Following physical quantity is constant where a planet that revolves around Sun in an elliptical orbit.

Options

A. kinetic energy
B. angular momentum about the sun
C. potential energy
D. Total energy

Answer

To solve the question regarding which physical quantity remains constant when a planet revolves around the Sun in an elliptical orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Motion**:
- A planet moves in an elliptical orbit around the Sun, which is located at one of the foci of the ellipse.

2. **Identifying Physical Quantities**:
- The key physical quantities to consider in this scenario are angular momentum, kinetic energy, potential energy, and total mechanical energy.

3. **Angular Momentum**:
- Angular momentum (L) is given by the formula \( L = mvr \sin(\theta) \), where \( m \) is the mass of the planet, \( v \) is its velocity, and \( r \) is the distance from the Sun.
- In an elliptical orbit, the torque (τ) acting on the planet about the Sun is zero because the gravitational force acts along the line joining the planet and the Sun. Thus, \( τ = rF \sin(θ) = 0 \).
- Since torque is zero, angular momentum remains constant throughout the orbit.

4. **Kinetic and Potential Energy**:
- Kinetic energy (K) and potential energy (U) change as the planet moves along its elliptical path. Kinetic energy varies with speed, which changes as the planet moves closer to or farther from the Sun.
- Potential energy also changes with distance from the Sun, as it is given by \( U = -\frac{GMm}{r} \), where \( G \) is the gravitational constant, \( M \) is the mass of the Sun, and \( r \) is the distance from the Sun.

5. **Total Mechanical Energy**:
- The total mechanical energy (E) of the system, which is the sum of kinetic and potential energy, remains constant. This is due to the conservation of energy principle, which states that energy cannot be created or destroyed, only transformed.

6. **Conclusion**:
- The physical quantities that remain constant are:
- **Angular Momentum** (constant due to zero torque)
- **Total Mechanical Energy** (constant due to conservation of energy)

### Final Answer:
The quantities that are constant when a planet revolves around the Sun in an elliptical orbit are:
- Angular Momentum
- Total Mechanical Energy