Simulated time0.00 yr

Speed1 yr/s

Bodies0 + 0

Step Δt—

Velocity Acceleration Hill sphere Roche limit +Barycentre Drag = launch · click = select · Shift/right-drag = pan · wheel = zoom

Gravity Sandbox

A 2D N-body simulation in real units (AU, years, solar masses). Pick a preset, or drag on the canvas to launch your own bodies.

Simulation

Time scale 1 yr/s

Accuracy Normal Softening 0.0001 AU

Add a body (drag on canvas)

Launch body Pan / select

Type Mass —

The arrow is the new body’s velocity (its length is the distance it would travel in 0.1 yr). A dashed preview shows the predicted orbit. Double-click drops a body at rest. While the camera follows a body, launch velocity is relative to it.

Selected body

Click a body on the canvas to inspect it. Use [ and ] to cycle with the keyboard.

Conservation check

ΔE / |E|0

ΔL / L0

Lost to collisions0

—

What am I seeing?

Every body attracts every other with Newton’s law, a = G m / r². In these units G = 4π² AU³ M☉⁻¹ yr⁻², so Earth orbits the Sun at 1 AU in exactly one year.
The integrator is a leapfrog (kick–drift–kick), a symplectic method: energy errors stay bounded instead of growing. The step is adaptive, shrinking to a fraction of the shortest local orbital time √(r³/GM) and snapped to powers of two. A small Plummer softening avoids singular close passes.
The drift readout compares the total energy and angular momentum with their starting values. Healthy runs sit around 10⁻⁶ or lower. It is rebased when you add or delete a body, and collision losses are tallied separately.
Collisions merge bodies inelastically: mass and linear momentum are conserved, kinetic energy is lost as heat (flash). Collision radii for planets and moons are exaggerated 25× so impacts are possible at this scale.
Asteroids and the grey dust in belts, clusters and Lagrange swarms are mass-less test particles: they feel gravity but exert none.
The Hill sphere ≈ a·(m/3M)^1/3 is where a body’s gravity beats its parent’s tide; moons must live inside it. The Roche limit ≈ 2.44 R (M/m)^1/3 is where tides tear apart a fluid satellite.
Lagrange points: L1–L3 lie on the line through the two bodies and are unstable; L4/L5 form equilateral triangles and are stable when the mass ratio is below ≈ 1/25. Use the co-rotating frame to watch trojans librate.
A planar model with point masses, no relativity, tides or spin. Orbital elements are measured against the dominant attractor (the smallest Hill sphere containing the body).