Result

Circular orbital speed

v = \frac{GM}{r}

Statement

The speed needed to maintain a circular orbit of radius r around a mass M.

Symbols and units

When it applies

Circular orbits only; elliptical orbits require the vis-viva equation instead.

Don't use when

Only valid for a circular orbit — an elliptical orbit requires the vis-viva equation, where speed varies with position.

Derivation

Set the gravitational force equal to the centripetal force required for circular motion:

\frac{GM m}{r ^{2}} = \frac{m v ^{2}}{r}

Solve for v; the orbiting mass cancels out entirely:

v = \frac{GM}{r}

Worked examples

Speed of a low Earth orbit satellite

At r = 6.77×10⁶ m:

v = \frac{( 6.674 \times 1 0 ^{- 11} ) ( 5.97 \times 1 0 ^{24} )}{6.77 \times 1 0 ^{6}} \approx 7.67 km/s

Watch out for

Orbital speed decreases with orbital radius — a higher orbit is a slower one, the opposite of everyday intuition.

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