Question

What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Answer 1

The work done by the force of gravity on a satellite moving round the Earth is zero.

Justification:

Work done is given by: \[ W = F \cdot d \cdot \cos \theta \] where \( \theta \) is the angle between the force and the displacement.

- The force of gravity acts towards the center of the Earth (radially).
- The satellite moves along a circular path, so its displacement is tangential to the circle.
- The angle between the force (toward the center) and the displacement (tangent) is \( 90^\circ \).
- Since \(\cos 90^\circ = 0\): \[ W = F \cdot d \cdot \cos 90^\circ = 0 \]

Conclusion: Gravity does not do any work on a satellite in circular orbit because the force is always perpendicular to its displacement. The satellite’s speed remains constant, only its direction changes.