Kepler’s third law states that the square of period of revolution T of a planet around the sun is proportional to the cube of average distance r between sun and planet i.e. T² = Kr³, where K is constant. If the masses of sun and planet are M and m respectively and as per Newton’s law of gravitation the force of attraction between them is F=(GMm)/(r²), where G is gravitational constant, the relation between G and K is described as:
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Kepler’s third law can be derived directly using:
Gravitational force = Centripetal force
Always compare final expressions term by term.