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Kepler’s Third Law indicates that the Period (P) of an orbit is related to the semi-major...

Kepler’s Third Law indicates that the Period (P) of an orbit is related to the semi-major axis (a) of the orbit with: P 2 = ka3 . Kepler noticed that the value of the constant k changes when we observe systems with different central objects. This means that the orbits of all of the planets in the Solar System have the same value for k, but that value is different for the Moon because all of the planets orbit the Sun, while the Moon revolves around the Earth. Find the value of k for the planets using the Earth’s orbit for two cases:

a) Find k for the Sun if Earth’s orbital parameters are given as a = 1 AU and P = 1 yr.

b) Find k for the Sun if Earth’s orbital parameters are given as a = 1.50 · 1011 m and P = 3.16 · 107 s.

c) Calculate the value of k from Kepler’s Third Law for the Earth and the Moon. The Moon has a semi-major axis of 3.84 · 108 m, and a period of 2.3604 · 106 s.

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