Derivation of Newton’s law of Gravitation from Kepler’s Law
Suppose a test mass is revolving around a source mass in a nearly circular orbit of radius ‘r’ with a constant angular speed (ω). Then, the centripetal force acting on the test mass for its circular motion is,
F = mrω2 = mr × (2π/T)2
According to Kepler’s 3rd law, T2 ∝ r3
Using this in force equation, we get,
F = 4π2mr/Kr3 [Where, K = 4π2/GM]
⇒ F = GMm/r2, which is the equation of Newton’s law of gravitation.
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