Chapter 14, Problem 4A

Why doesn’t gravitational force change the speed of a satellite in circular orbit?

To determine

To Explain: The gravitational force does not change the speed of satellite in the orbit.

Explanation of Solution

Introduction:

Work done is given as

  $W=Fd\text{cos}\theta$

Where,

W is the work done, F is the force, d is the displacement and $\theta$ is the angle between the direction of force and displacement.

The motion of the satellite is circular and the gravitational force act on the satellite along the radius of the circular orbit towards the center. So, the angle between the gravitational force and the direction of motion of the satellite is always $90°$ .

The work done on the satellite by the gravitational force is zero because the value of $\cos 90°$ is zero and hence speed of the satellite does not increase due to the gravitational force.

Conclusion:

Speed of satellite does not increase because work done by gravitational force on the satellite is zero.