How is Kepler’s second law related to the conservation of angular momentum?

In the context of celestial mechanics, Kepler’s second law of planetary motion—which states that a radius vector joining a planet to the Sun sweeps out equal areas in equal intervals of time—is a direct consequence of the law of conservation of angular momentum.12

Because the gravitational force exerted by the Sun on a planet is a central force (acting along the line connecting the two bodies), there is no torque acting on the planet relative to the Sun. In the absence of external torque, the angular momentum of the planet remains constant. This conservation ensures that the planet's orbital motion is confined to a plane and that its velocity varies predictably: the planet must move faster when closer to the Sun (perihelion) and slower when farther away (aphelion) to maintain a constant angular momentum. Consequently, the area swept out by the radius vector per unit of time remains uniform throughout the orbit.132