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 that is orbiting a planet in a circular orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Work Done**:
The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( F \) is the force, \( d \) is the displacement, and \( \theta \) is the angle between the force and the displacement vector.

2. **Identify the Forces Acting on the Satellite**:
In this case, the gravitational force is acting on the satellite. This force always points towards the center of the planet.

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

4. **Calculate the Angle**:
Since the gravitational force acts towards the center and the satellite's velocity is tangential to the orbit, the angle \( \theta \) between the gravitational force and the displacement (velocity) is 90 degrees.

5. **Apply the Work Done Formula**:
Substitute \( \theta = 90^\circ \) into the work done formula:
\[ W = F \cdot d \cdot \cos(90^\circ) \]
Since \( \cos(90^\circ) = 0 \), we have:
\[ W = F \cdot d \cdot 0 = 0 \]

6. **Conclusion**:
The work done by the gravitational force on the satellite as it orbits the planet is zero.

### Final Answer:
The work done by the gravitational force acting on the satellite is **0**.