Orbital Velocity Calculator
Calculate the speed needed for a circular orbit around any celestial body using v = √(GM ÷ r).
How it works
- 1Select a central body (Earth, Sun, Mars, Jupiter, Moon, or Custom) to set its mass M, then enter the orbital radius in kilometres measured from the centre.
- 2The calculator converts the radius to metres and evaluates v = √(GM ÷ r), where G = 6.6743×10⁻¹¹ N·m²/kg².
- 3Results are shown instantly in m/s, km/s, and km/h.
Use cases
- Verify the ISS speed (≈ 7.66 km/s at ~400 km altitude above Earth).
- Compute a geostationary satellite’s velocity at an orbital radius of 42,164 km (≈ 3.07 km/s).
- Explore orbital mechanics for custom mission designs or world-building.
Frequently asked questions
What formula does this calculator use?
The circular orbital velocity formula v = √(GM ÷ r), where G = 6.6743×10⁻¹¹ N·m²/kg², M is the central body’s mass in kg, and r is the orbital radius in metres, measured from the centre of the body (not the surface).
How do I find the correct orbital radius?
Orbital radius r is measured from the body’s centre: r = mean radius + altitude. The ISS orbits ~400 km up; Earth’s mean radius is ~6,371 km, so r ≈ 6,771 km. Enter 6771 to get the ISS speed.
What does a low Earth orbit work out to?
For a circular orbit 400 km up (r ≈ 6,771 km): v = √(6.6743×10⁻¹¹ × 5.972×10²⁴ ÷ 6,771,000) ≈ 7,672 m/s ≈ 7.67 km/s, matching real ISS telemetry.
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