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Gravitational Potential Energy (Orbital)

U=−GMmrU = -\frac{GMm}{r}
sig figs

Worked example: 1000 kg at r = 6.771e6 m from Earth → U = -5.887e10 J. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
G=6.6743×10−11 m3/(kg⋅s2)G = 6.6743 \times 10^{-11}\ \text{m}^{3}\text{/(kg}{\cdot}\text{s}^{2}\text{)}Newtonian constant of gravitation

Where Gravitational Potential Energy (Orbital) fits

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See also

Escape Velocity: Both use central mass and distance from central mass.Gravitational Field Strength: Both use central mass and distance from central mass.Orbital Period: Both use central mass and distance from central mass.Orbital Velocity: Both use central mass and distance from central mass.
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Gravitational Potential Energy (Orbital) explained

MmrU

Gravitational potential energy is negative by convention: the zero is set at infinite separation, and every real pair of masses sits below it, in an energy "well" of depth GMm/r. A 1 000 kg satellite at the ISS's orbital radius, r = 6.79 × 10⁶ m, has U = −6.674 × 10⁻¹¹ × 5.97 × 10²⁴ × 1 000 / 6.79 × 10⁶ ≈ −5.87 × 10¹⁰ J: about 59 GJ that a launch vehicle must partly repay to lift it there from the surface, plus the kinetic energy of orbit.

The minus sign carries real physics. A bound orbit has total energy E = U/2 (the virial theorem's ½ shows up here: kinetic energy equals half the well depth), and escaping requires pumping E up to zero, which is exactly where the escape-velocity formula comes from. It also produces gravity's strangest habit: drag a satellite down and it speeds up, because falling deeper into the well converts potential energy into more kinetic energy than the drag removes.

Gravitational Potential Energy (Orbital) formula

U=−GMmrU = -\frac{GMm}{r}
Where
  • UU= Potential energy (J)
  • MM= Central mass (kg)
  • mm= Orbiting mass (kg)
  • rr= Separation (m)
In this toolkit

Gravitation and orbital mechanics

8 formulasNewton's inverse-square law and what falls out of it in orbit — field strength, orbital speed and period, Kepler's third law, and escape velocity.

Revised 16 October 2026
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formula.expert. (2026, October 16). Gravitational Potential Energy (Orbital) Calculator. https://formula.expert/solvers/orbital-potential-energy

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