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Question

A planet has an orbital period of 4 years around the Sun. If Earth’s orbital radius is 1.5×1011m, what is the planet’s semi-major axis? (1year\=3.156×107s)

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Explanation

Kepler’s third law: T2∝a3, Tp2TE2 = ap3aE3. TE = 1year, Tp = 4years, aE = 1.5×1011m. 4212 = ap3(1.5×1011)3. 16 = ap33.375×1033. ap3 = 16×3.375×1033 = 5.4×1034. ap = (5.4×1034)1/3≈3.78×1011m.