Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is defined as the product of the moment of inertia and the angular velocity. In the context of a planet revolving around the sun, the angular momentum about the sun remains constant because there is no external torque acting on the planet-sun system.

Explanation:

- Angular Momentum Defined:
Angular momentum (L) is defined as the product of the moment of inertia (I) and the angular velocity (ω) of an object. Mathematically, it is given by the equation L = I * ω.

- Moment of Inertia:
The moment of inertia depends on the mass distribution of an object and is a measure of its resistance to changes in rotation. In the case of a planet revolving around the sun, the moment of inertia depends on the distribution of mass within the planet.

- Angular Velocity:
The angular velocity describes the rotational speed of an object. In the case of a planet revolving around the sun, the angular velocity is determined by the planet's orbital speed and the radius of its orbit.

- Conservation of Angular Momentum:
According to the law of conservation of angular momentum, the total angular momentum of an isolated system remains constant if no external torque acts on it. In the case of a planet-sun system, the gravitational force between the planet and the sun provides the centripetal force required to keep the planet in orbit. This force does not exert any torque on the system.

- Elliptical Orbit:
When a planet revolves around the sun in an elliptical orbit, its distance from the sun varies throughout its orbit. However, the planet's speed is not constant. According to Kepler's second law, a planet sweeps out equal areas in equal times, which means that the planet moves faster when it is closer to the sun and slower when it is farther away.

- Constant Angular Momentum:
Even though the planet's linear speed changes as it moves along its elliptical orbit, the product of its moment of inertia and angular velocity remains constant. This is because the change in moment of inertia is compensated by a corresponding change in angular velocity.

- Importance of Constant Angular Momentum:
The conservation of angular momentum plays a crucial role in determining the stability and dynamics of planetary orbits. It ensures that the planet's motion remains predictable and that it does not spiral inward or outward due to changes in its speed or distance from the sun.

In conclusion, a planet revolving around the sun in an elliptical orbit has a constant angular momentum about the sun because there is no external torque acting on the planet-sun system. The conservation of angular momentum ensures the stability and predictability of the planet's motion.