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Orbital Velocity

v=GMrv = \sqrt{\frac{GM}{r}}
sig figs

Worked example: ISS: Earth mass, r = 6.771e6 m → v = 7.672 km/s. Press Try an example to run it live, then adjust anything.

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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 Orbital Velocity fits

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See also

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

Mrv

A satellite stays in a circular orbit when gravity supplies exactly the centripetal force it needs: setting GMm/r² equal to mv²/r and cancelling the satellite's mass gives v = √(GM/r). The cancellation is the famous part: orbital speed depends only on the central body's mass and the orbit's radius, never on what is orbiting. The International Space Station, circling Earth (M ≈ 5.97 × 10²⁴ kg) at r ≈ 6.79 × 10⁶ m, moves at √(6.674 × 10⁻¹¹ × 5.97 × 10²⁴ / 6.79 × 10⁶) ≈ 7 660 m/s: about 7.7 km/s, one lap of the planet every 92 minutes.

The inverse square root also explains a counter-intuitive fact: higher orbits are slower. GPS satellites at r ≈ 26 600 km amble along at 3.9 km/s, half the ISS's speed. Astronomers run the formula in reverse constantly: measure a moon's or a star's orbital speed and radius, and M = v²r/G weighs the central body, which is how we know the mass of everything from Jupiter to the black hole at the centre of the Milky Way.

Orbital Velocity formula

v=GMrv = \sqrt{\frac{GM}{r}}
Where
  • vv= Orbital velocity (m/s)
  • MM= Central mass (kg)
  • rr= Orbital radius (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). Orbital Velocity Formula & Calculator. https://formula.expert/solvers/orbital-velocity

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