Orbital Velocity Calculator
Calculate the velocity required for a circular orbit, with written solution steps, formula substitution, gravity, and orbital period.
For a satellite altitude, add the planet radius to the altitude before entering r.
Circular Orbit Diagram and Values
Step-by-Step Orbital Velocity Solution
Step 1: Use the circular-orbit velocity formula
For a circular orbit, gravity provides the centripetal force needed to keep the object moving around the central body.
Step 2: Substitute the mass and orbital radius
Use the mass of the central body and the distance from its centre to the orbit.
Step 3: Calculate the orbital velocity
Related orbital values
At this orbital radius, the gravitational acceleration is g = GM/r squared and one complete circular orbit takes the period below.
Orbital Velocity Calculator
This Orbital Velocity Calculator finds the speed required for a stable circular orbit around a planet, moon, star, or other massive object. Enter the mass of the central body in kilograms and the orbital radius in metres. The result is shown in metres per second and kilometres per second, followed by written steps that explain the formula, substitution, and final calculation.
The calculator also estimates gravitational acceleration and orbital period at the selected radius. It is useful for physics homework, satellite-orbit examples, astronomy revision, and understanding how gravity determines the motion of orbiting objects.
Circular Orbital Velocity Formula
The circular orbital velocity formula is vorb = square root of GM divided by r. G is the gravitational constant, M is the mass of the central body, and r is the distance from its centre to the orbit. Use SI units: kilograms for mass and metres for radius. The result is a speed in metres per second.
A lower circular orbit needs a higher speed because gravity is stronger closer to the central body. A higher orbit moves more slowly but takes longer to complete one orbit. This equation assumes a circular orbit and a small orbiting object, so it is an ideal starting point rather than a complete mission-planning model.
How to Calculate Orbital Velocity
First identify the central body's mass. Next calculate the orbital radius from the centre, not simply the satellite altitude above the surface. For example, add Earth's radius to a satellite's altitude. Then substitute G, M, and r into the formula and take the square root. The step-by-step solution on this page shows each of these stages with your live values.
For a low Earth orbit approximately 400 km above the surface, the orbital radius is about 6.771 x 10 to the power of 6 m. The resulting circular orbital speed is roughly 7.67 km/s, and the orbital period is around 92 minutes. Actual satellite paths are affected by atmospheric drag, non-circular paths, and Earth's shape.
Orbital Velocity and Escape Velocity
At the same radius, escape velocity is square root of 2 times the circular orbital velocity. An orbiting satellite is not beyond Earth's gravity; it is continuously falling toward Earth while moving sideways fast enough to keep missing it. Escape velocity is the threshold speed for leaving the gravitational field without further propulsion in the ideal two-body model.
Use this calculator for circular-orbit estimates. Use an escape velocity calculator when you need the speed needed to leave the central body's gravity, and use the universal gravitation calculator when you need the gravitational force between two masses.
Frequently Asked Questions
What is orbital velocity?
It is the speed an object needs to maintain an orbit at a given distance from a central body.
Does orbital radius include a planet's radius?
Yes. Measure r from the centre of the planet to the orbiting object.
Why is orbital velocity lower at higher altitude?
Gravity is weaker farther from the central body, so a lower circular speed is needed.
Is escape velocity the same as orbital velocity?
No. Escape velocity is square root of 2 times circular orbital velocity at the same radius.