**Potential energy** or **potential** is energy stored in an object or substance. In most scientific circles, potential energy is symbolized by .

Table of contents |

2 Elastic potential energy 3 Chemical potential energy 4 Electrical potential energy 5 Relation between potential energy and force |

In relation to spacecraft and astronomy *g* is not constant and the formula becomes an integral. In the case of a sphere of uniform mass (such as a planet), with *h* measured above the surface, the integral takes the form:

Where is the radius of the sphere, *M* is the mass of the sphere, and *G* is the gravitational constant.

If *h* is instead taken to be the distance from the center of the sphere, then outside the sphere the potential energy relative to that at the center has two terms:

,

which evaluates to:

[We may also want to link to an explanation of that second term (the gravitational forces created by hollow spherical shells)]

A frequently adopted convention is that an object infinitely far away from an attracting source has zero potential energy. Relative to this, an object at a finite distance *r* from a source of gravitation has negative potential energy. If the source is approximated as a point mass, the potential energy simplifies to:

This energy is stored as the result of a deformed solid such as a stretched spring. As a result of Hooke's law, it is given by:

For example, gravity is a conservative force. The work done by a unit mass going from point A with to point B with by gravity is and the work done going back the other way is so that the total work done from

In practical terms, this means that you can set the zero of anywhere you like. You might set it to be zero at the surface of the Earth or you might find it more convenient to set it zero at infinity.

A thing to note about conservative forces is that the work done going from A to B does not depend on the route taken. If it did then it would be pointless to define a potential at each point in space. An example of a non-conservative force is friction. With friction, the route you take does affect the amount of work done, and it makes no sense at all to define a potential associated with friction.

All the examples above are actually force field stored energy (sometimes in disguise). For example in elastic potential energy, stretching an elastic material forces the atoms very slightly, further apart. Powerful electromagnetic forces try to keep the atoms at their optimal distance and so elastic potential is actually electromagnetic potential. Having said that, scientists rarely talk about forces on an atomic scale. Everything is phrased in terms of energy rather than force. You can think of potential energy as being derived from force or you can think of force as being derived from potential energy.