Kepler's third law states that square of period of revoluation (T) of… | NEET 2015 (AIPMT, Cancelled Paper)

Q24NEET 2015 · AIPMT · CANCELLED PAPERMedium

Kepler's Laws & Planetary Motion

Kepler's third law states that square of period of revoluation (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here 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 = $\frac{GMm}{r^2}$ , here G is gravitational constant. The relation between G and K is described as

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Answer: (d)

Gravity provides centripetal force: $\dfrac{GMm}{r^2} = m\dfrac{4\pi^2}{T^2}r$ .
$T^2 = \dfrac{4\pi^2}{GM}r^3 \Rightarrow K = \dfrac{4\pi^2}{GM}$
So $GMK = 4\pi^2$ , the answer is (d).

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