Solution:

Kepler's Second Law, also known as the **Law of Equal Areas**, states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This law implies that a planet moves faster when it is closer to the Sun and slower when it is farther away, resulting in an elliptical orbit.

### Connection to Angular Momentum Conservation:

1. **Angular Momentum Definition**:
Angular momentum (\( L \)) of a body moving around a point is given by:
\[
L = mvr
\]
where:
- \( m \) = mass of the body,
- \( v \) = tangential velocity,
- \( r \) = distance from the center of rotation (the Sun, in this case).

2. **Conservation of Angular Momentum**:
- In a system where no external torques act (like a planet orbiting the Sun), the angular momentum is conserved.
- This means that:
\[
L = mvr = \text{constant}
\]

3. **Implications for Planetary Motion**:
- As a planet moves in its elliptical orbit, its distance \( r \) from the Sun changes.
- To conserve angular momentum (\( L \)), if the planet is closer to the Sun (\( r \) decreases), its velocity \( v \) must increase. Conversely, when it is farther from the Sun (\( r \) increases), its velocity \( v \) must decrease.

4. **Area Swept Out**:
- The area swept out by the line segment joining the planet to the Sun in a time interval \( dt \) can be expressed in terms of angular momentum. The area (\( dA \)) swept out in time \( dt \) is:
\[
dA = \frac{1}{2} r^2 d\theta
\]
where \( d\theta \) is the angle subtended at the Sun during that time interval.

5. **Equal Areas in Equal Times**:
- Since angular momentum is conserved, the planet's motion adjusts in such a way that it sweeps out equal areas in equal times, which is the essence of Kepler's Second Law.

### Conclusion:
Kepler's Second Law reflects the conservation of angular momentum in planetary orbits. The relationship between distance from the Sun, velocity, and the areas swept out in equal time intervals illustrates that as a planet moves in its elliptical orbit, it adjusts its speed to conserve angular momentum, leading to the sweeping of equal areas in equal times.