What this calculator does
An orbit is a fall that keeps missing. A body in circular orbit is accelerating toward the centre continuously, but it is moving sideways fast enough that the surface curves away beneath it just as quickly as it falls.
The speed required depends only on the central mass and the orbital radius. Lower orbits need higher speeds, which is why the International Space Station circles Earth in about 90 minutes while a geostationary satellite takes a full day.
The formula
Orbital velocity is the square root of the gravitational constant times the central mass, divided by the orbital radius. The period follows from dividing the orbital circumference by that speed.
| Term | Meaning |
|---|---|
| Circular orbit | An orbit at constant radius, where gravity exactly supplies the centripetal acceleration needed to keep turning. |
| Orbital period (T) | The time to complete one full circuit. |
| Geostationary orbit | The radius at which the period equals one day, so a satellite appears to hover over a fixed point on the equator. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of the central body (kg) | The mass of the body being orbited, in kilograms. Earth is 5.972 × 10²⁴. |
| Orbital radius (km) | The orbital radius measured from the centre of the body, in kilometres. Add the body's radius to any altitude figure. |
When to use it
Working out a satellite's period
The orbital radius fixes the period exactly, which is what determines how often a satellite passes overhead.
Understanding geostationary orbit
Only one radius gives a period of exactly one day, which is why that orbit is so crowded and so valuable.
Comparing low and high orbits
Lower orbits are faster and shorter; higher orbits are slower and longer, and the trade-off is set entirely by radius.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How do speed and period change with orbital radius?
Circular orbits around Earth at a range of radii.
| Orbital radius | Orbital velocity | Orbital period |
|---|---|---|
| 6,771 km | 7.672 km/s | 92.4 minutes |
| 10,000 km | 6.313 km/s | 165.9 minutes |
| 20,000 km | 4.464 km/s | 469.1 minutes |
| 42,164 km | 3.075 km/s | 1,436.1 minutes |
Questions
Why do lower orbits move faster?
Because gravity is stronger closer in, so a faster sideways motion is needed to balance it. It is counterintuitive that speeding up moves a spacecraft to a higher, slower orbit, but that is exactly what happens once the new orbit settles.
Does the satellite's mass matter?
No. It cancels out of the equation entirely, so a small cubesat and a large station at the same altitude travel at the same speed and share the same period.
Why is the space station's orbit not permanent?
Because at that altitude there is still a trace of atmosphere. The drag is tiny but continuous, so the orbit decays and has to be raised periodically with reboost burns.
How does this relate to escape velocity?
Circular orbital velocity is always escape velocity divided by the square root of two, about 71 per cent of it. Reaching orbit is therefore a substantial fraction of the way to leaving entirely.
For the speed needed to leave rather than circle, see the escape velocity calculator. For elliptical orbits and their periods, see the Kepler's third law calculator.