Orbital Velocity Calculator
Work out how fast an object must travel to stay in orbit. Pick a planet or enter the central mass, choose a circular or elliptical orbit, and get the orbital velocity, period, escape velocity, orbital energy, and the speeds at the closest and farthest points, all with the math shown.
Formula
Worked example
A low Earth orbit uses M = 5.972×10²⁴ kg and r = 6.371×10⁶ m. v = √(6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6.371×10⁶) = √(6.26×10⁷) ≈ 7,910 m/s ≈ 7.91 km/s. Escape velocity there is √2 times that, about 11.2 km/s.
What orbital velocity means
Orbital velocity is the exact speed at which an object must travel, perpendicular to the line joining it to the central body, to maintain a stable circular orbit. At that speed the inward pull of gravity is precisely the centripetal force needed to keep the object curving around the body instead of falling into it or flying away. Setting gravity equal to centripetal force, G·M·m / r² = m·v² / r, the orbiting mass m cancels from both sides and rearranging gives v = √(G·M / r). This is why a feather and a satellite at the same altitude need the same orbital speed: only the central mass M and the orbital radius r matter, never the mass of the orbiting object itself. The product G·M is used so often that it has its own name, the standard gravitational parameter μ.
How radius and central mass change the speed
Because the radius sits under a square root in the denominator, orbital velocity falls off slowly as you move outward: doubling the orbital radius reduces the required speed by a factor of about 1.41, not by half. This is why satellites in low Earth orbit race around the planet at nearly 7.9 km/s, while the Moon, roughly sixty Earth radii away, only needs about 1 km/s to stay in its orbit. The central mass works the opposite way, a more massive body pulls harder, so orbiting it at a given radius demands a higher speed. Orbiting the Sun at its surface would require over 400 km/s, reflecting its enormous mass. You can enter the orbit either as an altitude above the surface or as a radius from the centre; the calculator adds the body radius for you when you give an altitude.
Elliptical orbits and the vis-viva equation
Most real orbits are ellipses, not perfect circles, so the speed is not constant. The vis-viva equation, v² = μ(2/r − 1/a), gives the speed at any distance r when the semi-major axis is a (the average of the closest and farthest radii). The object moves fastest at periapsis, its closest approach, and slowest at apoapsis, its farthest point, trading kinetic for potential energy as it climbs and falls. The shape is captured by the eccentricity e, which runs from 0 for a circle toward 1 for a very stretched ellipse. Switch the orbit type to elliptical and enter the periapsis and apoapsis altitudes to get both speeds, the eccentricity, the semi-major axis and the period.
From orbital speed to period, energy and escape velocity
Once the orbital velocity is known, the orbital period follows from Kepler’s third law, T = 2π√(a³/μ), giving the time for one complete loop. The total orbital energy, E = −μ·m / 2a, is negative for any bound orbit and depends only on the semi-major axis, not the eccentricity, so enter the orbiting object’s mass to see it. Orbital velocity also connects directly to escape velocity, the speed needed to break free of the body’s gravity entirely: escape velocity is exactly √2 (about 1.41) times the circular orbital velocity at the same radius. These relationships make the orbital velocity equation a foundation of mission planning, from sizing the burn that places a satellite in low Earth orbit to estimating the speed of a planet around its star.
Approximate low-orbit velocities
| Body | Central mass (kg) | Radius (m) | Orbital velocity | Escape velocity |
|---|---|---|---|---|
| Moon | 7.34×10²² | 1.74×10⁶ | 1.68 km/s | 2.38 km/s |
| Mars | 6.42×10²³ | 3.39×10⁶ | 3.55 km/s | 5.03 km/s |
| Earth | 5.97×10²⁴ | 6.37×10⁶ | 7.91 km/s | 11.2 km/s |
| Jupiter | 1.90×10²⁷ | 6.99×10⁷ | 42.6 km/s | 60.2 km/s |
| Sun | 1.99×10³⁰ | 6.96×10⁸ | 437 km/s | 618 km/s |
Circular orbital speed just above the surface of each body, using v = √(G·M / r).
Frequently asked questions
Does the mass of the orbiting object affect orbital velocity?
No. In the equation v = √(G·M / r), M is the mass of the central body being orbited; the mass of the orbiting object cancels out of the derivation. A small satellite and a large space station at the same altitude need the same orbital speed. The orbiting mass only matters if you want the total orbital energy, which scales with it.
What is the difference between orbital velocity and escape velocity?
Orbital velocity keeps an object in a stable circular orbit at a given radius. Escape velocity is the speed needed to leave the body’s gravity for good, and it is exactly √2 (about 1.41) times the circular orbital velocity at the same radius. This calculator reports both side by side.
How do I find the speed in an elliptical orbit?
Use the vis-viva equation, v² = μ(2/r − 1/a), where μ = G·M, r is the current distance and a is the semi-major axis (the average of the closest and farthest distances). The object is fastest at periapsis and slowest at apoapsis. Switch the orbit type to elliptical and the calculator returns both speeds, the eccentricity and the period.
Why does a higher orbit need a slower speed?
Orbital radius appears under a square root in the denominator, so a larger radius lowers the required speed. Gravity also weakens with distance, meaning less centripetal force, and therefore a slower speed, is needed to hold the orbit at greater altitude.