Kepler's second law is based on

Options

A. Newton's first law
B. Newton's second law
C. special theory of relativity
D. conservation of angular momentum

Explanation

To solve the question "Kepler's second law is based on," we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kepler's Second Law**:
- Kepler's second law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This implies that the areal velocity (the area swept out per unit time) is constant.

2. **Defining Areal Velocity**:
- Areal velocity can be mathematically expressed as \( \frac{dA}{dt} \), where \( A \) is the area swept out by the radius vector in time \( t \). This can also be related to angular momentum.

3. **Relating Areal Velocity to Angular Momentum**:
- The areal velocity can be expressed in terms of angular momentum \( L \) and mass \( m \) of the planet as:
\[ \frac{dA}{dt} = \frac{L}{2m} \]
- Since the mass \( m \) of the planet remains constant, for the areal velocity to remain constant, the angular momentum \( L \) must also remain constant.

4. **Conclusion**:
- Therefore, Kepler's second law is fundamentally based on the principle of conservation of angular momentum. This means that as a planet moves in its elliptical orbit, its angular momentum does not change, leading to the constant areal velocity.

5. **Choosing the Correct Option**:
- Among the given options:
- Newton's first law: Incorrect
- Newton's second law: Incorrect
- Special theory of relativity: Incorrect
- Conservation of angular momentum: Correct
- Hence, the correct answer is **option 4: conservation of angular momentum**.