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Gravitational energy is the gravitational potential energy a body with mass has in relation to another massive object. It is potential energy associated with the gravitational field. Gravitational energy is dependent on the masses of two bodies, their distance apart and the Gravitational constant (G).
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In cases where the acceleration is fairly constant – such as dropping a ball on Earth – the gravitational energy of one of the bodies relative to the other is:
where
Newtonian mechanics
In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative. The gravitational potential energy is the potential energy an object has because it is within a gravitational field.
The force on point mass
To get the total work done by the gravitational force from infinity to the final distance
Because
General relativity
In general relativity gravitational energy is extremely complex, and there is no single agreed upon definition of the concept. It is sometimes modeled via the Landau–Lifshitz pseudotensor which allows for the energy-momentum conservation laws of classical mechanics to be retained. Addition of the matter stress–energy–momentum tensor to the Landau–Lifshitz pseudotensor results in a combined matter plus gravitational energy pseudotensor which has a vanishing 4-divergence in all frames; the vanishing divergence ensures the conservation law. Some people object to this derivation on the grounds that pseudotensors are inappropriate in general relativity, but the divergence of the combined matter plus gravitational energy pseudotensor is a tensor.