In elliptical orbit of a planet, as the planet moves from apogee position to perigee position to perigee position, match the following columns
`{:(,"Column-I",,"Column-II"),("(A)","Speed of planet","(p)","Remains same"),("(B)","Distance of planet from centre of sun","(q)","Decreases"),("(C)","Potential energy","(r)","Increase"),("(D)","Angular momentum about centre of sun","(s)","Cannot say"):}`

Explanation

To solve the question regarding the behavior of a planet in an elliptical orbit as it moves from apogee to perigee, we will analyze each aspect mentioned in the columns.

### Step-by-Step Solution:

1. **Speed of the Planet (A)**:
- As the planet moves from apogee (farthest point from the Sun) to perigee (closest point to the Sun), its speed increases due to the conservation of angular momentum. The gravitational force acting on the planet increases as it gets closer to the Sun, causing it to accelerate.
- **Conclusion**: The speed of the planet increases.
- **Match**: (A) Speed of planet → (r) Increases.

2. **Distance of the Planet from the Centre of the Sun (B)**:
- The distance from the Sun decreases as the planet moves from apogee to perigee. At apogee, the distance is at its maximum, and at perigee, it is at its minimum.
- **Conclusion**: The distance of the planet from the centre of the Sun decreases.
- **Match**: (B) Distance of planet from centre of Sun → (q) Decreases.

3. **Potential Energy (C)**:
- The gravitational potential energy (U) of the planet is given by the formula \( U = -\frac{GMm}{r} \), where \( r \) is the distance from the Sun. As the planet gets closer to the Sun (decreasing \( r \)), the potential energy becomes more negative, indicating an increase in potential energy in terms of absolute value.
- **Conclusion**: The potential energy decreases (becomes more negative).
- **Match**: (C) Potential energy → (r) Decreases.

4. **Angular Momentum about the Centre of the Sun (D)**:
- Angular momentum (L) is conserved in an orbiting system, meaning it remains constant as the planet moves along its elliptical path. The angular momentum can be expressed as \( L = mvr \), and since the product of speed and radius remains constant, L does not change.
- **Conclusion**: The angular momentum remains the same.
- **Match**: (D) Angular momentum about centre of Sun → (p) Remains same.

### Final Matches:
- (A) Speed of planet → (r) Increases
- (B) Distance of planet from centre of Sun → (q) Decreases
- (C) Potential energy → (s) Cannot say (it decreases)
- (D) Angular momentum about centre of Sun → (p) Remains same