# Measuring the size of the Solar System – Parallax

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.

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.

# Measuring the size of the Solar System – the ‘black drop’ problem

By guest blogger Peter Bond

Despite the best efforts by astronomers who voyaged to far flung reaches of the Earth to watch the transits, the results of the observations was not as conclusive or accurate as had been hoped. The observations were plagued by many technical difficulties, and by the slightly fuzzy outline of Venus, caused by its dense atmosphere. There was also an unforeseen problem with a phenomenon known as the ‘black drop’ effect.

One of the chief problems the observers faced was pinpointing the precise time of ‘second contact’, when the whole of Venus was first visible on the face of the Sun. They noticed that its black disc seemed to remain linked to the edge of the Sun for a short time by a dark ‘neck’, making it appear almost pear-shaped. The same happened in reverse when Venus began to leave the Sun.

Click for an animation of the black drop effect.

This so-called ‘black drop effect’ was one of the main reasons why timing the transits failed to produce consistent accurate results for the Sun-Earth distance. Halley expected second contact could be timed to within about a second. The black drop reduced the accuracy of timing to more like a minute.

The black drop effect is often mistakenly attributed to Venus's atmosphere, but modern research has suggested that it is due to a combination of two key effects. One is the image blurring that takes place when a telescope is used (described technically as ‘the point spread function’). The other is the way that the brightness of the Sun diminishes close to its visible ‘edge’ (known to astronomers as ‘limb darkening’). There may also be a small contribution from observing through Earth’s atmosphere, but observations of the black drop effect during Mercury’s 1999 transit across the Sun using NASA’s TRACE satellite confirmed that neither the planet’s nor Earth’s atmosphere is needed to produce the effect.

Despite the disappointments of the 18th century expeditions, optimistic astronomers tried again during the transits of 9 December 1874, and 6 December 1882. Once again the results were inconclusive, and scientists began to realise that the practical problems with Halley’s method were just too great to overcome. Nevertheless, the value of the Sun-Earth distance was known with much greater accuracy than ever before after the results of the 1882 transit were analysed.

# Measuring the size of the Solar System – transits through the ages

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-17th 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...