus to the Earth at certain times – resulting in a far larger parallax effect. In a similar vein to the idea for using the transits of Venus, measurement of the movement of Eros as it passes close to the Earth from various points on the Earth’s surface can allow its parallax to be determined. This can then be used to calculate the solar parallax to an unprecedented degree of accuracy.

Since then, this accuracy has been improved upon further with the development of radar. As technology improved, it became possible to bounce radio waves off of bodies such as Venus and use the time taken to observe the return signal to calculate their distances.


Observations of the transit of Venus, while they did not achieve the level of accuracy hoped for by Halley and others, still represent a fascinating moment in the history of science. For one, they did achieve the most accurate value for the distance between the Earth and the Sun (and therefore the key to the size of the solar system) for that time period. This has since been greatly improved upon, but these expeditions were remarkable for the level of international cooperation they required and the great lengths that were gone to by the people involved. It is a story that emphasises the fact that science thrives when scientists can collaborate across borders as a truly international community.

The transits of 2004 and 2012 were observed by millions of people across the globe. It’s rather heartwarming to consider that for all the time that has passed since that first observation in 1639, people still experience that same sense of awe on watching the tiny dot of Venus trace its path over the Sun. I have no doubt that the people of 2117 will also look to the skies.

References / suggestions for further reading

The Transit of Venus: The Quest to Find the True Distance of the Sun by David Sellers – great popular science book on the transit of Venus.

Exploratorium – http://www.exploratorium.edu/venus/ -website with videos of the transit as well as some information on its importance.

Sky & Telescope – http://www.skyandtelescope.com/astronomy-news/observing-news/transits-of-venus-in-history-1631-1716/ – a nice 3 part article on some of the history of the transit of Venus.

Chapman, A. Horrocks, Crabtree and the 1639 transit of Venus. Astron. Geophys. 45, 5.26-5.31 (2004). DOI: https://doi.org/10.1046/j.1468-4004.2003.45526.x – open access article on Horrocks and Crabtree

Encyclopaedia Britannica – https://www.britannica.com/biography/Johannes-Kepler – encyclopaedia entry on Johannes Kepler

Encyclopaedia Britannica – https://www.britannica.com/biography/Edmond-Halley – encyclopaedia entry on Edmond Halley

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s