Gravitational Potential

Definition

The potential energy per kilogram at a point in a gravitational field — the energy you would gain or spend moving 1 kg there.

$V = -\frac{GM}{r}$

Symbol: $V$ · Unit: joule per kilogram (J/kg)

Technical definition

V = −GM/r, with zero defined at infinity. The field follows from g = −∇V; only potential differences determine work done.

Example

At Earth's surface V ≈ −62.6 MJ/kg — launching 1 kg to escape needs +62.6 MJ of energy, which is why escape velocity is 11.2 km/s.

Common confusion

Gravitational potential is negative by convention (zero at infinity), which confuses students. 'Higher' potential means less negative — a high satellite has higher potential energy than a low one.