Work Done in Gravitational Fields

Whenever an object moves from one point to another in a gravitational field, in which its gravitational potential energy changes, work is done on the object by the field. This is because work done is equal to a change in energy.

The total energy of an object consists of the sum of its kinetic energy (Ek) and gravitational potential energy (Ep). The equations for both are as follows:

Since we are on the topic of gravitational fields, we only need to focus on gravitational potential energy and the changes in it. So if the gravitational potential energy of an object changes, then work has been done on the object by the gravitational field. The amount of work done by the field can be calculated by finding the change in the gravitational potential energy of the object. If there is no change, then the gravitational field hasn’t done any work. It is also important to remember that another equation for work is:

This equation comes in useful when you aren’t given any information about the changes in gravitational potential energy, but instead a graph similar to the one below. In the diagram, the area under the line is equal to the work done.