A planet is revolving around the sun in an elliptical orbit. Which out of the following remains constant.
(a) Linear speed (b) angular momentum
( c) kinetic energy (d) potential energy (e) total energy throughout its orbit.

Explanation

To solve the problem, we need to analyze the different quantities that can change as a planet revolves around the sun in an elliptical orbit.

### Step-by-Step Solution:

1. **Understanding the Forces**:
- The planet is under the influence of gravitational force from the sun. This force is directed towards the sun and is responsible for the planet's motion in its elliptical orbit.

**Hint**: Identify the forces acting on the planet and their direction.

2. **Angular Momentum**:
- Angular momentum (L) is defined as \( L = r \times p \) where \( p \) is the linear momentum. Since the gravitational force acts along the line connecting the planet and the sun, the torque (τ) about the sun is zero.
- Torque is given by \( τ = r \times F \). Since \( r \) is the radius vector pointing towards the sun and \( F \) is along this line, \( r_{\perpendicular} = 0 \). Thus, \( τ = 0 \) implies that angular momentum is conserved.

**Hint**: Recall that torque is related to the change in angular momentum.

3. **Linear Speed**:
- The linear speed of the planet is not constant. As the planet moves in its elliptical orbit, it speeds up when it is closer to the sun (perihelion) and slows down when it is farther away (aphelion) due to the conservation of angular momentum.

**Hint**: Consider how the distance from the sun affects the speed of the planet.

4. **Kinetic Energy**:
- Kinetic energy (KE) is given by \( KE = \frac{1}{2} mv^2 \). Since the linear speed (v) changes as the planet moves in its orbit, the kinetic energy will also change.

**Hint**: Think about how changes in speed affect kinetic energy.

5. **Potential Energy**:
- Gravitational potential energy (U) is given by \( U = -\frac{GMm}{r} \). As the distance (r) from the sun changes, the potential energy also changes.

**Hint**: Remember that potential energy depends on the distance from the source of the gravitational field.

6. **Total Energy**:
- The total mechanical energy (E) of the system is the sum of kinetic energy and potential energy. Although kinetic and potential energy change, the total energy remains constant because there are no non-conservative forces acting on the system.

**Hint**: Total energy conservation is a key principle in closed systems.

### Conclusion:
From the analysis, we conclude that:
- **Constant**: Angular momentum (b)
- **Not Constant**: Linear speed (a), kinetic energy (c), potential energy (d), total energy (e) varies but remains conserved.

Thus, the correct answer is **(b) angular momentum** remains constant.