Question

A planet is moving in an elliptical orbit around the sun. If T, V, E and L stand 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 ?

• A. T is conserved
• B. V is always positive
• C. E is always negative
• D. L is conserved but direction of vector L changes continously

Answer 1

The Correct Option is C

To determine the correct answer, let's analyze each option based on the principles of celestial mechanics and physics.

• Option 1: T is conserved
  The kinetic energy of a planet in an elliptical orbit is not conserved. The kinetic energy varies as the planet moves closer to or farther from the sun due to changes in velocity according to Kepler's second law. Hence, this option is incorrect.
• Option 2: V is always positive
  Gravitational potential energy is generally considered to be negative because it is defined with respect to the point at infinity, where potential energy is zero. As the planet is within the gravitational influence of the sun, the potential energy is negative, not positive. This option is incorrect.
• Option 3: E is always negative
  For a planet bound in an elliptical orbit, the total mechanical energy (E) is negative. This is because the total energy is the sum of kinetic and potential energies, and its negative value indicates a bound system, where the planet is gravitationally bound to the sun. This option is correct.
• Option 4: L is conserved but the direction of vector L changes continuously
  Angular momentum (L) of the planet about the sun is conserved in both magnitude and direction. According to the law of conservation of angular momentum, the vector itself does not change direction. Thus, this statement is incorrect.

Based on the reasoning above, the correct answer is: E is always negative. It reflects the nature of bound gravitational systems like planets orbiting the sun.