Orbital Period Calculator

Kepler's Third Law puts the central mass in the denominator of T² = (4π²/GM) × a³, so a larger M directly shrinks T for the same semi-major axis. Physically, more mass means stronger gravitational pull, which forces the orbiting body to move faster to avoid falling in — a faster orbit at the same distance means less time to complete one lap. Doubling the central mass while holding the semi-major axis fixed shortens the period by a factor of √2, not by half.

The velocity shown here is the mean orbital velocity — the orbit's circumference (2πa) divided by the period — not the instantaneous speed at any specific point. Real orbital speed actually changes continuously across an elliptical orbit, moving fastest at perihelion and slowest at aphelion, a consequence of angular momentum conservation (Kepler's Second Law). Only for a perfectly circular orbit (eccentricity 0) does the instantaneous speed match this average value everywhere.

The calculator multiplies the semi-major axis by (1 − e) for perihelion and (1 + e) for aphelion, where e is the orbital eccentricity you enter. At e = 0 both values collapse to the semi-major axis itself, since a circular orbit has no near or far point. Entering a value above 0.99 isn't accepted because eccentricities approaching 1 describe parabolic, not elliptical, trajectories where this closed-orbit math no longer applies.

The chart plots Kepler's Third Law across six fixed semi-major-axis values roughly matching Mercury through Jupiter, so you can see how period scales with distance around your chosen central mass — it isn't meant to trace your specific planet's position. Each point still uses your entered central mass in the calculation, so changing that mass reshapes the whole reference curve, not just your single result.