According to Kepler's second law, a planet sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of which quantity?

Solution

1. Kepler's second law states that a planet sweeps out equal areas in equal time intervals, implying a constant areal velocity.
2. The gravitational force exerted by the Sun on a planet is a central force, meaning it acts along the line joining the two bodies.
3. For any central force, the torque acting on the planet is zero because the force vector and the position vector are collinear.
4. Since torque is the rate of change of angular momentum, a zero torque implies that the angular momentum of the planet remains constant.
5. Hence the answer is (C).