Orbital Velocity Calculator
Solve v = √(GM/r) for the circular orbital velocity around a body, or rearrange to find the central mass or orbital radius. Two 3D diagrams show concentric orbits at different radii and compare fast, tight orbits to slow, wide ones, with charts showing how orbital velocity falls off with radius and comparing real orbits across the solar system.
Reviewed by the ToolNestr Editorial Team — July 2026
Pick a preset orbit, or enter a custom mass and radius.
Orbits at different radii
1. Concentric orbits around a central body
A central sphere with three concentric orbital paths at different radii, each carrying its own satellite — the wider orbits sit farther from the central body.
2. Tight, fast orbit vs wide, slow orbit
The tight inner orbit has a long velocity arrow (fast), while the wide outer orbit has a short velocity arrow (slow) — both tangent to their respective paths.
Orbital velocity graphs
How it works
The core idea in one line: Orbital velocity is the exact speed at which gravity's pull on an orbiting object supplies precisely the centripetal force needed to keep it moving in a stable circle, rather than falling in or flying away.
v = √(GM / r)
circular orbital velocity from central mass and radius
G = 6.674 × 10⁻¹¹ N·m²/kg²
universal gravitational constant
Setting gravitational force equal to the centripetal force requirement, GMm/r² = mv²/r, and canceling the orbiting mass m gives v = √(GM/r). Rearranged, M = v²r/G solves for the central mass, and r = GM/v² solves for the orbital radius. Because v falls off as 1/√r, an orbit four times farther out needs only half the speed to stay in a stable circle.
Worked example 1 — low Earth orbit (LEO)
Given: A satellite orbits Earth at 400 km altitude: M = 5.972×10²⁴ kg, r = 6,771,000 m (Earth radius 6.371×10⁶ m + 4×10⁵ m altitude).
This roughly 7.67 km/s speed is why LEO satellites, including the ISS, orbit the Earth in only about 90 minutes.
Worked example 2 — geostationary orbit (GEO)
Given: A geostationary satellite orbits at r = 4.216×10⁷ m, with Earth's mass M = 5.972×10²⁴ kg.
GEO satellites orbit much slower than LEO satellites because they are far higher up — but their orbital period still matches Earth's 24-hour rotation, keeping them fixed above one point on the ground.
Orbital velocity across the solar system
Radius dominates: even though the Sun is vastly more massive than Earth, Mars orbits it slower than a satellite orbits close to Earth, because Mars is so much farther from its central body.
| Orbit | Central masskg | Radiusm | v_orbitkm/s |
|---|---|---|---|
| Moon around Earth | 5.972 × 10²⁴ | 3.844 × 10⁸ | 1.018 |
| GEO satellite ★ | 5.972 × 10²⁴ | 4.216 × 10⁷ | 3.075 |
| LEO satellite (400 km) | 5.972 × 10²⁴ | 6.771 × 10⁶ | 7.672 |
| Mars around Sun | 1.989 × 10³⁰ | 2.279 × 10¹¹ | 24.135 |
| Earth around Sun | 1.989 × 10³⁰ | 1.496 × 10¹¹ | 29.788 |
★ GEO reference. Orbital velocity ∝ √(M/r) — Earth around the Sun is faster than Mars around the Sun purely because Earth orbits closer, despite both circling the same central mass.
Where orbital velocity actually matters
🛰️ Satellite mission design
Engineers use v = √(GM/r) to determine exactly how fast to launch a satellite into a target orbit, whether a fast low-Earth orbit for imaging or a slower geostationary orbit for communications that stays fixed above one location.
🚀 Rendezvous and docking
Spacecraft docking with the International Space Station must match both the ISS's orbital radius and its orbital velocity almost exactly — any mismatch in speed means drifting away or a dangerously fast collision.
🌕 The Moon's stable orbit
The Moon's roughly 1.02 km/s orbital velocity around Earth has stayed remarkably stable for billions of years, a natural demonstration of the same physics used to design every artificial satellite orbit today.
🔭 Exoplanet detection
Astronomers infer a planet's orbital velocity around its star from the periodic Doppler wobble it induces, then use v = √(GM/r) in reverse to estimate the star's mass or the planet's orbital radius.
Common misconceptions
"A more massive central body always means a faster orbit at any given distance."
Mass increases orbital velocity, but distance matters just as much: v = √(GM/r) falls off with the square root of radius. A satellite very close to a small planet can orbit faster than one very far from a much larger star.
"Objects in orbit are not affected by gravity — that's why they float."
Orbiting objects are very much affected by gravity — it is the entire force providing the centripetal acceleration that curves their path into a circle. "Floating" (weightlessness) happens because both the spacecraft and everything inside it are in continuous free-fall together, not because gravity has vanished.
"A heavier satellite needs a higher orbital velocity."
Just like escape velocity, the orbiting object's own mass cancels out of the physics entirely — a heavier or lighter satellite at the same radius around the same central body needs exactly the same orbital velocity.
"Higher orbits mean faster speeds, since they cover more ground."
The opposite is true for orbital velocity — v = √(GM/r) actually decreases as radius increases. Higher orbits are slower (though they can still take a longer total time to complete one revolution, or a shorter one, depending on the combination of speed and circumference).
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §13.4 "Satellite Orbits and Energy" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 13, Gravitation (Satellites: Orbits and Energy).
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 13, Universal Gravitation (Kepler's Laws).
v = √(GM/r) with G ≈ 6.674×10⁻¹¹ N·m²/kg² (CODATA), for a stable circular orbit. Preset masses and radii are standard textbook/NASA reference values. Results are rounded for display.
How to use this calculator
Pick a preset orbit
Choose LEO, GEO, the Moon, or Mars around the Sun to auto-fill mass and radius.
Choose the unknown
Solve for orbital velocity, central mass, or orbital radius from the other two.
Compare on the chart
See how orbital velocity falls off with radius, and how it compares across real orbits.
Related tools
Frequently asked questions
What is orbital velocity?
Orbital velocity is the speed an object needs to maintain a stable circular orbit around a central body at a given radius, where gravity exactly supplies the centripetal force needed to keep the orbit circular: v = √(GM/r), with G the gravitational constant and M the central body's mass.
How is orbital velocity different from escape velocity?
Orbital velocity (v = √(GM/r)) keeps an object in a stable circular orbit, while escape velocity (v_esc = √(2GM/r)) is the speed needed to leave the body's gravity entirely. Escape velocity is always exactly √2 (about 1.414) times the circular orbital velocity at the same radius.
Why is the International Space Station's orbital velocity so high?
At an altitude of about 400 km, the ISS needs roughly 7.67 km/s to maintain a stable low Earth orbit — gravity is still nearly as strong there as at the surface, so a very high speed is needed to "fall around" the Earth rather than straight down.
Why does the Moon orbit slower than satellites near Earth?
Orbital velocity falls off as 1/√r — since the Moon orbits at about 3.84×10⁸ m, roughly 57 times farther than a low-Earth-orbit satellite, its required orbital velocity is much lower (about 1.02 km/s) despite orbiting the same planet.
Does orbital velocity depend on the mass of the orbiting object?
No — just like escape velocity, the mass of the orbiting satellite cancels out of the equations of motion entirely. Orbital velocity depends only on the mass of the central body M and the orbital radius r, not on how heavy the satellite itself is.