Orbital Velocity Calculator
Why Satellites Don't Fall
An object in circular orbit is falling continuously — it just happens to be moving sideways fast enough that the ground curves away underneath it at the same rate it drops. Orbital velocity is the specific speed at which that balance holds for a given orbital radius: any slower and the orbit decays inward, any faster and it stretches into an ellipse (or escapes entirely, past √2 times this speed). This calculator computes that balance point for any central body and orbital radius.
The Formula
Where G is the gravitational constant, M is the mass of the central body, and r is the orbital radius measured from that body's center. As with the escape velocity calculation, the calculator uses each body's standard gravitational parameter (GM) directly for precision.
Where This Applies
- Satellite deployment — every satellite, from a low-Earth-orbit CubeSat to a geostationary communications satellite, is placed at an altitude chosen specifically because it matches the orbital velocity for that radius.
- Understanding orbital decay — atmospheric drag slowly bleeds speed from low-orbit satellites; once their velocity drops below the value this formula predicts for their altitude, they spiral inward.
- Comparing planets and moons — the same formula explains why the Moon orbits Earth far more slowly than the International Space Station does, despite both being in "orbit" — the Moon's orbital radius is over 60 times larger.
Orbital Velocity at Surface Radius
| Central body | Radius used | Orbital velocity |
|---|---|---|
| Earth | 6,371 km | 7.910 km/s |
| Moon | 1,737.4 km | 1.680 km/s |
| Mars | 3,389.5 km | 3.555 km/s |
| Jupiter | 69,911 km | 42.569 km/s |
| Sun | 696,340 km | 436.561 km/s |
These are theoretical surface-skimming speeds (no atmosphere or terrain considered), computed from each body's own GM constant — real satellites orbit at higher altitudes, which lowers the required velocity slightly compared to these figures.
How to Use This Calculator
- Choose a mode: "Select Known Body" or "Custom Mass & Radius."
- In known-body mode, select the central body (Earth, Moon, Mars, Jupiter, or Sun) and enter the orbital radius in kilometers.
- In custom mode, enter the central body's mass in kilograms along with the orbital radius in kilometers.
- Select Calculate to get the circular orbital velocity.
Related Calculations
Multiply this result by √2 and you'd have the local escape velocity — check it directly with the Escape Velocity Calculator, or see how orbital radius relates to orbital period via the Orbital Period Calculator.