By guest blogger Peter Bond

Edmond Halley’s method, which involved observations of a transit made from widely spaced places, was based on the principle of parallax. This uses the fact that objects appear to shift position against a fixed background if they are observed from two different places. The further the object, the smaller the parallax shift.

This principle can be shown by holding one finger in front of your face. Look at it with the left eye, then with the right eye. You will notice that the finger seems to shift position, even though it has not been physically moved.

If you move the finger further from your face and carry out the same experiment, you will notice that the amount of parallax shift is smaller. If the distance between your eyes is known, and the angle from each eye to the finger is measured, it is possible to use simple trigonometry to calculate the distance of the finger.

For the transit of Venus, observers on the Earth are separated by thousands of kilometres, so they will see the disc of Venus at slightly different locations on the Sun’s disc. By making observations from two widely spaced points on the Earth’s surface, and timing the start and end of the transit accurately at each place, you can work out the solar parallax, the apparent difference in the position of the Sun from those two locations.

By measuring the angular shift between the apparent locations of Venus across the Sun, and taking into account the baseline distance between the two observing sites, you can calculate the distance to Venus by using triangulation.

In practice, however, this is an extremely difficult measurement to make because the disc of Venus is so small (1/60 of a degree) and the parallax angles are very difficult to measure directly (1/120 of a degree). This is why astronomers use each entire path of Venus (the ‘chord’) across the Sun’s disc as a better way of determining the parallax angle.

An explanation of the calculation method used by Halley can be found here.

For your own transit of Venus parallax calculator, click here.

Today, distances in the Solar System are calculated with great precision through very different means, such as ground-based radar and time delays in radio signals from spacecraft.

By guest blogger Peter Bond

The first person to predict a transit of Venus was the German mathematician and astronomer, Johannes Kepler, who calculated that one would take place on 6 December 1631. Unfortunately, the transit was not visible from Europe and there is no record of anyone seeing it.

Jeremiah Horrocks, a young English astronomer, studied Kepler’s planetary tables and discovered, only a month in advance, that a previously unrecognised transit of Venus would occur on 24 November 1639. (Note: two calendars were used at that time. According to the Gregorian calendar, which added 10 days to the older Julian calendar, the date of the 1639 transit took place on 4 December).

Horrocks observed part of the transit from his home at Much Hoole, near Preston. His friend, William Crabtree, also saw it from Manchester, having been alerted by Horrocks. As far as is known, they were the only people to witness the event.

By the mid-17^th century, the relative distances of the planets from the Sun were well known. According to Kepler’s third law of planetary motion, if Earth was at one astronomical unit (1 AU), then Venus orbited the Sun at 0.72 AU, Mars at 1.52 AU, and so on.

However, the actual distance of the Sun and planets from Earth was not known with any degree of accuracy. The best estimate of the time was that the Sun-Earth distance was 137.7 million km. (The actual figure is about 150 million km.)

Edmond Halley (of comet fame) suggested that observations of transits of Venus could, in principle, be used to find out how far the Sun is from Earth.

He suggested that observers in widely separated locations would carefully measure the time that either side of Venus’s disc first ‘touched’ one edge of the Sun, and then exited on the opposite limb of the Sun. This sequence comprised four separate events, called contacts. Each of these had to be timed with split-second accuracy at the far-flung observing sites.

Once the precise contact times were determined, a complex mathematical calculation was performed to determine the observed path of Venus across the Sun from each location. The angular difference between these paths resulted from a parallax shift. Corrections had to be made for the slight differences in contact times caused by east-west differences in longitude.

Halley died in 1742, but hundreds of scientists travelled across the world to try out his method during the transits of 1761 and 1769. Captain James Cook’s expedition to Tahiti in 1769 is one of the most famous expeditions, part of a voyage in which he discovered the east coast of Australia.

One of the unluckiest expeditions was led by Guillaume le Gentil, who set out for Pondicherry, a French colony in India. As his ship was nearing India, he learned that the British had occupied Pondicherry, so he returned to Mauritius. Unable to make proper observations of the 1761 transit, he decided to stay on the island until the next transit, eight years later.

Unfortunately, when the long-awaited day arrived, the Sun was hidden behind a blanket of cloud. When he finally arrived back in Paris in October 1771, he had been declared legally dead, his wife had remarried and all of his possessions had been divided up among his relatives!

Continue reading in part 2: the 'black drop' problem...