Chapter 14, Problem 9A

The sum of PE and KE for a satellite in a circular orbit is constant. Is this sum also constant for a satellite in an elliptical orbit?

To determine

Whether the sum of PE and KE remains constant for a satellite in an elliptical orbit like in a circular orbit.

Answer to Problem 9A

Yes

Explanation of Solution

Introduction:

A satellite revolves around a planet in an elliptical path. The total mechanical energy of the satellite remains conserved.

When a satellite would be at the closest position in the elliptical orbit towards the planet, its speed would be maximum which means it would have maximum KE and least PE. When the satellite moves farther, the kinetic energy would convert to potential energy. The satellite would have minimum speed at the farthest point which means minimum KE but maximum PE.

Conclusion:

Thus, the sum of PE and KE remains constant for a satellite in an elliptical orbit