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

1. Gravitational Force Direction:
– The gravitational force acts as the centripetal force that keeps the satellite in its orbit around the Earth.
– This force acts toward the center of the Earth.

2. Circular Orbital Motion:
– For a satellite in a circular orbit around the Earth, its motion is perpendicular to the force of gravity acting on it.
– The satellite’s path is tangential to the force of gravity.

3. Perpendicular Force and Motion:
– At every point along the circular orbit, the force of gravity is perpendicular to the direction of the satellite’s motion.
– The angle between the force of gravity and the displacement of the satellite is 90°.

4. Work Calculation:
– Work is calculated as the product of force and displacement in the direction of the force, given by (W = F x d x cos(θ), where (θ) is the angle between force and displacement.

5. Cosine of (90°) Angle:
– When the force and displacement are perpendicular (cos(90°) = 0), the cosine of (90°) is zero.
– Zero cosine implies that the work done by the force of gravity is zero.

6. Conclusion:
– Due to the perpendicular relationship between the force of gravity and the satellite’s motion in its circular orbit, the angle between the force and displacement is (90°), resulting in zero work done by gravity on the orbiting satellite.

Understanding these points demonstrates that in a circular orbital motion, the force of gravity acting as the centripetal force does not perform any work on the satellite since the force is perpendicular to the direction of the satellite’s motion, leading to a zero work done by gravity on the orbiting satellite.