For a planet moving around the sun in an elliptical orbit of semimajor and semiminor axes a and b respectively and period T.

For a planet moving around the Sun, angular momentum is a critical concept that remains conserved throughout its orbit. Angular momentum is a measure of the rotational motion of an object and is dependent on both the mass of the planet and its distance from the Sun, as well as its velocity. As the planet travels along its elliptical path, it experiences varying distances from the Sun, resulting in changes in its speed.

When a planet is closer to the Sun, it moves faster, and when it is farther away, it moves slower. Despite these changes in speed and distance, the total angular momentum of the planet remains constant, provided there are no external torques acting on it. This conservation principle is a result of the symmetry in the gravitational forces acting between the planet and the Sun.

The conservation of angular momentum has significant implications for understanding planetary motion, including the shape and stability of orbits. It explains why planets sweep out equal areas in equal times, a key observation made by Johannes Kepler. This principle not only applies to planets but also to moons, satellites, and other celestial bodies in orbit, highlighting the fundamental laws governing motion in the universe.