Where is Earth today?

Earth doesn't move around the Sun at a steady pace. It's fastest in early January, when it's closest, and slowest in early July. In this tutorial you'll find where Earth is on its orbit today, using three equations and the idea that ties them together: Kepler's equation.

• You'll use: PLANETS, trueToMeanAnomaly, solveKepler, eccentricToTrueAnomaly, norm2pi
• Time: about 10 minutes

1. Three ways to describe a position

An orbit position can be given as three different angles, all measured from perihelion (the closest point to the Sun):

• Mean anomaly $M$: where Earth would be if it moved at a steady pace. It grows by the same amount every day, so it's easy to compute.
• Eccentric anomaly $E$: a helper angle on a circle drawn around the orbit.
• True anomaly $\nu$: where Earth actually is.

Drag the sliders. With $e=0$ all three are the same; the more stretched the orbit, the further they drift apart.

LiveKepler's equation M = E - e·sin E

Eccentricity e

0.50

Mean anomaly M

60°

Mean M

60.0°

Eccentric E

88.6°

True ν

118.8°

Distance r / a

0.988

2. Mean anomaly today

Start from Earth's orbit in the PLANETS dataset. Its orbit.angle is the true anomaly at J2000 (1 January 2000, 12:00), so first turn it into a mean anomaly with trueToMeanAnomaly. That's the easy direction, with a closed-form formula. The mean anomaly then advances by the same $2\pi /P$ every day:

import { PLANETS } from '@interstellar-tools/constants';
import { norm2pi, trueToMeanAnomaly } from '@interstellar-tools/equations';
import type { Radians } from '@interstellar-tools/types';

const earth = PLANETS.find((planet) => planet.id === 'earth')!;
const { e, angle, period } = earth.orbit!; // e 0.0167, P 365.256 days
const M0 = trueToMeanAnomaly(angle, e); // -2.47°: just before perihelion
const days = 9786; // J2000 to 17 October 2026
const M = norm2pi(
  M0 + ((2 * Math.PI) / period.value) * days
) as Radians; // 282.7°

Shortcut

meanAnomalyAt(earth.orbit!, new Date('2026-10-17T12:00:00Z')) does this step for any date, measuring from J2000 for you, and trueAnomalyAt does all three steps of this tutorial in one call.

3. Solve Kepler's equation

Going from $M$ to $E$ means solving $M=E-e\sin E$, which has no algebraic solution. solveKepler does it numerically, and eccentricToTrueAnomaly takes the last step:

import {
  eccentricToTrueAnomaly,
  solveKepler
} from '@interstellar-tools/equations';

const E = solveKepler(M, e); // 281.8°
const nu = eccentricToTrueAnomaly(E, e); // 280.8°

In practiceEarth, 17 October 2026

280.8°

True anomaly, 287 days past perihelion

Earth is 0.9966 au from the Sun, a little closer than average, and heading for perihelion on 3 January.

4. Try it yourself

• Set the widget to $e=0.0167$. How far apart are $M$ and $\nu$ at most?
• Repeat the calculation for Mars ($e=0.0934$, $P=687$ days). Why is the difference bigger?