Documentation / @interstellar-tools/equations / gravitationalParameter

Function: gravitationalParameter()

function gravitationalParameter(M: number, m?: number, G?: number): number;

Defined in: gravity/gravitational-parameter.ts:50

Two-body gravitational parameter ($\mu$).

Definition

$$\mu =G(M+m)$$

Common approximation, when ($M\gg m$)

$$\mu \approx GM$$

Units

• Inputs: masses in kg, ( $G$ ) in m³·kg⁻¹·s⁻² (defaults to G_SI).
• Output: ($\mu$) in m³/s².

TIP

• Use m = 0 (default) for the standard published ($\mu$) of a central body.
• When modelling a binary with comparable masses, pass both M and m.

Parameters

Parameter	Type	Default value	Description
M	number	undefined	Mass of the primary body (kg).
m	number	0	Mass of the secondary body (kg). Defaults to 0.
G?	number	G_SI	Gravitational constant. Defaults to G_SI.

Returns

number

Gravitational parameter ($\mu$) in m³/s².

Throws

Error If M is non-finite or negative.

Throws

Error If m is non-finite or negative.

Throws

Error If G is non-finite or negative.

Example

// Standard gravitational parameter for Earth (approximate: m ~ 0)
const muEarth = gravitationalParameter(5.97219e24); // ≈ 3.986004e14 m³/s²

// Earth + 1000 kg satellite: practically identical to GM
const muExact = gravitationalParameter(5.97219e24, 1000);

// Earth–Moon system (two-body μ)
const muEarthMoon = gravitationalParameter(5.97219e24, 7.342e22);