Please explain how to find the answer. The correct answer is circled 17. A geosy

Question

Please explain how to find the answer. The correct answer is circled 17. A geosynchronous satellite moves directly above the equator in a circular orbit of radius 4.22 × 107 m, which is about 6.6 Earth radii. It takes such a satellite 24 hours to orbit the Earth, and thus it remains directly above a fixed point on Earth, which is useful for communication since a receiving antenna on Earth can point to a fixed direction in the sky. How long does it take a different satellite, in a circular orbit of radius one-quarter that of the communications satellite, to orbit the Earth? (a) 24 (b) 8 (c) 6

Explanation / Answer

using kepler's third law

(T1/T2)2 = (r1/r2)3

(24/T2) = (r1/(r1/4))3

T2 = 3

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