Documentation / @interstellar-tools/equations / advanceMeanAnomaly

Function: advanceMeanAnomaly()

function advanceMeanAnomaly(
  orbit: Pick<OrbitInterface, 'e' | 'angle' | 'period'>,
  timeStep: TemporalInterface
): Radians;

Defined in: anomalies/advance-mean-anomaly.ts:66

Advances an orbit by a time step and returns its new mean anomaly ($M$).

The orbit's angle (true anomaly) is the starting point. To get the eccentric anomaly from the result, pass it to solveKepler. To find a body at a given date, use meanAnomalyAt or trueAnomalyAt.

Mathematical Explanation:

The mean anomaly is a measure of the position of an orbiting body as if it moved with uniform angular motion along a circular orbit with the same period as the actual elliptical orbit. It grows linearly with time:

$M=M_0+n\cdot \mathrm{\Delta }T,n=\frac{2\pi }{|P|}$

where:

• $M_0$ is the initial mean anomaly, converted from the true anomaly angle.
• $n$ is the mean motion, from the period $P$ in days. $P$ is a positive duration; a negative one, from data in the old 0.x convention, is read as its absolute value. A positive step always moves the body forward.
• $\mathrm{\Delta }T$ is the time step, converted to days from its unit.

The step can be any length, from a fraction of a second to many orbits, and negative to go back in time. The result is wrapped to $[0,2\pi )$.

Parameters

Parameter	Type	Description
orbit	Pick<OrbitInterface, "e"	"angle"
timeStep	TemporalInterface	How far to advance, in any temporal unit; negative goes back in time.

Returns

Radians

The mean anomaly after the time step, in $[0,2\pi )$.

Throws

RangeError If the orbit's eccentricity is outside the range $0\le e<1$.

Example

import { advanceMeanAnomaly } from '@interstellar-tools/equations';

const marsOrbit = {
  e: 0.0934, // Eccentricity of Mars' orbit
  angle: 1.047 as Radians, // Initial true anomaly (in radians)
  period: { value: 687, unit: 'd' } // Orbital period in days
};

advanceMeanAnomaly(marsOrbit, { value: 1, unit: 'd' }); // one day on
advanceMeanAnomaly(marsOrbit, { value: 10, unit: 'yr' }); // ten years on
advanceMeanAnomaly(marsOrbit, { value: -1, unit: 'd' }); // one day back

See

• solveKepler to convert the mean anomaly to the eccentric anomaly.
• Mean Anomaly (Wikipedia)
• Orbital Mechanics (NASA)