2. Measuring the AU (6 pts). Determining the
distance from the Earth to the Sun was one of the biggest
historical challenges in astronomy. Even Copernicus and Kepler did
not know the actual value of this distance. (a) (b) Explain why
information that was available to Copernicus (such as the angular
size of the Sun and the relative sizes of the planetary orbits) was
insufficient to determine the Earth—Sun distance. The approach
used by the British navy in 1769 was to observe a transit of Venus
(when Venus crosses in front of the Sun’s disk) from two widely
separated locations at the same time. The position of Venus
relative to the Sun, and thus the timing of the transit, would
differ slightly due to parallax. Suppose you were to take
simultaneous pictures of such a transit from two locations on
opposite sides of the Earth (so one observer is experiencing
sunrise and the other sunset). What is the expected angular shift
in the position of Venus that would be measured, relative to the
center of the Sun? (Hint: This is the difference between the angle
made by the red lines in the sketch below and the angle made by the
black lines.) What fraction of the Sun’s angular diameter (1900
arcseconds) is this?
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