Documentation / @interstellar-tools/equations / sphereOfInfluenceRadius

Function: sphereOfInfluenceRadius()

function sphereOfInfluenceRadius(a: number, m: number, M: number): number;

Defined in: orbits/sphere-of-influence-radius.ts:52

Compute sphere of influence radius (patched conics approximation).

Equation:

$$r_{\text{SOI}}\approx a{\left(\frac{m}{M}\right)}^{2/5}$$

Where:

• a is the semi-major axis of the secondary body's orbit about the primary (m or km)
• m is the mass of the secondary body (e.g., planet) (kg)
• M is the mass of the primary body (e.g., Sun) (kg)

Units:

• Output rSOI has the same distance unit as a (since the mass ratio is dimensionless).

In practiceEarth's sphere of influence

925 000 km

Where Earth's gravity outweighs the Sun's

The Moon, at 384 400 km, is well inside it. Beyond this distance, a spacecraft's path is best described as an orbit around the Sun.

const au = 1.495978707e11; // m

sphereOfInfluenceRadius(au, 5.972e24, 1.989e30); // ≈ 9.245e8 m

Parameters

Parameter	Type	Description
a	number	Semi-major axis a of the secondary around the primary (finite, > 0).
m	number	Mass of the secondary body m (finite, > 0).
M	number	Mass of the primary body M (finite, > 0).

Returns

number

Sphere of influence radius rSOI in the same distance units as a.

Throws

If any input is not finite.

Throws

If a <= 0, m <= 0, or M <= 0.

Example

// Example (Earth around Sun; km-based a):
const aKm = 149_597_870.7; // km
const mEarth = 5.972e24; // kg
const mSun = 1.9885e30; // kg

const rSoiKm = sphereOfInfluenceRadius(aKm, mEarth, mSun);