**Gravitational Potential Energy - A level standard**

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 m^{2} kg^{-2};

M = mass of Earth or another planet;

r = distance from centre of the planet.

Now, g = GM/r^{2} 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} = GM_{1}M_{2}/r

Links to related pages

GPE - pre-A Level

Gravity

Gravitational field strength (g)

Gravitational force