When a satellite is orbitting round a planet in circular orbit, workdone by the gravitational force acting on the satellite is

Options

A. zero on completing one revolution only
B. zero always
C. infinite
D. negative

Answer

To solve the question regarding the work done by the gravitational force acting on a satellite in a circular orbit around a planet, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces Acting on the Satellite**:
- When a satellite is in circular orbit around a planet, the primary force acting on it is the gravitational force, which acts towards the center of the planet.

2. **Identify the Direction of Motion**:
- The satellite moves in a circular path. At any point in its orbit, the direction of its velocity (tangential to the orbit) is perpendicular to the gravitational force (which points towards the center of the planet).

3. **Recall the Work Done Formula**:
- The work done \( W \) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where:
- \( F \) is the magnitude of the force,
- \( d \) is the distance moved in the direction of the force,
- \( \theta \) is the angle between the force and the direction of motion.

4. **Determine the Angle**:
- In the case of a satellite in circular orbit, the angle \( \theta \) between the gravitational force (which is radial) and the direction of motion (which is tangential) is \( 90^\circ \).

5. **Calculate the Work Done**:
- Since \( \cos(90^\circ) = 0 \), the work done by the gravitational force can be calculated as:
\[ W = F \cdot d \cdot \cos(90^\circ) = F \cdot d \cdot 0 = 0 \]

6. **Conclusion**:
- Therefore, the work done by the gravitational force acting on the satellite while it is in circular orbit is **zero**.

### Final Answer:
The work done by the gravitational force acting on the satellite is **zero**.

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