Kepler Equation Solver

Solve Kepler equation to find the position of an orbiting body at any time, converting mean anomaly to true anomaly via eccentric anomaly.

Mean Anomaly (degrees)

Orbital Eccentricity

Semi-Major Axis (AU)

Formula

M = E - e sin(E) (Kepler equation, solve iteratively for E); True Anomaly: nu = 2 x atan2(sqrt(1+e) x sin(E/2), sqrt(1-e) x cos(E/2)); Radius = a x (1 - e x cos(E))

Frequently Asked Questions

What is Kepler equation?

Kepler equation relates the mean anomaly M to the eccentric anomaly E through M = E - e sin(E). It must be solved iteratively because E cannot be expressed as a simple function of M.

What is the true anomaly?

The true anomaly is the actual angular position of the orbiting body measured from the closest approach point (periapsis). It describes where the body is in its orbit at a given time.

Why does eccentricity matter?

For circular orbits (e = 0) the true anomaly equals the mean anomaly. For highly elliptical orbits, the body spends more time near apoapsis and moves quickly through periapsis, making the anomalies very different.

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