Orbital Velocity Calculator
Enter the central body's mass and the orbit radius to find the speed of a circular orbit and how long one lap takes, using v = sqrt(GM/r).
How to use the orbital velocity calculator
- Enter the central body's mass in kilograms or in solar masses.
- Enter the orbital radius in metres or kilometres.
- Read the orbital velocity and the time for one full orbit.
Examples
Low Earth orbit
mass = 5.972e24 kg, radius = 6771 km
v = 7.67 km/s, period about 92 minutes
Earth around the Sun
mass = 1 solar mass, radius = 1 AU
v = 29.8 km/s
Frequently asked questions
What is orbital velocity?
Orbital velocity is the speed a body needs to stay in a circular orbit at a given radius, where gravity exactly supplies the centripetal force.
What is the orbital velocity formula?
For a circular orbit, v = sqrt(G x M / r), where G is the gravitational constant, M is the central mass and r is the orbit radius from the centre.
How is the orbital period found from the velocity?
The period is the circumference divided by the speed, T = 2 x pi x r / v. It is the time the body takes to complete one full circular orbit.
Why is low Earth orbit about 7.7 km/s?
At roughly 400 km altitude the orbit radius is about 6771 km, and Earth's mass gives a circular speed near 7.67 km/s with a period of about 92 minutes.
Does the orbiting body's own mass matter?
No, for a small body around a much larger one it cancels out. The circular speed depends only on the central mass and the orbit radius.
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