Space · Orbits
Orbital velocity calculator.
Enter an orbit height to get the speed, the period and the escape speed at that distance.
Inputs
Orbit
Enter an orbit height.
How orbital velocity is calculated
For a circular orbit of radius r around a body with gravitational parameter μ = GM, the speed is v = √(μ/r). For an ellipse the vis-viva equation gives the speed at any distance r: v = √(μ (2/r − 1/a)), where a is the semi-major axis, the average of the closest and farthest distances from the centre. The period is T = 2π √(a3/μ). GM values are the JPL DE440 figures; body radii come from the NASA fact sheets.
Worked example. A circular orbit 400 km above Earth is r = 6,378 + 400 = 6,778 km from the centre. v = √(398,600.4 / 6,778) = 7.67 km/s, about 27,600 km/h, and one lap takes 92.6 minutes. At the geostationary radius of 42,164 km the speed drops to 3.07 km/s and the period is about 23.9 hours.
Higher orbits are slower, not faster, because gravity is weaker and the path is longer. Atmospheric drag, a non-round planet and other bodies are ignored.
Frequently asked questions
How fast is the speed needed to orbit Earth?
About 7.7 km/s (roughly 27,600 km/h) at 400 km altitude, from v = √(GM/r). It falls as the orbit gets higher.
Why are higher orbits slower?
Gravity weakens with distance, so less speed is needed to balance it, and the circle is longer, so one lap takes much longer. The speed scales with 1/√r.
What is the orbital velocity at geostationary altitude?
About 3.07 km/s at a radius of 42,164 km from Earth’s centre, with a period close to one day.
How does orbital velocity relate to escape velocity?
Escape speed at the same distance is √2 (about 1.41) times the circular orbital speed.
How do I calculate an elliptical orbit?
Enter the lowest and highest heights. The tool takes the semi-major axis as their average and applies the vis-viva equation at each end.
Sources
Checked
- NASA JPL SSD: Astrodynamic Parameters (GM values, DE440)
- Wikipedia: Vis-viva equation
- NASA NSSDCA: Planetary Fact Sheet (metric)
- NASA NSSDCA: Moon Fact Sheet
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Scope
Ideal two-body orbits with no drag or perturbations. Education only.