Question

Kepler's third law states that the square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance, r between the sun and the planet i.e. $T^2 = Kr^3$.
Here, K is constant.
If masses of the sun and the planet are M and m respectively, then as per Newton's law of gravitation, force of attraction between them is $F = \frac{GMm}{r^2}$, where G is gravitational constant.
The relation between G and K is described as

• A. $GK = 4\pi^2$
• B. $GMK = 4\pi^2$
• C. $K = G$
• D. $K = \frac{1}{G}$

Hint:

Kepler's laws can be derived and connected with Newton's law using dimensional analysis to relate the gravitational constant with the planetary motion.

Answer 1

The Correct Option is B

From Kepler's third law and the law of gravitation, using dimensional analysis and considering the constant G, we find that the correct relation is $GMK = 4\pi^2$.