Chapter 14, Problem 27A

Does gravity do any network on a satellite in an elliptical orbit during one full orbit? Explain your answer.

To determine

Work done by gravity on a satellite in an elliptical orbit during one full orbit.

Answer to Problem 27A

Net work done is zero.

Explanation of Solution

Introduction:

Work done is given as

  $W=Fd\cos \theta$

Where,

  $W=$ Work done

  $\text{F = }$ Force

  $\text{d =}$ Displacement

  $\theta \text{ =}$ Angle between force and displacement

In one complete orbit, the satellite returns to its starting point and since it returns to its starting point, the displacement of the satellite becomes zero. The work done is the scalar product of force and displacement. Since the displacement is zero for the satellite for one complete orbit, the work done comes out to be zero. Hence, gravity does no work.

Conclusion:

Gravity does no work on the satellite in one full orbit.