Documentation / @interstellar-tools/equations / meanMotion

Function: meanMotion()

function meanMotion(a: number, mu: number): number;

Defined in: orbits/mean-motion.ts:51

Compute mean motion for a (near-)circular reference orbit.

Mean motion is the angular rate of the reference orbit:

$$n=\sqrt{\frac{\mu }{a^3}}$$

Where:

• $\mu$ is the standard gravitational parameter of the central body
• $a$ is the (circular) orbit radius / semi-major axis

Unit consistency

• If $\mu$ is in m³/s², then $a$ must be in m and the result is in rad/s.
• If $\mu$ is in km³/s², then $a$ must be in km and the result is in rad/s.

Common usage: reference rate for relative motion models (e.g., Clohessy–Wiltshire / Hill), orbital period estimates, and circular-orbit dynamics.

In practiceThe ISS, orbit by orbit

15.51 orbits/day

Mean motion at 420 km altitude

The function returns 0.001128 rad/s. Multiply by 86 400 s and divide by 2π for orbits per day, the unit used in a satellite's two-line elements (TLEs).

meanMotion(6.371e6 + 420e3, 3.986004418e14); // ≈ 0.001128 rad/s

Parameters

Parameter	Type	Description
a	number	Semi-major axis $a$ (finite, > 0).
mu	number	Standard gravitational parameter $\mu$ (finite, > 0).

Returns

number

Mean motion $n$ in rad/s.

Throws

If a or mu is not a finite number.

Throws

If a <= 0 or mu <= 0.

Example

// Earth example (km-based):
const mu = 398600.4418; // km³/s²
const a = 7000; // km
const n = meanMotion(a, mu); // rad/s