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Gravitational potential energy
Intermediate
Negative energy of attracting masses.
U = −GMm/rFor two masses U = −GMm/r, with zero at infinity. It is negative because work must be done to separate them. Near the surface ΔU ≈ mgh.
U for a 1 kg object on Earth's surface = −62.6 MJ.
mgh works only for small height changes.
In more detail
Gravitational potential energy between two masses is U = −GMm/r, which is negative and approaches zero at large separation. Bound systems have negative total energy.
Real-world uses
- Planets are bound to the Sun because their total energy is negative.
- Satellite energy is calculated from this potential.
- A satellite's total energy depends on its gravitational potential energy, which is negative, to keep it bound to the planet.
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Frequently asked questions
Why is it negative?
Because gravity is attractive, and zero potential is chosen at infinite separation.
Is it the same as mgh?
Near Earth's surface, mgh is an approximation of the change in this potential.
Why is gravitational potential energy negative?
It is defined to be zero at infinity, and bringing masses together releases energy, so the energy at closer separations is lower.
Related topics in Gravitation & Orbits
Variation of g with depth · Effect of Earth's rotation on g · Gravitational field · Gravitational potential · Field of a spherical shell · Field inside a uniform sphere