Every planet revolves around the Sun in an elliptical orbit: [2023]

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Solution

Q.
Every planet revolves around the Sun in an elliptical orbit: [2023]

A. The force acting on a planet is inversely proportional to the square of the distance from the Sun.

B. Force acting on a planet is inversely proportional to the 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 the time period of revolution of a planet around the Sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.

Choose the correct answer from the options given below:

1 A and D only

2 B and C only

3 A and C only

4 C and C only

Ans.
(1)

$F = \frac{G m_{1} m_{2}}{r^{2}}$

$\Rightarrow F \propto \frac{1}{r^{2}}$

$\Rightarrow F \propto m_{1} m_{2}$

$\Rightarrow This force provides centripetal force and acts towards the Sun.$

$T^{2} \propto a^{3} (Kepler’s third law)$

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