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

Answer: (A)

The gravitational force between the satellite and earth is acting along the centre of gravity of both object, therefore the acceleration of the satellite is also directed towards the centre of the earth.
Thus, the acceleration of $S$ is always directed towards the centre of the earth.
From Kepler's 2nd law planets the angular momentum remains conserved and its direction is perpendicular to the plane of the orbital motion of the satellite.
Therefore, the angular momentum of $S$ about the centre of the earth does not change in direction as well as in magnitude.
The net external force acting on the system of earth and satellite is zero and only gravitational force is acting in between the system which is a conservative force. Therefore, the total mechanical energy of $S$ remains conserved.
The linear momentum changes of satellite keeps on changing at every instant due to circular motion, Hence linear momentum of $S$ is not constant.