For the planet - sun system identify the correct satatement.

Options

A. (a)the angular momentum of the planet is conserved about any point
B. (b)the total energy of the system is conserved
C. (c)the momentum of the planet is conserved
D. (d)All of the above

Explanation

To solve the question regarding the planet-sun system and identify the correct statements, we will analyze each statement provided in the question step by step.

### Step-by-Step Solution:

1. **Analyze the First Statement**:
- The first statement claims that "the angular momentum of the planet is conserved about any point."
- **Explanation**: Angular momentum is conserved when there is no net external torque acting on the system. In the case of the planet-sun system, the only significant force is the gravitational force exerted by the sun, which acts as a central force. The torque about the sun is zero, meaning angular momentum is conserved about the sun. However, if we consider other points (not at the sun), there may be a net torque due to the gravitational force, which means angular momentum is not conserved about those points.
- **Conclusion**: This statement is **incorrect**.

2. **Analyze the Second Statement**:
- The second statement claims that "the total energy of the system is conserved."
- **Explanation**: The forces acting in the planet-sun system (gravitational forces) are conservative in nature. In a closed system where only conservative forces are acting, the total mechanical energy (kinetic + potential) remains constant.
- **Conclusion**: This statement is **correct**.

3. **Analyze the Third Statement**:
- The third statement claims that "the momentum of the planet is conserved."
- **Explanation**: While the total energy of the system is conserved, the momentum of the planet is not conserved. This is because the gravitational force exerted by the sun changes the velocity of the planet as it moves in its orbit, leading to changes in both kinetic and potential energy. Since the velocity is changing, the momentum (which is the product of mass and velocity) is also changing.
- **Conclusion**: This statement is **incorrect**.

### Final Conclusion:
Based on the analysis:
- The first statement is incorrect.
- The second statement is correct.
- The third statement is incorrect.

Thus, the correct option regarding the statements about the planet-sun system is **option B** (the total energy of the system is conserved).