Orbital Period Calculator

Enter the orbital period calculator, where you can calculate the orbital period of a binary system, a satellite around the Earth, and much more while learning about the universe and the laws that rule it.

Orbital period92.414 minfor the circular orbit at this altitude

Orbital velocity7,672.6 m/s7.6726 km/s at a radius of 6,771 km, measured from the CENTRE of Earth — not from the surface

Escape velocity from this radius10,850.69 m/s√2 times the circular speed — always, at every radius and about every body

Orbital radius6,771 kmsurface radius 6,371 km plus an altitude of 400 km

Standard gravitational parameter GM3.98601e+14 m³/s²

Surface gravity of Earth9.8203 m/s²1.0014× Earth's

Gravity at orbital altitude8.6943 m/s²88.53% of the surface value — orbit is not weightlessness because gravity is absent, but because everything is falling together

Orbits per day15.582

Kepler's constant T²/a³9.90426e-14 s²/m³4π²/GM — the same for every orbit about Earth, which is the whole content of the third law

Geostationary-style radius42,164.1 kmwhere the period matches one sidereal day — 35,786 km altitude for Earth

Two-body period92.414 minindistinguishable from the figure above — at 7.03e-20 of the central mass the satellite may be treated as massless

Orbital kinetic energy12.3624 TJ

Total orbital energy-12.3624 TJnegative because the orbit is bound — reaching zero is exactly escape

The formula

v = √(GM/r); T = 2π√(a³/GM); v² = GM(2/r − 1/a)

Radius from the centre, not the surface

Every orbital formula takes the distance from the centre of mass of the body being orbited. A "400 km orbit" is at a radius of 6,771 km, not 400 km, and using the altitude by mistake overstates the orbital speed by a factor of four. This calculator takes the altitude and adds the radius for you.

Escape velocity is always exactly √2 times the circular orbital speed at the same radius. That holds at every altitude and around every body, because both come from the same GM/r and differ only by the factor of two between kinetic energy and potential well depth.

Orbit is not weightlessness caused by an absence of gravity. At the space station's altitude, gravity is still about 89% of its surface strength. Everything simply falls together, so nothing presses against anything else.

Kepler's laws, in one relation

The vis-viva equation, v² = GM(2/r − 1/a), covers every conic at once: put a = r and it gives the circular speed; let a go to infinity and it gives escape velocity. The period depends on the semi-major axis alone, so a wildly eccentric orbit and a circular one with the same semi-major axis take exactly the same time to go round.