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

The correct option is A The acceleration of $S$ is always directed towards the centre of the earth

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