Question

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

Answer 1

Work:

1. Work is defined as the measure of energy transfer that occurs when an object is moved over a distance by an external force.
2. The dimension of work is $[M{L}^2{T}^{-2}]$.
3. The mathematical expression for work is $W=F.sCos\theta$, where $F$ is the force, $W$ is the work, $s$ is the displacement covered, and $\theta$ is the angle between force and displacement.
4. The SI unit of work is the joule.

An illustrative diagram of work :

Explanation:

1. The direction of gravitational force acting on the satellite is towards the center.
2. As the motion of the satellite is in the horizontal plane, therefore, the force of gravity of the earth on the satellite and the direction of motion of the satellite are perpendicular to each other.
3. So the work on satellite is by the earth's gravity is $W=F.sCos90°$, as the value of $Cos90°$ is zero, so the work done on satellite is zero.

Hence, the work done by the force of gravity on a satellite moving around the earth is equal to zero.