Question
Physics Question on Gravitation
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,
the linear momentum of S remains constant in magnitude
the acceleration of S is always directed towards the centre of the earth
the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
the total mechanical energy of S varies periodically with time
the acceleration of S is always directed towards the centre of the earth
Solution
Force on satellite is always towards earth, therefore, acceleration of satellite S is always directed towards centre of the 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.