Orbital Period Calculator
Kepler's third law links how big an orbit is to how long it takes. Find the period of a planet, moon or satellite, or work out the orbit you need for a chosen period.
Orbital period
Kepler's third law: how long an orbit takes, or how big it must be.
Measured from the centre of the central body, not its surface.
In Earth masses, for a two-body orbit. Leave blank for a satellite or spacecraft.
Orbital period
1 year
- Period in days
- 365.251
- Period in years
- 1
- Semi-major axis in km
- 149,598,000
- Semi-major axis in AU
- 1
- Mean orbital speed
- 29.79 km/s
Kepler's third law for two point masses. The speed is the average for a circular orbit; an elliptical orbit is faster near its closest point. Real orbits drift a little under other bodies' pull.
How this is calculated
- 1
Kepler's third law
T = 2π √(a³ ÷ G(M₁ + M₂)), where a is the semi-major axis in metres, G = 6.6743 × 10⁻¹¹ m³ kg⁻¹ s⁻² and M₁ and M₂ are the two masses in kilograms.
- 2
Orbit size from the period
Rearranged, a = ∛(G(M₁ + M₂) T² ÷ 4π²). One sidereal day of 23 h 56 min 4 s around Earth gives 42,164 km, the geostationary orbit.
- 3
Orbital speed
The average speed of a circular orbit is v = √(G(M₁ + M₂) ÷ a). The ISS, about 6,791 km from Earth's centre, moves at about 7.66 km/s.
- 4
Altitude
The semi-major axis is measured from the centre of the central body, so subtract its radius (6,371 km for Earth) to get the height above the surface.
Frequently asked questions
What is Kepler's third law?
The square of an orbit's period is proportional to the cube of its semi-major axis. For planets around the Sun, T in years squared equals a in AU cubed, so Mars at 1.524 AU takes 1.88 years.
How long does the ISS take to orbit the Earth?
About 92 to 93 minutes at its usual height of around 420 km, so it circles the planet roughly 15.5 times a day. The figure changes slightly as its orbit decays and is boosted.
Why is a geostationary orbit 35,786 km high?
That is the height at which one orbit takes exactly one sidereal day, 23 hours 56 minutes, so the satellite keeps pace with Earth's rotation and stays over the same spot on the equator.
Does the mass of the orbiting body matter?
Only when it is a sizeable fraction of the central mass. The Moon is 1.23% of Earth's mass, which shortens its period by about 0.6%. For an artificial satellite the effect is far too small to measure.