Match the following
`{:(,"Column-I",,"Column-II"),("(A)","Kepler's first law","(p)",T^(2)propr^(3)),("(B)","Kepler's second law","(q)","Areal velocity is constant"),("(C)","Kepler's third law","(r)","Orbit of planet is elliptical"):}`

Answer

To solve the matching question regarding Kepler's laws, we will analyze each law and its corresponding description.

### Step-by-Step Solution:

1. **Identify Kepler's First Law**:
- Kepler's first law states that "the orbit of a planet is elliptical with the Sun at one of the foci."
- **Match**: (A) Kepler's first law → (r) Orbit of planet is elliptical.

2. **Identify Kepler's Second Law**:
- Kepler's second law states that "a planet sweeps out equal areas in equal times," which means that the aerial velocity of the planet is constant.
- **Match**: (B) Kepler's second law → (q) Areal velocity is constant.

3. **Identify Kepler's Third Law**:
- Kepler's third law states that "the square of the time period of revolution of a planet is directly proportional to the cube of the semi-major axis of its orbit."
- Mathematically, this is expressed as \( T^2 \propto R^3 \).
- **Match**: (C) Kepler's third law → (p) \( T^2 \propto R^3 \).

### Final Matching:
- (A) Kepler's first law → (r) Orbit of planet is elliptical
- (B) Kepler's second law → (q) Areal velocity is constant
- (C) Kepler's third law → (p) \( T^2 \propto R^3 \)