Which of the following quantities remain constant in a planetary motion (consider elliptical orbits)as seen from the sun?

Options

A. Angular speed
B. Speed
C. Kinetic energy
D. Angular momentum

Answer

To solve the question regarding which quantities remain constant in planetary motion (considering elliptical orbits) as seen from the Sun, let's break down the concepts step by step.

### Step-by-Step Solution:

1. **Understanding Elliptical Orbits**:
- In an elliptical orbit, a planet moves around the Sun in a path that is not a perfect circle. This means that the distance between the planet and the Sun changes as the planet moves along its orbit.

**Hint**: Remember that in an elliptical orbit, the distance from the Sun varies, which affects the planet's speed.

2. **Variation in Speed**:
- Due to the elliptical nature of the orbit, the speed of the planet is not constant. The planet moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion).

**Hint**: Consider how gravitational force affects the planet's speed depending on its distance from the Sun.

3. **Kinetic Energy**:
- Since the speed of the planet changes, the kinetic energy (KE = 1/2 mv²) also changes. Thus, kinetic energy is not constant in elliptical orbits.

**Hint**: Think about how kinetic energy depends on the square of the velocity.

4. **Angular Speed**:
- Angular speed (ω) is related to linear speed (v) and the radius (r) of the orbit (ω = v/r). Since both v and r change in an elliptical orbit, angular speed is also not constant.

**Hint**: Remember that angular speed is influenced by both the distance from the center and the speed of the object.

5. **Angular Momentum**:
- Angular momentum (L) is given by the formula L = mvr, where m is the mass of the planet, v is its linear speed, and r is the distance from the Sun. In the case of a planet orbiting the Sun, the only force acting on it is the gravitational force, which acts along the line connecting the planet and the Sun. This means that there is no net torque acting on the planet, and thus, angular momentum remains constant.

**Hint**: Consider the conservation of angular momentum and how torque relates to angular momentum.

### Conclusion:
The quantity that remains constant in planetary motion (considering elliptical orbits) as seen from the Sun is **angular momentum**.