Orbital Period Calculator
Orbit period and speed from altitude (Kepler's third law).
About this tool
Pick the central body (Earth, Moon, Mars, Jupiter or the Sun) and describe the orbit by circular altitude, perigee and apogee, or distance in AU. You get the period, speeds and orbits per day. Enter a period to find the matching circular altitude.
Kepler's third law
The time to complete an orbit depends only on the orbit's size and the central body's mass: T = 2ฯโ(aยณ รท GM), where a is the semi-major axis, the average of the closest and farthest distances from the body's centre. Low orbits are fast: the International Space Station, about 420 km up, circles Earth every 93 minutes at 7.66 km/s. Higher orbits take longer, and at 35,786 km above the equator the period equals one sidereal day (23 h 56 min), so the satellite seems to hover. That's geostationary orbit, used for TV and weather satellites. The same law gives a year for Earth at 1 AU from the Sun. For elliptical orbits, the speed at perigee and apogee comes from the vis-viva equation, v = โ(GM(2/r โ 1/a)). Honest limits: this assumes a two-body system with a much smaller orbiting object, and ignores atmospheric drag, which slowly lowers low orbits, Earth's equatorial bulge and the Moon's and Sun's pull. The escape velocity calculator and the light-year converter are related.
Frequently asked questions
How long does the ISS take to orbit Earth?
About 93 minutes at around 420 km altitude, so roughly 15.5 orbits a day.
What altitude is geostationary orbit?
35,786 km above the equator, where the orbital period matches Earth's rotation (23 h 56 min).
What is Kepler's third law?
The square of the orbital period is proportional to the cube of the semi-major axis: Tยฒ = 4ฯยฒaยณ รท GM.
Why do lower orbits go faster?
Gravity is stronger closer in, so a higher speed is needed to keep falling around the body rather than into it.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.