Drag on empty space to launch a body · right-drag / shift-drag to pan · wheel to zoom · click a body to select

Orbital Mechanics

A gravity sandbox. Every body pulls on every other one; orbits are not drawn, they emerge.

Time scale 1×

Presets

New body

Mass Radius

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System

Bodies
Total energy
Energy drift
Angular momentum
Integrator	leapfrog, adaptive

Selected body

Click a body (or a row below) to inspect it.

	Name	Mass	Speed

Kepler's laws

Ellipses. Each orbit is an ellipse with the heavier body at one focus; eccentricity e = 0 is a circle, 0 < e < 1 an ellipse, e ≥ 1 escapes.
Equal areas. The line joining a body to its primary sweeps equal areas in equal times, so it moves fastest at closest approach. That is conservation of angular momentum.
Harmonic law. T² = 4π²a³ / G(M+m). Distant orbits are slower; the readout below checks it live.

Elements are osculating (instantaneous) and relative to the strongest-pulling body at least as heavy as the selected one. With three or more bodies they drift, since Kepler's laws are exact only for two.

Leapfrog (kick-drift-kick) is symplectic, so energy error stays bounded instead of growing. The timestep shrinks automatically during close encounters. Mergers conserve momentum but not energy.