Drag on empty space to launch a body (arrow = velocity, dashed = predicted path). Click a body to select it. Wheel = zoom, right/shift-drag = pan. Space = play/pause, R = reset, F = fit, Del = remove selected.

Orbital Mechanics SandboxN-body gravity in the plane: symplectic leapfrog or RK4, adaptive substeps (AU, years, solar masses)

Presets

Simulation

Time scale

Integrator

Precision

Trail length

Camera

Launch new body

Mass

Drag length 120 px = local circular speed around the dominant body; launches are relative to that body's motion. The ghost path integrates the real N-body system.

Conservation

Kinetic energy
Potential energy
Total energy E
Energy drift ΔE/\|E₀\|
Angular momentum L
L drift ΔL/\|L₀\|
Substeps / s · last dt
Merges / escapes

cyan energy drift, pink angular-momentum drift (auto-scaled). Baseline resets when mass is added, merged or lost.

Selected body — orbital elements

Relative to

What to look for

Kepler's laws

1st: the dashed osculating orbit is an ellipse with the primary at one focus.
2nd: coloured wedges are swept in equal times (1/12 of the period). They are thin and long near periapsis and fat and short near apoapsis, yet have equal area.
3rd: T²(M+m)/a³ = 1 in these units for every orbit around the same primary.