About this calculator
How fast does a satellite move, and how long does one lap take? For a circular orbit, v = √(G M ÷ r) and the period T = 2π r ÷ v.
Choose the body and enter the orbit's height above the surface. Try 400,000 m (the International Space Station) or 35,786,000 m (a geostationary satellite, one lap a day).
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Space station height (400 km)
- Orbital speed
- 7,672.490413 m/s (27,620.965488 km/h)
- Orbital period
- 1.540259 hours (5,544.933317 s)
- Orbits per day
- 15.581792
- Orbit radius from the centre
- 6,771 km
A circular orbit 400 km above Earth has a speed of 7,672.490413 m/s and takes 1.540259 hours to go round.
Show the working
- For a circular orbit gravity supplies the centripetal force: G M m ÷ r² = m v² ÷ r, so v = √(G M ÷ r).
- r = radius + height = 6.371 × 10^6 + 400,000 = 6.771 × 10^6 m, so v = 7,672.490413 m/s.
- Period T = 2π r ÷ v = 2π × 6.771 × 10^6 ÷ 7,672.490413 = 5,544.933317 s. Higher orbits are slower and take longer. This ignores the air drag that low orbits suffer.
Geostationary orbit
- Orbital speed
- 3,074.878164 m/s (11,069.561392 km/h)
- Orbital period
- 23.928703 hours (86,143.329532 s)
- Orbits per day
- 1.00298
- Orbit radius from the centre
- 42,157 km
A circular orbit 35,786 km above Earth has a speed of 3,074.878164 m/s and takes 23.928703 hours to go round.
Show the working
- For a circular orbit gravity supplies the centripetal force: G M m ÷ r² = m v² ÷ r, so v = √(G M ÷ r).
- r = radius + height = 6.371 × 10^6 + 35,786,000 = 4.2157 × 10^7 m, so v = 3,074.878164 m/s.
- Period T = 2π r ÷ v = 2π × 4.2157 × 10^7 ÷ 3,074.878164 = 86,143.329532 s. Higher orbits are slower and take longer. This ignores the air drag that low orbits suffer.
100 km above the Moon
- Orbital speed
- 1,633.082767 m/s (5,879.09796 km/h)
- Orbital period
- 1.96369 hours (7,069.283271 s)
- Orbits per day
- 12.22189
- Orbit radius from the centre
- 1,837.4 km
A circular orbit 100 km above the Moon has a speed of 1,633.082767 m/s and takes 1.96369 hours to go round.
Show the working
- For a circular orbit gravity supplies the centripetal force: G M m ÷ r² = m v² ÷ r, so v = √(G M ÷ r).
- r = radius + height = 1.7374 × 10^6 + 100,000 = 1.8374 × 10^6 m, so v = 1,633.082767 m/s.
- Period T = 2π r ÷ v = 2π × 1.8374 × 10^6 ÷ 1,633.082767 = 7,069.283271 s. Higher orbits are slower and take longer. This ignores the air drag that low orbits suffer.
The formulas
- Speed: v = √(G M ÷ r)
- Period: T = 2π r ÷ v = 2π √(r³ ÷ G M)
- r is the distance from the centre: the body's radius plus the height
Higher means slower
It seems odd, but satellites in higher orbits move slower and take longer to circle. A low orbit around Earth takes about 90 minutes; the Moon, at 384,000 km, takes 27 days. At about 35,786 km up the period is one day, so a satellite stays above the same spot: a geostationary orbit.
Limits
This models a perfectly circular orbit around a single body. Real low orbits lose speed to the thin upper atmosphere, and the pull of the Moon, Sun and the planet's shape perturb orbits slightly.
Frequently asked questions
How fast does the space station move?
About 7.7 km/s (27,600 km/h), one lap in about 92 minutes.
What is a geostationary orbit?
An orbit with a period of one sidereal day, so the satellite hovers over one point on the equator: about 35,786 km up.
Why do higher orbits take longer?
The path is longer and gravity is weaker, so the speed is lower. Kepler's third law says T² grows with r³.
Does the satellite's mass matter?
No. The orbit depends only on the central body's mass and the radius.
Does the height mean above the surface?
Yes: the calculator adds the body's radius to find the distance from the centre.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.