Let Us get Kepler's Law from Newton's Law of Gravitation.
Let two masses m and M be revolving around their C.M. such that the Gravitational Force of attraction be providing the Centripetal Force. Let R1 and R2 be the respective distances of m and M from their common C.M. and let R be the distance between the two masses.
Therefore mR1 = MR2 --------------------(1)
And R1 + R2 = R -----------------------(2)
Solving (1) and (2) we get R1 = M R / (m + M) ----------------------(3)
Also
GMm / R2 = m w2 R1 --------------------------(4)
From (3) and (4) we get
G(m + M) = w2 R3 ------------------------- (5)
Therefore T2 is proportional to R3 . Which is nothing but Kepler?s Third Law.
Moderation Team
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