This simulator runs a 2D N-body model of core accretion in a protoplanetary disc. Hundreds of point-mass dust grains start on near-circular orbits between 80 and 290 pixels from a central protostar, each nudged every frame by an inverse-square gravitational pull scaled by disc density Σ and a linear velocity-proportional gas-drag term (F = −β·v) that slowly damps orbital speed. Pairwise distance checks detect collisions: bodies meeting below the sticking-velocity threshold merge inelastically, conserving momentum and combining mass (radius scales as mass1/3, i.e. constant bulk density), while faster impacts bounce elastically off the collision normal. Bigger bodies present a larger cross-section, so runaway accretion naturally emerges as the largest planetesimals sweep up material fastest.
Particles are colour-coded by growth stage — red dust (<3 m₀), orange pebbles (3–8 m₀), yellow rocks (8–20 m₀), green planetesimals (20–60 m₀), and blue protoplanets (>60 m₀) — orbiting a glowing protostar inside a dashed snowline ring at ~3 AU. The live stats panel tracks body count, the largest accumulated mass, elapsed simulation time in kyr, and the running merge count as runaway accretion thins the population into fewer, larger bodies.
Pick a Disc Preset (Dense, Sparse, Beyond Snowline, Inner System) to load a matched set of parameters, or drag the Particle count N, Disc density Σ, Sticking velocity v_stick, and Drag coefficient β sliders yourself. Press Run to start the physics loop, adjust Speed to fast-forward, toggle Show Snowline for the reference ring, and hit Reset to reseed a fresh disc.
Beyond the real Solar System's snowline (~3 AU), water and other volatiles freeze into ice, roughly doubling the solid material available for cores to sweep up. That extra icy mass is why Jupiter and Saturn's cores could grow large enough, fast enough, to capture their thick hydrogen-helium envelopes before the gas disc dispersed — while the inner, ice-free terrestrial planets stayed comparatively small and rocky.
Every particle feels an inverse-square pull toward the central protostar, computed as grav = density × 800 / distance², so the disc density slider Σ directly scales the strength of gravity felt by every body. Σ also sets each particle's initial near-circular orbital speed at spawn time (speed = √(density × 20 / r)), so a denser disc both starts particles moving faster and pulls them inward more strongly during the run.
When two bodies' radii overlap, the simulator compares their relative speed to the Sticking velocity v_stick slider. Below that threshold they merge inelastically — a new body forms at their mass-weighted average position and velocity, conserving total momentum — and the merge counter increments. At or above the threshold they instead undergo a standard elastic collision, exchanging velocity along the line connecting their centres without combining mass.
Merged bodies get a new radius from r = 2.5 × mass^(1/3), which is the geometric relationship between radius and mass for an object of constant bulk density (volume, and hence mass, scales with the cube of radius). This keeps larger, merged planetesimals visually proportionate rather than ballooning linearly with every collision, matching how real solid bodies of similar composition scale in size as they accumulate mass.
After each physics step, any body within 30 pixels of the protostar (fallen in) or beyond 340 pixels (ejected past the disc's outer edge) is removed from the simulation. This keeps the particle count from drifting unboundedly and approximates real mass loss to accretion onto the star or dynamical ejection from the system.
The ring drawn at radius 200 px is a purely visual marker labelled "Snowline ~3AU," toggled on or off with the Show Snowline button — it does not itself alter gravity, drag, or sticking calculations for any particle. The physical idea it represents is captured instead by the separate Beyond Snowline preset, which loads a higher sticking velocity and disc density approximating the extra icy solid material available past the real ice line.