What is orbital velocity?

Orbital velocity is the exact speed at which a satellite must travel tangentially to maintain a stable circular orbit at a given altitude. Too slow and gravity pulls the satellite inward; too fast and it climbs to a higher orbit or escapes entirely.

What formula is used?

The circular orbital velocity formula is v = sqrt(GM / r), where G = 6.6743 x 10^-11 m^3 kg^-1 s^-2 is the gravitational constant, M is the central body mass in kg and r is the orbital radius (body radius plus altitude) in metres.

How is escape velocity related to orbital velocity?

At any given orbital radius, the escape velocity is exactly sqrt(2) times the circular orbital velocity, so about 1.414 times faster. For a low Earth orbit at 408 km, orbital velocity is roughly 7 670 m/s and escape velocity from that point is about 10 845 m/s.

What altitude is needed for a geostationary orbit?

Above Earth, the geostationary radius works out to about 42 164 km from the centre, which puts the satellite roughly 35 786 km above the surface. At that altitude the orbital period matches Earth's sidereal rotation (86 164.1 s), so the satellite appears stationary over a fixed point on the equator.

Does orbital velocity change with altitude?

Yes. Higher altitude means a larger orbital radius r, so v = sqrt(GM/r) decreases. Counterintuitively, to raise an orbit you first fire the engine to speed up, which stretches the orbit to an ellipse; you then fire again at the far end to circularise at the higher altitude — the satellite ends up moving slower overall, but you had to speed up to get there.

What is specific orbital energy?

Specific orbital energy (energy per unit mass) is E = -GM / (2r) in joules per kilogram. It is always negative for a bound orbit — the more negative it is, the more tightly bound the satellite is to the central body. At the escape threshold E would equal zero.

Orbital Velocity Calculator

Any satellite — whether the International Space Station 408 km above you or a GPS satellite 20 200 km up — is simply falling around the planet fast enough that the curved surface of Earth drops away at the same rate as the satellite falls toward it. The orbital velocity calculator finds that precise speed from first principles, applies it to any central body from the Moon to the Sun, and also solves the inverse problem: given a desired speed, what altitude is needed?

How it works

The fundamental equation for a circular orbit comes from balancing gravitational and centripetal acceleration:

v = sqrt(GM / r)

where:

G = 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻² (gravitational constant)
M is the central body mass in kilograms
r is the orbital radius in metres — the body’s own radius plus your chosen altitude

The calculator also derives several related quantities from this single result:

Escape velocity at that radius: v_esc = sqrt(2) × v_circ (always ~1.414 × the orbital speed)
Orbital period: T = 2πr / v (how long one complete orbit takes)
Specific orbital energy: E = -GM / (2r) in MJ/kg (negative = bound orbit)

The geostationary mode works backwards from the rotation period: setting T equal to Earth’s sidereal day (86 164.1 s) and solving r_geo = (GM·T² / 4π²)^(1/3) gives the unique radius at which an orbit stays fixed over one equatorial point.

The reverse-solve mode rearranges v = sqrt(GM / r) to r = GM / v², then subtracts the body’s radius to return the altitude corresponding to any desired orbital speed.

Worked example

The International Space Station orbits at approximately 408 km altitude above Earth (M = 5.972 × 10²⁴ kg, R = 6 371 km):

r = 6 371 + 408 = 6 779 km = 6.779 × 10⁶ m
v = sqrt(6.6743×10⁻¹¹ × 5.972×10²⁴ / 6.779×10⁶)
v ≈ 7 668 m/s ≈ 27 600 km/h

Orbit	Altitude	Velocity	Period
ISS (LEO)	408 km	~7 668 m/s	~92 min
GPS	20 200 km	~3 874 m/s	~12 h
GEO	35 786 km	~3 075 m/s	~24 h
Moon around Earth	~378 000 km	~1 025 m/s	~27.3 days

All three vary because r appears in the denominator under the square root: doubling the orbital radius reduces the velocity by a factor of sqrt(2) and increases the period by a factor of 2sqrt(2) — Kepler’s third law in disguise.

Formula note

The formula v = sqrt(GM / r) is exact for circular orbits and is an excellent approximation for low-eccentricity elliptical orbits when r is interpreted as the semi-major axis a. For highly elliptical orbits (comets, transfer orbits) the instantaneous speed varies along the orbit and the vis-viva equation must be used: v² = GM(2/r - 1/a). The calculator uses the circular case throughout, which is correct for the presets shown and for any user-defined altitude interpreted as a circular orbit radius.

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