Question

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small as compared to the mass of the earth.

• A. The acceleration of S is always directed towards the centre of earth.
• B. The angular momentum of S about the centre of earth changes in direction but its magnitude remains constant.
• C. The total mechanical energy of S varies periodically with time.
• D. The linear momentum of S remains constant in magnitude.

Answer 1

Answer: (A)

The acceleration of S is always directed towards the centre of earth.

Force on the satellite is always towards the earth; therefore acceleration of satellite $S$ is always directed towards the centre of the earth. Net torque of this gravitational force $N$ about the centre of the earth is zero. Therefore, angular momentum (both in magnitude and direction) of $S$ about the centre of the earth is constant throughout. Since force $F$ is conservative in nature, therefore mechanical energy of the satellite remains constant. Speed of $S$ is maximum when it is nearest to the earth and minimum when it is farthest.