A planet is moving in an elliptical orbit around the sun. If T.V and L stands respectively for its kinetic energy, gravitational potential energy, total energy and magnitude of angular momentum about the centre of force, which of the following is correct?

When a planet revolves in an elliptical orbit around the sun, a variety of energies and angular momentums are involved. The total energy, E in this context, is thus very important since it stands for the sum of kinetic energy T and gravitational potential energy V of the planet.

In any bound elliptical orbit of a planet, total energy is always negative. This negative value means that the planet is gravitationally bound to the sun, with insufficient energy to leave the influence of the gravitational pull from the sun. The reason why the gravitational potential energy is negative is because of the attraction caused by gravity; the more negative this energy gets as the planet approaches the sun, the greater is its kinetic energy, which peaks at periapsis, the closest point of the orbit to the sun.

On the other hand, at apoapsis, where the planet is farthest from the sun, its kinetic energy is lower, but the gravitational potential energy is still negative. The total energy is consistently negative, and this is what reflects the stability of the orbit. Therefore, it is evident that for a planet in an elliptical orbit, the total energy is always negative, which is a further proof of the concept of gravitational binding in celestial mechanics.