Gravitational potential

Intermediate

Potential energy per unit mass.

Key relationV = −GM/r

V = −GM/r is the potential energy per unit mass. The field is the negative gradient of V. Potential differences give the work per unit mass.

Worked example

On Earth's surface V = −62.6 MJ/kg.

Common mistake

Potentials are scalars, so simply add.

In more detail

Gravitational potential is the potential energy per unit mass, V = −GM/r. It gives a simple way to compute energies and escape speeds.

Mission designers compute energy budgets for spacecraft using potential.
Astronomers use gravitational potential to model galaxy dynamics.
Engineers use the gravitational potential to find how much energy is needed to move a payload between two points in space.

What are the units?

Joules per kilogram, equal to metres squared per second squared.

Is it the same as gravitational potential energy?

It is potential energy per unit mass, so multiply by the mass to get energy.

How does potential differ from potential energy?

The potential is the potential energy per unit mass, so it does not depend on the mass of the object.