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Potential energy is stored energy showing various forms of appearance, i.e. gravitational potential energy, elastic, chemical, or electrical potential energy. The energy is stored by doing work against a force such as gravity or the spring in a clockwork motor.
Gravitational potential energy is an important form of energy, having much impact on our daily lives (think of the increased gas consumption when driving a car up a mountain road, or think of power utilities storing energy in water reservoirs).
The gravitational potential energy Ug of an object is equal to the work that would have to be done by a constant gravitational force F = mg on the object to move it against the force by a distance h, and is equal to
Ug = mgh
where m is the mass of the object, and g the acceleration due to gravity (typical units would be kilograms for m, m/s-2 for g, and meters for h). In relation to spacecraft and astronomy g is not constant and the formula becomes an integral. More on gravitational potential energy can be found in Lectures in Physics