Orbital Velocity Calculator

What the orbital velocity calculator does

An object circling in orbit moves at a definite speed set by the size of its orbit and the time it takes to go around. This calculator finds that orbital velocity from the radius of the orbit and the period of the rotation.

Below is what orbital velocity is, the equation behind it, why an orbit is really continuous falling, and a worked example.

How to use it

1. Enter the radius of the orbit, the distance from the centre of rotation, with its power of ten.
2. Enter the period, the time for one full revolution, with its power of ten.
3. Press Calculate for the orbital velocity, or Reset to clear it.

What orbital velocity is

Orbital velocity is the speed at which an object travels along its orbit around a central body. A satellite circling Earth, the Moon going around our planet, or Earth itself sweeping around the Sun all have a particular orbital speed, set by how big the orbit is and how long each circuit takes. The International Space Station, for instance, races around Earth at nearly 7.7 kilometres per second, completing an orbit roughly every hour and a half.

This speed is not arbitrary. For a stable circular orbit at a given distance, there is exactly one speed that works, fast enough that the object keeps missing the ground as it falls, but not so fast that it flies off into space. Understanding orbital velocity is essential for launching satellites, planning space missions, and understanding the motion of planets and moons. This calculator computes it directly from the geometry of the orbit and its period.

The equation it uses

For a circular orbit, the orbital velocity is the distance travelled in one orbit divided by the time taken:

v = 2 π R ÷ T

Here v is the orbital velocity, R is the radius of the orbit, and T is the period, the time for one revolution. The numerator, two pi times the radius, is simply the circumference of the circular orbit, the full distance the object travels in going around once. Dividing that distance by the time it takes gives the speed. The calculator works out the circumference from the radius and divides by the period.

Why an orbit is endless falling

An orbit can seem mysterious, with satellites apparently hanging in space, but the reality is simpler and stranger: an orbiting object is constantly falling. Gravity pulls it toward the central body just as it pulls a dropped ball toward the ground. The difference is that the orbiting object is also moving sideways so fast that, as it falls, the curved surface of the planet falls away beneath it at the same rate. It keeps falling but never gets any closer, endlessly missing the ground.

This is why astronauts float inside the space station. They are not beyond gravity, which is nearly as strong up there as on the ground; they are in free fall, falling around the Earth together with their spacecraft, and falling things feel weightless. The orbital velocity is exactly the sideways speed that makes this perpetual falling into a stable circle. Too slow and the object spirals down; too fast and it climbs away. The calculator gives the speed that keeps an orbit balanced at its radius.

The link to mass and gravity

This calculator works from the geometry of the orbit, its radius and period, which is handy when you know how big an orbit is and how long it takes. But orbital velocity is also tied directly to the gravity of the central body. The same orbital speed can be written in terms of the central mass and the orbital radius, since it is gravity that holds the orbit together and sets how fast the object must move at a given distance.

Seen this way, an object orbiting closer to a body must move faster, and one orbiting farther out moves more slowly, which is exactly why inner planets race around the Sun while outer ones crawl. The two descriptions agree: the speed that balances gravity at a given radius is the same speed that carries the object once around in its period. This calculator uses the geometric form, but the underlying cause is always the pull of the central body's gravity.

Units and precision

The calculator takes the orbital radius and the period as numbers with a power of ten, which makes it easy to enter the very large distances and times common in astronomy, such as millions of kilometres or thousands of seconds. It returns the orbital velocity in scientific notation. The calculation is exact for a circular orbit, treating the path as a perfect circle travelled at constant speed.

A worked example

Take the International Space Station, orbiting at a radius of about 6,778 kilometres from Earth's centre, completing one orbit in about 5,556 seconds, roughly 92 minutes.

The orbital velocity is v = 2 π R ÷ T = (2 π × 6.778 × 10⁶) ÷ 5,556 ≈ 7.67 kilometres per second. At this tremendous speed, the station circles the whole planet in an hour and a half, which is why astronauts aboard see a sunrise or sunset every 45 minutes. A higher orbit would mean a slower speed and a longer period.

Questions people ask

How do you calculate orbital velocity?

For a circular orbit, divide the circumference by the period, v = 2πR/T, where R is the orbital radius and T is the time for one revolution.

How fast does the space station orbit?

About 7.7 kilometres per second, completing an orbit roughly every 92 minutes. That speed is what keeps it falling around the Earth in a stable circle.

Why do astronauts float if gravity is still strong?

Because they are in free fall, falling around the Earth with their spacecraft. Gravity is nearly full strength up there, but falling objects feel weightless, which is why astronauts float.

Do higher orbits move faster or slower?

Slower. An object orbiting farther from the central body moves more slowly and takes longer to go around, which is why outer planets orbit the Sun far more slowly than inner ones.

References

A quick note on where the physics comes from. Orbital velocity and the nature of orbits as free fall are standard gravitation, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. NASA describes orbital motion for satellites and the space station. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 1, Section 13.4, Satellite Orbits and Energy. https://openstax.org/books/university-physics-volume-1/pages/13-4-satellite-orbits-and-energy
2. HyperPhysics, Circular Orbit Velocity. http://hyperphysics.phy-astr.gsu.edu/hbase/orbv.html
3. NASA, What Is an Orbit? https://www.nasa.gov/learning-resources/for-kids-and-students/what-is-an-orbit-grades-5-8/