Engineering Expert Witness Blog

      We’ve been working on calculating Earth’s distance to the sun and discussing how past scientists, including Johannes Kepler and Edmund Halley, contributed to the discussion.    Today we’ll see how Halley used his theory on the transit of Venus together with Kepler’s Third Law of Planetary Motion and combined them with known mathematical principles to solve the riddle of this enormous distance, known as one astronomical unit, or AU.

      Halley’s solution began with stationing two observers with telescopes aimed at Venus on opposite sides of the Earth.    Their different lines of sight would cause the principle of parallax to come into play, resulting in them seeing Venus from different perspectives.    Their sight would converge at Venus’ center and an angle, α, would form between them.   Halley posited that if this angle could be measured, it would be an important first step in calculating the distance between Earth and the sun.    See Figure 1.

Figure 1

      Due to their differing perspectives, Observer A would see Venus traveling a path lower on the sun’s face, while Observer B would see it following a path higher up.    See Figure 2.

Figure 2

      The net result was that the length, L_A, of Venus’ path as seen by Observer A was significantly shorter than length, L_B, of Venus’ path as seen by Observer B.    Because of this, Observer B would have seen Venus pass in front of the sun before Observer A.    These differing observations meant that even if both observers were to set their telescopic crosshairs on Venus at the exact same moment it became visible to each of them, it would serve no purpose, because they lacked a common point of reference at which to aim in order to take measurements.    This fact made measuring the angle α with a physical device such as a protractor impossible.

      So Halley gave up on the idea of physically measuring α.    Instead, he proposed calculating it based on the time it took for Observers A and B to watch Venus traverse the sun’s face from one side to the other along each of their observational paths.

      Next time we’ll see how Halley put his idea to work to calculate α and used it in conjunction with Kepler’s Third Law to calculate the AU.

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