Every planet revolves around the sun in an elliptical orbit :-
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The Centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Write Newton's law of gravitation once, and three of these four statements sort themselves out.

1. The force law. The sun pulls the planet with F = GMm/r². So F falls as 1/r², which makes A true. F grows with the product Mm, so it is directly proportional to it, not inversely, which makes B false.
2. Direction of force. Gravity is attractive, so the force on the planet points towards the sun. This pull is the centripetal force, and centripetal means centre-seeking. So C is false.

   T² ∝ a³

3. Kepler's third law. This is the law of periods: the square of the time period is proportional to the cube of the semi-major axis a. So D is true.
4. So. Only A and D are correct, which is option (c).

The idea to keep. Gravity is GMm/r²: directly proportional to the masses, inversely to r², always pulling towards the sun. Add T² ∝ a³ and you can check any Kepler statement.

Answer from the NTA final answer key. Solution by PrepWiser.