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A satellite orbits very close to Earth above the equator with an orbital period of 1.5 hours, moving in the same sense as Earth's rotation. If at some instant it is directly above a point P on the equator, after what time interval will it again be directly above P?

1. 1.6 hours
2. 1.5 hours
3. 24 hours
4. 3.0 hours

Correct answer: 1.6 hours

Solution

Both the satellite and the point P rotate in the same direction. The satellite returns over P after the relative angular displacement is 2*pi. The relative period is 1/(1/T_sat - 1/T_earth). Substituting T_sat = 1.5 h and T_earth = 24 h gives about 1.6 h.

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