Question

When a planet revolves around the Sun, in general, for the planet

• A. linear momentum and aerial velocity are constant.
• B. kinetic and potential energy of the planet are constant.
• C. angular momentum about the Sun and aerial velocity of the planet are constant.
• D. linear momentum and linear velocity are constant.

Answer 1

The Correct Option is C

Given: 

A planet revolves around the Sun.

Step 1: Understanding Key Concepts

• Linear Momentum: Changes due to the variation in velocity and direction.
• Angular Momentum: Conserved due to the absence of external torque.
• Areal Velocity: Given by Kepler’s second law, remains constant.
• Kinetic and Potential Energy: They vary as the planet moves in an elliptical orbit.

Step 2: Identifying the Correct Statement

Since angular momentum and areal velocity remain constant:

Correct answer: C (Angular momentum about the Sun and aerial velocity of the planet are constant).

Answer 2

When a planet revolves around the Sun, it follows an elliptical orbit as per Kepler's laws of planetary motion.

- Angular momentum about the Sun is conserved for a planet moving in an elliptical orbit around the Sun. 
- The aerial velocity, or the rate at which the planet sweeps out area, is also constant due to the conservation of angular momentum.

Thus, the angular momentum about the Sun and the aerial velocity of the planet remain constant during its orbit.

Therefore, the correct answer is:
\({\text{(C) angular momentum about the Sun and aerial velocity of the planet are constant.}}\)