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Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power 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 then as per Newton's law of gravitation force of attraction between them is F = GMm / r², here G is gravitational constant.

1. GMK = 4π²
2. K = G
3. K = 1 / G
4. GK = 4π²

Correct answer: GMK = 4π²

Solution

Using Newton's law of gravitation and centripetal force, we equate GMm/r² = mω²r, where ω = 2π/T. Substituting ω and simplifying, we find that GMK = 4π².

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