Case 1
- Mass of the central body
- 5.97210²⁴ kg
- Orbital radius from the centre
- 6771000m
7,672.490m/s
Open with these valuesOrbital Velocity Calculator
7,672.490m/s
Result: 7,672.490 m/sA satellite in low Earth orbit travels at 7672 m/s, about 7.67 km/s. The speed depends only on the central mass and the orbital radius, and it falls as the orbit widens — geostationary satellites manage on 3.07 km/s. Enter the mass in units of 10²⁴ kg: Earth is 5.972.
Worked examples
Case 2
- Mass of the central body
- 5.97210²⁴ kg
- Orbital radius from the centre
- 42164000m
3,074.623m/s
Open with these valuesCase 3
- Mass of the central body
- 198900010²⁴ kg
- Orbital radius from the centre
- 149600000000m
29,788.899m/s
Open with these valuesHow it's calculated
v = √(G × M ÷ r)
- StepEnter the central mass in units of 10²⁴ kg — Earth is 5.972.
- StepEnter the orbital radius in metres, measured from the centre.
- ResultRead the speed in m/s; divide by 1000 for km/s.
What this number means
A higher orbit means a slower satellite
The radius sits in the denominator under the square root, so the speed drops as the orbit widens. Low Earth orbit needs 7672.490413 m/s, while a geostationary satellite six times farther out gets by on 3074.622911 m/s.
The radius runs from the centre, not the ground
A satellite 400 km up orbits at 6771000 m: the mean Earth radius of 6371000 m plus the altitude. Entering the 400000 m of altitude on its own would return 31567 m/s, more than four times too fast.
Escape velocity is √2 times this speed
Escaping puts 2GM/r under the root where a circular orbit puts GM/r, so it takes about 1.414 times the orbital speed at the same radius. A body needs roughly 41 percent more speed to leave than to keep circling.
Mass in units of 10²⁴ kg, radius in metres
Earth goes in as 5.972 and the Sun as 1989000, the way planetary tables list them. The answer arrives in m/s; divide by 1000 to read it in km/s.
Commonly misread
A satellite in a higher orbit has to fly faster to stay up.
It flies slower, because gravity is weaker farther out and less speed is needed to balance it. Geostationary is 3074.622911 m/s against 7672.490413 m/s in low Earth orbit.
Entering 400000 m for a satellite 400 km above the ground.
The radius is measured from Earth's centre, so it is 6371000 plus 400000, that is 6771000 m. The altitude alone yields 31567 m/s instead of 7672.490413 m/s.
Four times the radius should quarter the orbital velocity.
The square root halves the effect, so four times the radius gives half the speed. Nine times the radius leaves a third of it.
Reference table
| Central mass, radius | Orbit | Orbital velocity (m/s) |
|---|---|---|
| 5.972, 384400000 | Earth at the Moon's distance | 1018.289046 |
| 5.972, 42164000 | Geostationary orbit | 3074.622911 |
| 5.972, 6771000 | Low Earth orbit, about 400 km up | 7672.490413 |
| 5.972, 6371000 | At Earth's surface radius | 7909.680822 |
| 1989000, 149600000000 | Earth around the Sun | 29788.899321 |
Questions
How do I calculate orbital velocity?
Take the square root of the gravitational constant times the central mass, divided by the orbital radius: v = √(G × M / r), with G = 6.6743e-11. For a low Earth orbit at r = 6.771e6 m around Earth this gives about 7672 m/s. The mass box counts in units of 10²⁴ kg, so Earth is entered as 5.972.
What is orbital velocity?
Orbital velocity is the speed a body must travel to stay in a stable circular orbit around a central mass. At that speed gravity supplies exactly the centripetal force needed to keep bending the path into a circle, so the body neither spirals in nor flies away. It depends only on the central mass and the orbital radius.
Why does a higher orbit mean a slower speed?
Because the radius sits in the denominator under a square root. As the orbit widens gravity weakens, so less speed is needed to balance it. That is why a geostationary satellite at 3.07 km/s moves far slower than one in low Earth orbit at 7.67 km/s.
How is orbital velocity related to escape velocity?
Escape velocity is exactly √2, about 1.414 times the circular orbital velocity at the same radius, because escape uses 2GM/r under the root and a circular orbit uses GM/r. A body therefore needs roughly 41 percent more speed to break free than to circle at that distance.
Is the radius measured from the surface or the centre?
From the centre of the central body. A satellite 400 km above the ground orbits at a radius of about 6771000 m, which is Earth's mean radius of 6371000 m plus the altitude. Using the altitude alone would overstate the speed badly.
Why is the mass entered in units of 10²⁴ kg?
Because planetary tables list it that way, and because it keeps every central body inside the input range: Earth is 5.972, the Sun 1989000. Multiply by 10²⁴ to get kilograms again. The calculation itself works in kilograms.
Sources and last check
Information, not professional advice.