Satellite Orbit Calculator (Speed and Period)

Compute orbital speed, period, orbit radius, and angular speed for a circular satellite orbit from altitude. Works for other bodies too.

Input

Enter a satellite altitude to compute the circular orbital speed and period. Change the central body mass and radius to find orbits around other bodies.

Altitude h

Height above the body surface. Low Earth orbit is around 400 km.

Central body mass M

The default is Earth mass.

Central body radius R

The default is Earth mean radius of 6371 km.

Result

Orbital speed

7.67249km/s

Orbital period

92.415555min

Orbit radius r

6,771 km

Orbital speed in m/s

7,672.490413 m/s

Angular speed omega

0.001133 rad/s

Period in hours

1.540259 h

Geostationary radius

42,163.773091 km

Ratio to geostationary radius

0.160588 times

For a circular orbit, v = sqrt(GM / r) and T = 2 pi sqrt(r^3 / GM), where GM is the gravitational constant times the central body mass. This idealized circular orbit ignores air drag and orbital eccentricity.

How it works

For a circular orbit, gravity equals the centripetal force, giving orbit radius r = R + h (R is body radius, h is altitude), orbital speed v = sqrt(GM / r), period T = 2 pi sqrt(r^3 / GM), and angular speed omega = v / r.
GM is the product of the gravitational constant G and the central body mass M. We use G = 6.6743e-11 m^3 kg^-1 s^-2.
Earth defaults are mass M = 5.972e24 kg and mean radius R = 6371 km, which give GM of about 3.986e14 m^3/s^2.
The geostationary orbit radius is found for a circular orbit whose period equals the sidereal day of 86164 seconds, r_geo = (GM T^2 / (4 pi^2))^(1/3), and is used as a comparison ratio.
Altitude and radius are entered in km and mass in kg, then converted to SI units (m) internally. This is an idealized circular orbit and ignores air drag, orbital eccentricity, and the oblateness of the body.

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