Question

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

Answer 1

Hint In this question, consider the diagram to understand the orbiting of earth by the satellite. A satellite moves in a circular path to make a round of the earth. Work done is equal to the potential energy.

Complete step by step answer
 As we know that the work is defined as the transfer of energy from one form to another form and that is equal to the product of the force and the direction of the displacement.
The gravitational force is the force in which two objects have masses. And they attract each other. That is known as gravity.
Work done is the gravitational force when a satellite revolves around the earth. We know that the satellite moves in the circular path. Thus, the velocity vector and the force are not perpendicular to each other.

Work done by the gravitational force depends upon the vertical displacement of the satellite or object.
Work done doesn’t depend on path of the satellite
Therefore, work done by the gravitational force is,
\[ \Rightarrow W = Fs\cos \theta \]
We have to displace the satellite in a horizontal direction.
Gravity works in the vertical direction and force is perpendicular to the displacement.
So, work done is,
\[ \Rightarrow W = Fs\cos {90^{\text{o}}}\]
We know that \[\cos {90^{\text{o}}} = 0\]
Now we substitute the value,
\[ \Rightarrow W = F.s \times 0\]
Further solving, we get,
\[W = 0\]

Therefore, work done by the satellite is zero while orbiting around the earth.

Note
In this question, we have concluded that there is no work done on the satellite by gravity of the earth while rotating around the Earth. As we know that the work done is the transfer of the energy from one form to another form. It is the potential energy. And potential energy depends upon position, or the substance.