Orbital Velocity Calculator
Enter central mass and orbital radius to compute the circular orbital velocity v = √(G·M/r).
Input Data
Results
At a glance:The circular orbital velocity is the speed at which the centripetal acceleration v²/r is provided entirely by gravity GM/r², giving v = √(GM/r) = √(μ/r), with μ = GM the gravitational parameter. It is the speed a satellite needs to stay in a circular orbit at radius r (the first cosmic velocity at a planet's surface). It is smaller than the escape velocity by a factor √2: v_esc = √2·v. At larger r the required speed is lower. This tool computes v from central mass M and radius r.
Formula
v = √(GM/r) = √(μ/r)
v_esc = √2·v
$$v = \sqrt{\dfrac{G\,M}{r}}$$How to Use
- Enter the central mass M (kg).
- Enter the orbital radius r (m).
- The calculator returns v.
Case Studies
LEO speed
M = 5.97e24, r = 6.77e6 m.
v = √(3.986e14/6.77e6) ≈ 7670 m/s.
About 7.7 km/s for a 400 km orbit.
FAQ
Is this the launch speed?
No — it is the speed once in orbit at radius r, ignoring atmosphere and losses. Reaching it requires rockets; the 'first cosmic velocity' at Earth's surface is ~7.9 km/s.
How is it related to escape velocity?
v_esc = √2·v_orbit at the same radius. Escape needs about 41% more speed than a circular orbit.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.