Earth Orbit Calculator
Enter an orbital altitude to instantly compute the satellite orbital speed, orbital period, orbital radius, angular velocity, centripetal acceleration, and the escape velocity at that height. Switch between kilometres and miles, and see the full step-by-step derivation below. Real-world orbit benchmarks - LEO, ISS, GPS and geostationary - are listed for reference.
Formula
Worked example
ISS at 400 km: R = 6,371 + 400 = 6,771 km. Speed = sqrt(3.986e14 / 6.771e6) = 7,672 m/s = 7.67 km/s. Period = 2*pi*sqrt(6,771,000^3 / 3.986e14) = 5,559 s = 92.7 min. Escape velocity = sqrt(2) * 7.67 = 10.85 km/s.
How Earth orbit works
A satellite stays in orbit because it is falling toward Earth while simultaneously moving forward fast enough that the planet curves away beneath it. The required forward speed comes from balancing the centripetal acceleration (provided by gravity) with the centrifugal tendency of the moving satellite. Lower orbits require faster speeds because gravity is stronger there; higher orbits allow slower travel. This is why the ISS at 400 km completes a lap in about 92 minutes while a geostationary satellite at 35,786 km takes 24 hours.
The key formulas
Three equations govern circular Earth orbits. The orbital speed formula, v = sqrt(GM/r), where G is the gravitational constant (6.674e-11 m^3 kg^-1 s^-2), M is Earth mass (5.972e24 kg), and r is the distance from Earth centre, gives the velocity needed. The orbital period formula, T = 2*pi*sqrt(r^3/GM), comes from Kepler's third law and gives the time per revolution. The escape velocity formula, v_esc = sqrt(2GM/r), gives the minimum speed needed to break free of Earth gravity from that altitude - it is always exactly sqrt(2) times the circular orbital speed at the same height.
Orbital zones and their uses
Earth orbits are divided into zones by altitude. Low Earth Orbit (LEO, 160-2,000 km) offers short signal round trips of about 5-20 ms, making it ideal for broadband internet (Starlink), Earth observation, and crewed spaceflight. Medium Earth Orbit (MEO, 2,000-35,786 km) is occupied primarily by navigation constellations like GPS (20,200 km), GLONASS, and Galileo, which benefit from the wide coverage footprint. Geostationary Orbit (GEO, exactly 35,786 km above the equator) is where the orbital period matches Earth's rotation, so satellites appear stationary and are used for television broadcast and weather monitoring. Above GEO lie highly elliptical and cislunar transfer orbits.
Angular velocity and centripetal acceleration
Angular velocity (omega = 2*pi/T, in rad/s) tells you how fast the satellite sweeps angle around Earth. A geostationary satellite has omega equal to Earth's own spin rate (7.27e-5 rad/s), which is why it stays fixed over one point. Centripetal acceleration (a = GM/r^2) equals local gravitational acceleration at that altitude - this is the familiar "g" value, which at LEO is still about 8.7 m/s^2 (close to the 9.8 m/s^2 on the surface). Astronauts aboard the ISS are not in zero gravity; they are in free fall, which is why they feel weightless.
Escape velocity vs. orbital velocity
Escape velocity at any altitude is always sqrt(2) times the circular orbital speed at that same altitude. At the surface this gives the well-known 11.2 km/s figure. At LEO (400 km) it is about 10.85 km/s. This means that to send a satellite from LEO to escape Earth entirely, you only need a delta-v boost of roughly 10.85 - 7.67 = 3.18 km/s. As altitude increases both values drop, but the ratio between them stays fixed at sqrt(2).
Common Earth orbits - reference values
| Orbit | Altitude | Orbital speed | Period | Notable satellites |
|---|---|---|---|---|
| Very low / decay | < 160 km | > 7.9 km/s | < 87 min | Briefly occupied (re-entry) |
| Low Earth Orbit (LEO) | 160 - 2,000 km | 7.8 - 6.9 km/s | 88 - 127 min | ISS (400 km), Starlink, Hubble |
| ISS (example) | 400 km | 7.67 km/s | 92 min | International Space Station |
| GPS orbit (MEO) | 20,200 km | 3.87 km/s | 12 h | GPS, GLONASS, Galileo |
| Geostationary (GEO) | 35,786 km | 3.07 km/s | 23 h 56 min | Weather, TV broadcast sats |
| Lunar distance (ref) | ~384,400 km | ~1.02 km/s | 27.3 days | The Moon |
Speeds and periods computed with G = 6.674e-11 m^3 kg^-1 s^-2, M_E = 5.972e24 kg, R_E = 6,371 km.
Frequently asked questions
Why does orbital speed decrease as altitude increases?
Gravity weakens with the square of distance. At higher altitudes the gravitational pull is weaker, so a satellite needs less forward speed to stay on a curved path that matches the curvature of Earth below. The formula v = sqrt(GM/r) captures this: a larger radius r gives a smaller speed v.
What is geostationary orbit and what altitude is it at?
Geostationary orbit (GEO) sits at 35,786 km above the equator. At that altitude the orbital period is exactly one sidereal day (23 hours 56 minutes), matching Earth's rotation rate. From the ground, a GEO satellite appears stationary, which makes it ideal for television broadcasting, weather monitoring, and telecommunications where a fixed pointing direction is needed.
How fast does the ISS travel?
The International Space Station orbits at roughly 400 km altitude and travels at about 7.67 km/s (27,600 km/h or 17,100 mph). At that speed it completes one full orbit in approximately 92 minutes and circles the globe about 15.5 times per day.
What is escape velocity and how is it related to orbital speed?
Escape velocity is the minimum speed an object needs to break free from Earth's gravity without any further propulsion. At any given altitude, escape velocity is exactly the square root of 2 (about 1.414) times the circular orbital speed at that same altitude. At Earth's surface this gives 11.2 km/s; at the ISS altitude it is about 10.85 km/s.
Why do astronauts feel weightless in orbit if gravity is still present?
At LEO (400 km) gravitational acceleration is still about 8.7 m/s^2, nearly 90% of its surface value. Astronauts feel weightless because both they and the spacecraft are in free fall together, falling at the same rate around Earth. There is no surface beneath them to push back, so there is no normal force and no sensation of weight.
Can a satellite orbit below 160 km?
Briefly, yes - during launches or re-entry vehicles pass through very low altitudes. But for a sustained stable orbit, altitudes below about 160 km are impractical because the thin atmosphere still exerts enough drag to cause rapid orbital decay within hours or days. The ISS requires periodic reboost maneuvers even at 400 km because of residual atmospheric drag.
What is the difference between angular velocity and orbital speed?
Orbital speed (linear velocity) measures how many kilometres the satellite covers each second. Angular velocity measures how many radians of angle around Earth it sweeps each second. A satellite in a high orbit moves more slowly in km/s but sweeps a smaller angle per second, while a low-orbit satellite moves faster in km/s and sweeps a larger arc. They are related by v = omega * r, where r is the orbital radius.