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.
Which of the following options is/are incorrect?

• 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

Answer: (B), (C), (D)

The linear momentum of $S$ remains constant in magnitude.

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.