The gravitational potential at a point in space is defined as:

The work done on a unit mass when moving it to that point from a point at infinity.

The zero point for gravitational potential is at infinity, so as we are moving towards the Earth, we are getting work out of the system rather than having to put effort in. That is because the force of gravity tugs on a mass and accelerates it towards the Earth. Therefore gravitational potential is negative.

If we moved the object away to infinity, we would have to do work on the object so the gravitational energy would be positive.

The equation for gravitational potential is:

V = -GM/r

Where:

G = 6.67 x 10^-11 N m² kg^-2;

M = mass of Earth or another planet;

r = distance from centre of the planet.

Now, g = GM/r² and so GM/r = gr

therefore V = gr

If we look at a graph of gravitational field strength against distance, the gravitational potential is going to be the area under the graph.

If we plot V against r, we get the following graph:

Ep = mgh is only true when we are very close to the Earth's surface. So do NOT use it for objects out in space. Instead use:

E_p = F_g x r

E_p = GM₁M₂/r

Links to related pages

GPE - pre-A Level

Gravity

Gravitational field strength (g)

Gravitational force