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#### Equipotential

Look at any of the green lines on the diagram above. The line is drawn a distance from the centre of the Earth. The potential at any point on that dotted line is the same, calculated from:

As this is a series of points of equal potential, we call it an equipotential.

If you follow a path along an equipotential, your Ep doesn't change. Therefore you don't lose or gain energy. No work is done.

That's the theory behind why satellites can remain in space without always using energy to stay there. They follow equipotentials. It also applies to the Moon orbiting the Earth and the Earth orbiting the Sun. They all follow equipotentials (almost!).

If you draw equipotentials showing uniform, regular changes (steps) in potential i.e. an equipotential every 10MJkg-1, you will notice that the space between them increases as you move away from the Earth.

This shows that the potential changes more rapidly for changes in height near the Earth than for changes of height a long distance away from the Earth.

In fact, it can be shown that:

Potential gradient = gravitational field strength, g.

Or, for the mathematicians amongst you: