Kepler’s second law is based on

The correct answer is Conservation of angular momentum.

Step-by-Step Explanation:

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.

Let us analyze this mathematically. The areal velocity (the rate at which area is swept out by the radial vector $r$ per unit time $t$) is given by the relation:
$\frac{dA}{dt}=\frac{L}{2m}$
where:
- $dA/dt$ is the areal velocity,
- $L$ is the magnitude of the angular momentum of the planet, and
- $m$ is the mass of the planet.

For any planet orbiting the Sun, the gravitational force acting on the planet is a central force. This force is always directed along the line joining the planet to the center of the Sun. Therefore, the torque ($\tau$) acting on the planet about the Sun is zero because the angle between the position vector $r$ and the force vector $F$ is either 0° or 180°:
$\tau =r\times F=0$

Since torque is the rate of change of angular momentum:
$\tau =\frac{dL}{dt}=0$
This implies that the angular momentum $L$ remains constant (conserved) throughout the planet's motion.

Since the angular momentum $L$ and the mass $m$ of the planet are both constant, the areal velocity $dA/dt$ must also be constant:
$\frac{dA}{dt}=\text{constant}$
This directly leads to Kepler's second law. Thus, Kepler's second law is a direct consequence of the conservation of angular momentum.