Orbital Period Calculator
This orbital period calculator uses Kepler’s third law, T = 2π·√(a³ / GM), with the orbit radius and the central body. Example: the ISS at 408 km altitude needs about 92.6 minutes for one orbit of the Earth.
Example: Central body: Earth · What do you want to calculate: Period from the orbit · The distance is: Altitude above the surface · Distance 408 · Unit: km → Result: Orbital period: 92.578 min. Source: Wikipedia – Keplersche Gesetze. Updated: .
How it is calculated
Kepler’s third law links the orbital period of a body to the semi-major axis of its orbit: T² / a³ is the same for all bodies around the same centre. With the gravitational parameter GM of the central body this becomes T = 2π·√(a³ / GM).
How it is calculated
The orbit radius a is measured from the centre of the central body, so for an altitude it is radius plus altitude. The ISS flies at about 408 km, so a is 6,779 km and T comes out at roughly 92.6 minutes at 7.67 km/s. A geostationary satellite must orbit once per sidereal day (23 h 56 min), which needs a ≈ 42,164 km, an altitude of 35,786 km. The Moon at 384,400 km gets about 27.5 days; the real value is a little lower because its own mass counts too. Earth around the Sun needs one year at 1 AU.
Backwards and with a custom body
In the second mode you set the period you want and get the orbit radius and altitude needed. With “Custom body” you can calculate for any mass, such as asteroids or exoplanets.
- The period does not depend on the satellite’s mass, only on orbit radius and central body.
- The higher the orbit, the slower the satellite and the longer one orbit takes.
- Escape velocity is √2 times the circular orbit speed.
Frequently asked questions
How do you calculate the orbital period of a satellite?
With T = 2π·√(a³ / GM). For Earth GM = 3.986·10¹⁴ m³/s², and a is Earth’s radius plus the altitude. At 408 km that gives about 92.6 minutes.
How high is a geostationary satellite?
About 35,786 km above the equator, an orbit radius of roughly 42,164 km. One orbit takes exactly one sidereal day, so the satellite seems to stand still in the sky.
Why does the orbital period not depend on the satellite’s mass?
Because the satellite’s mass cancels between gravitational force and inertia. Only the mass of the central body (GM) and the orbit radius determine the period.
Sources and legal basis
- Wikipedia – Keplersche Gesetze
- Wikipedia – Standard gravitational parameter
- Wikipedia – Orbital period
As of: · Editorial policy
Related tools
- Sidereal Time CalculatorSidereal time calculator: Greenwich mean and apparent sidereal time and local sidereal time for any date, UT time and longitude, with the USNO formulas.
- Escape velocity calculatorEscape velocity calculator for Earth, Moon, Mars, Jupiter, the Sun and more, at any altitude. With circular orbit speed and orbital period. Free to use.
- Centripetal force calculatorCentripetal force calculator from mass, radius and speed, period or rpm, plus acceleration, g-force and the cornering speed limit for each road surface.
- Speed of Light CalculatorSpeed of light calculator: how long does light take for a distance, and how far does it go in a given time? For vacuum, air, water and fibre, with examples.
- Weight on the Moon calculatorWeight on the Moon calculator: see what you would weigh on the Moon, Mars, Jupiter and every planet, with scale reading, force in newtons and jump height. Free.
- Sun Position CalculatorSun position for any place and date: azimuth and altitude through the day as a chart, sunrise, solar noon, sunset and twilight – NOAA method, no app needed.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Gravitational force calculatorGravitational force calculator using Newton’s law: force in newtons from two masses and their distance, both accelerations and the steps, with CODATA 2022 G.
- Angular Velocity CalculatorAngular velocity calculator from rpm, frequency, angle and time, or linear speed and radius: results in rad/s, degrees per second, rpm, Hz and the period.