Question

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,
A. The acceleration of S is always directed towards the centre of the earth.
B. The angular momentum of S about the centre of the 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

Hint: The satellite is moving in elliptical orbit it means it’s speed will be changing at every instant but since there is no external torque on the satellite and torque due to earth is zero as direction of force and line connecting the satellite and earth is parallel so angular momentum will be conserved.

Complete step by step answer:
Lets check each option and see whether it is true or not. Option-A is correct because only force on the satellite is gravitational force by earth and gravitational force always acts along the line joining satellite and centre of earth therefore acceleration of S is always directed towards the centre of the earth.

Option-B is false because there is no external torque on the satellite and torque due to earth is zero as direction of force and line connecting the satellite and earth is parallel so angular momentum will be conserved (both magnitude and direction will remain the same).

Option-C is also false because energy total energy of satellite S is constant because gravitational force is always perpendicular to the motion of the satellite so no work is done by the gravity, only energy changes from one form to other but total energy remains constant.

Option-D is also false because the satellite is moving in an elliptical orbit so velocity keeps changing at every instant therefore the magnitude of linear momentum will not remain constant.

Hence Option A is correct.

Note: Here only force acting is gravitational force which is always perpendicular to motion of the satellite so no work is done by the gravitational force therefore energy remains constant and also there is no external torque on the satellite hence angular momentum will remain constant too.