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 resolve this issue, we must first establish the nature of the work performed by Earth's gravitational force on a satellite in circular orbit.

1. Foundational Concepts:

- Definition of Work: Work is quantified as the product of the applied force and the displacement aligned with the force's direction.
- The mathematical representation is:
\[ \text{Work} = \vec{F} \cdot \vec{d} = Fd \cos \theta \] where \( \theta \) denotes the angle between the force vector and the displacement vector.
- Gravitational Force Characteristics: This force is invariably directed towards the Earth's center (radially inward).
- Satellite Motion: The satellite travels tangentially to its circular path, implying that its instantaneous displacement is orthogonal to the gravitational force.

2. Analysis of Gravitational Work:

- Given that the gravitational force acts centrally and the satellite's instantaneous displacement is perpendicular (forming a 90° angle) to this force,
- The angle \( \theta \) is \( 90^\circ \), and \( \cos 90^\circ \) equals 0.
- Consequently, the work done by gravity over any portion of the circular trajectory is calculated as:
\[ \text{Work} = Fd \times 0 = 0 \]

3. Conclusion:

- Gravity influences the direction of the satellite's velocity but not its magnitude (speed).
- As a result, no work is done on the satellite by gravity, as its kinetic energy remains invariant during uniform circular motion.

Final Determination:

The work performed by the gravitational force on a satellite executing a circular orbit around the Earth is definitively zero.