Kepler determined distances in the solar system from his data. For example, he f
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Question
Kepler determined distances in the solar system from his data. For example, he found the relative distance from the Sun to Venus (as compared to the distance from the Sun to Earth) as follows. Because Venus's orbit is closer to the Sun than is Earth's orbit, Venus is a morning or evening star—its position in the sky is never very far from the Sun. If we suppose the orbit of Venus is a perfect circle, then consider the relative orientation of Venus, Earth, and the Sun at maximum extension, that is, when Venus is farthest from the Sun in the sky.
A. If the maximum elongation angle a between Venus and the Sun is 50°, what is the distance between Venus and the Sun in AU?
B. Use this result to estimate the length of a Venusian "year."
Explanation / Answer
A. venus, earth and sun form a right triangle
with the earth-sun segment as the hypotenuse or length = 1
and the venus-sun segment as the side opposite the angle 50°
so
sin(50°) = opp/hyp
which means the distance of venus to the sun is:
approx. 0.766AU
B. The time required for Venus to complete one orbit about the Sun, its sidereal period, is 224.701 days, whereas the time for Venus to repeat alignments with respect to the Sun and Earth is 584 days.I
In general, Venusian transits are seen in pairs. Each of the transits in a pair are eight years apart, and the pair-cycle repeats on an alternating cycle of 121.5 and 105.5 years.
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