Parallax And Distance Of The

After Halley's death, others took up the cudgels in persuading the British government that the 1761 and 1769 transits of Venus represented an opportunity that should be seized, confident that the problems of maritime navigation would be solved once the distance to the Sun was known with sufficient accuracy.

This distance was largely a matter of conjecture. Halley him self had decreased his estimate for the astronomical unit by a factor of four, but even his final value was about 30 percent too high. On the Continent, astronomers had tried using observations of Mars to measure this parameter, but their results did not agree.

The basis of the method used was parallax. This is easy to demonstrate. Hold your arm out straight, with one finger pointing upwards and some far-flung background beyond it. Repetitively looking at the background with one eye shut and then the other, your finger seems to jump left and right. If you measure the distance it appears to move, and also the separation of your eyes, then you could determine the length between your head and your finger. A tape measure may be a simpler way, but one cannot stretch a tape measure to Mars. In the astronomical context Mars is equivalent to the finger, and the far panoply of stars is the unmoving background. So what is the analogue of the separation between your eyes, providing the parallax effect? In 1751 French astronomers observed the apparent position of Mars against the stars both from Paris and the Cape of Good Hope (South Africa), providing a baseline of over six thousand miles. From their derived distance to Mars they calculated the astronomical unit, but their value was too high.

Remember these were the days before photography. Unlike in Eddington's 1919 eclipse expedition, it was not possible to photograph Mars surrounded by a star field at a particular time, bringing the plates home for close comparison. A more accurate visual method was needed, and a transit of Venus afforded just that. The basis of the technique was as follows.

Just as your finger moves as you blink eyes, if observers are well separated they will see Venus take different paths or chords across the Sun during a transit. That's parallax, and the idea in this context is represented in Figure 13-2. If the distance between those chords is determined, then it is feasible to compute the distance to Venus, and to the Sun. The trick is in measuring the locations of the chords with sufficient precision. This could not be done directly because of the uncertainty of the azimuthal positions on the Sun's face of the contact points, the finite size of the disk of Venus, and so on. But there was a refinement, as follows, making the path determination possible.

The rate at which Venus appears to move across the sky during a transit may be calculated quite accurately on a theoretical basis. If the transit is timed, then the angle Venus moved through during that time interval may be calculated, and from that the chord taken across the solar disk determined with some precision. It was anticipated that, if the contact junctures were timed to within a few seconds, then with a transit lasting for five or six hours the chord would be extremely well defined. With two observers separated by some known distance (that is, if their latitudes and longitudes were known), it would be feasible to arrive at the solar distance with an accuracy far superior to all previous measures.

The simple idea that Cook and his party were sent to Tahiti to measure the distance to the Sun is a little misleading, however. From the above description, it is clear that two observation points are required, separated by as far as possible. Cook's expedition provided just one of them, so it is incorrect to think that the Tahiti measures could be used on a stand-alone basis. We will come back to this later.

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