Documentation / @interstellar-tools/equations / meanAnomalyAt

Function: meanAnomalyAt()

function meanAnomalyAt(
  orbit: Pick<OrbitInterface, 'e' | 'angle' | 'period'>,
  date: Date
): Radians;

Defined in: anomalies/anomaly-at.ts:53

The mean anomaly ($M$) of an orbit at a given date.

Every orbit.angle in the datasets is the true anomaly at J2000 (2000-01-01 12:00 TT), so this advances the orbit from J2000 to date with advanceMeanAnomaly. Dates before J2000 work too.

$M=M_0+\frac{2\pi }{|P|}(t-t_{J2000})$

The time is measured in UTC, as JavaScript dates are, against J2000_UTC. Leap seconds since 2000 are ignored, which moves a body by a few seconds of its orbit at most.

Parameters

Parameter	Type	Description
orbit	Pick<OrbitInterface, "e"	"angle"
date	Date	The date to find the body at.

Returns

Radians

The mean anomaly at date, in $[0,2\pi )$.

Throws

If date is not a valid Date.

Throws

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

Example

import { PLANETS } from '@interstellar-tools/constants';
import { meanAnomalyAt } from '@interstellar-tools/equations';

const earth = PLANETS.find((planet) => planet.id === 'earth')!;

meanAnomalyAt(earth.orbit!, new Date('2026-10-17T12:00:00Z')); // ≈ 4.934 rad (282.7°)

See

trueAnomalyAt for where the body actually is.