Conservation of Angular Momentum in Planetary Motion

The correct answer to the question is option 'C', which states that planetary motion in the solar system describes the conservation of angular momentum. In order to understand why this is the correct answer, let's delve into the concept of angular momentum and its conservation in planetary motion.

Angular momentum is a physical quantity that measures the rotational motion of an object around a particular axis. It depends on both the object's moment of inertia and its angular velocity. Mathematically, angular momentum (L) is given by the equation L = Iω, where I is the moment of inertia and ω is the angular velocity.

In the context of planetary motion, the conservation of angular momentum refers to the fact that the total angular momentum of a planet remains constant as it orbits the Sun. This means that the product of a planet's moment of inertia and its angular velocity remains the same throughout its orbit.

There are several factors that contribute to the conservation of angular momentum in planetary motion:

1. Kepler's Laws: Johannes Kepler's laws of planetary motion provide a mathematical description of how planets move around the Sun. Kepler's laws, particularly the second law known as the law of equal areas, imply that a planet sweeps out equal areas in equal times as it orbits the Sun. This means that the planet's angular velocity is not constant throughout its orbit but changes in such a way that the product of its moment of inertia and angular velocity remains constant.

2. Gravitational Force: The gravitational force between the planet and the Sun acts as a centripetal force that keeps the planet in its orbit. This force causes the planet to experience an acceleration towards the Sun, resulting in a change in its velocity. However, since the gravitational force acts along the radial direction towards the Sun, it does not exert any torque on the planet. As a result, the planet's angular momentum remains conserved.

3. Conservation of Energy: The conservation of angular momentum is closely related to the conservation of energy in planetary motion. As the planet moves in its elliptical orbit around the Sun, it experiences changes in potential energy and kinetic energy. However, the total mechanical energy of the planet, which is the sum of its potential and kinetic energies, remains constant. This conservation of energy is directly linked to the conservation of angular momentum.

In conclusion, the motion of planets in the solar system is described by the conservation of angular momentum. This conservation arises from the mathematical description of planetary motion provided by Kepler's laws, the gravitational force acting as a centripetal force, and the conservation of energy. These factors collectively ensure that the product of a planet's moment of inertia and angular velocity remains constant throughout its orbit.