Documentation / @interstellar-tools/equations / residual

Function: residual()

function residual(E: number, e: number, M: number): number;

Defined in: helpers/misc.ts:137

Compute the Kepler equation residual for an elliptical orbit:

$$E-e\sin (E)=M$$

This function returns:

$$r(E)=E-e\sin (E)-{\mathrm{wrap}}_{2\pi }(M)$$

where wrap_{2π} normalizes M into [0, 2π) to keep the residual well-behaved.

Common usage: root-finding / iteration (Newton–Raphson, Halley, etc.) to solve for eccentric anomaly E given eccentricity e and mean anomaly M.

Parameters

Parameter	Type	Description
E	number	Eccentric anomaly E (radians).
e	number	Eccentricity e (dimensionless).
M	number	Mean anomaly M (radians).

Returns

number

Residual value E - e*sin(E) - M_wrapped.

Example

// If E solves Kepler's equation, residual(E,e,M) ≈ 0
const r = residual(1.0, 0.1, 0.9);