Question

The work done by the force of gravity on a satellite moving in a circular orbit around the Earth is:

• A. Positive
• B. Negative
• C. Zero
• D. Infinite

Answer 1

The Correct Option is C

To solve the problem, we need to understand the nature of the work done by the force of gravity on a satellite moving in a circular orbit around Earth.

1. Understanding the Concepts:

- Work Done by a Force: Work is defined as the force applied times the displacement in the direction of the force.
- Mathematically, \[ \text{Work} = \vec{F} \cdot \vec{d} = Fd \cos \theta \] where \( \theta \) is the angle between force and displacement.
- Force of Gravity: Always acts towards the center of the Earth (radially inward).
- Satellite Movement: Satellite moves tangentially to its circular orbit, meaning its displacement at any instant is perpendicular to the gravitational force.

2. Analyze the Work Done by Gravity:

- Since the gravitational force acts towards the center and the satellite's instantaneous displacement is perpendicular (at 90°) to this force,
- The angle \( \theta = 90^\circ \), and \( \cos 90^\circ = 0 \).
- Therefore, the work done by gravity over any segment of the circular path is: \[ \text{Work} = Fd \times 0 = 0 \]

3. Interpretation:

- Gravity changes the direction of the satellite's velocity but not its speed.
- Hence, it does no work on the satellite because the satellite's kinetic energy remains constant in uniform circular motion.

Final Answer:

The work done by the force of gravity on a satellite moving in a circular orbit around the Earth is zero.