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A satellite moves around a planet in an elliptical orbit whose minor and major axes have lengths a and b respectively. If its orbital period is T, then T² is proportional to which of the following?

1. ((a + b)/2)³
2. ((a - b)/2)³
3. a³
4. b³

Correct answer: b³

Solution

By Kepler's third law T² is proportional to the cube of the semi-major axis. With the major axis length equal to b, the semi-major axis is b/2, so T² ~ (b/2)³ ~ b³.

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