In the news: in 2026 James Webb Space Telescope observations were reported to show signs of Mars-sized worlds smashing together around another star - the same kind of event that is thought to have made our Moon. Crash two planets here and see whether they merge, bounce on, or leave a debris disk.
Regime map for the current γ and mass. Tap the map to set speed and angle. Vertical dashed line: critical angle θcrit. Circles: sampled runs from the experiment below (M merger, H hit-and-run, P partial accretion, G grazing capture, E erosion, D disruption).
Geometry and speed. With target and impactor radii Rt, Ri (equal bulk density, so R ∝ M1/3) and Rs = Rt + Ri, the speed of one body relative to the other at first contact is vimp. The two-body escape speed of the pair at contact is
v_esc = sqrt( 2 G (M_t + M_i) / (R_t + R_i) )Impact parameter b = sinθ (θ = 0 is head-on). Angular momentum of the orbit: L = μ vimp Rs sinθ, μ = MtMi/(Mt+Mi). The simulator starts the bodies 2.6 Rs apart on a point-mass Kepler orbit chosen so that they arrive at contact with exactly the speed and angle you set (verified by the Kepler experiment).
Critical angle and hit-and-run. If the impactor's centre of mass passes the limb of the target, b > bcrit, only part of it overlaps the target and a grazing collision can leave the impactor mostly intact and moving on (Asphaug 2006; Leinhardt & Stewart 2012; Genda et al. 2012):
b_crit = sin(theta_crit) = R_t / (R_t + R_i)Hit-and-run needs both b > bcrit and enough speed; below roughly 1.2 vesc grazing impacts tend to be captured and merge. The 1.2 used for the shaded analytic map is a rule of thumb, not a published constant - the true boundary depends on γ and θ, which is exactly what the sampled-map experiment probes.
Disruption threshold. Specific impact energy in the reduced-mass form and the catastrophic disruption threshold Q*RD (largest remnant = half the total mass), after Leinhardt & Stewart (2012):
Q_R = (1/2) mu v_imp^2 / M_tot Q*_RD = [ (gamma+1)^2 / (4 gamma) ]^( 2/(3 mubar) - 1 ) * Q*_RD,gamma=1 Q*_RD,gamma=1 = c* (4/5) pi rho_1 G R_C1^2 (c* ~ 1.9, mubar ~ 0.36, rho_1 = 1000 kg/m3)RC1 is the radius of a sphere of the combined mass at 1000 kg/m³. These are published fits for strength-less rocky bodies; they are shown for reference and are not computed by the toy model. Planet-size collisions in the 1-2 vesc range have QR well below Q*RD unless the masses are comparable.
Moon-forming scenario. The canonical giant impact (Hartmann & Davis 1975; Cameron & Ward 1976; Canup & Asphaug 2001) is a Mars-sized body (about 0.1 M⊕, γ ~ 0.12) striking the proto-Earth at about 1.0-1.1 vesc, θ ~ 45°, delivering about 1.1 LEM (LEM ~ 3.5 x 1034 kg m2/s, the present Earth-Moon system) and putting of order 1-2 lunar masses (MMoon = 0.0123 M⊕) into a disk. Alternatives with a fast-spinning proto-Earth or a nearly equal-mass impactor (Cuk & Stewart 2012; Canup 2012) are active research; this lab shows the geometry-and-energy picture, not a resolved prediction.
The model (SPH-lite). 103 particles of equal lattice spacing; mantle particles have mass m, iron-core particles 2.4 m (core mass fraction 0.30). Number density ni = Σj W(rij, h) (cubic spline), and each particle stores an elastic energy only when compressed beyond the rest density n0:
e_i = m_i c^2 (n_i - n0)^2 / (2 n0^2) (n_i > n0) F_i = - sum_j ( e'_i + e'_j ) grad_i W_ij + Monaghan viscosity (alpha=1.2, beta=2.4) + Plummer gravityBecause the pressure force comes from a potential, linear and angular momentum are conserved by construction; energy is conserved up to the integration error and the viscous heat Q (tracked and shown as glow). Gravity is advanced with a RESPA split (kicked every 3 sound-speed sub-steps). Honest simplifications: no real equation of state (no Tillotson/ANEOS, no melting or vapour), no material strength, no tension (so the remnant is held together by gravity only), the code sound speed is about 1.8 x the target escape speed (real rock is slower, relative to vesc), both bodies share bulk density and core fraction, no spin before impact, no tidal pre-deformation, ~103 particles instead of the 105-107 of research codes - so debris-disk and moon masses carry an uncertainty of a few particles and the late accretion shown is only the first hours-to-days of a process that takes years. The colours show where material started, not its real composition.
Classification (largest remnant Mlr, second clump M2, found with a friends-of-friends search; mass counts as bound if its two-body energy about the remnant is negative; disk = bound with periapsis outside ~0.9 Rlr): hit-and-run if an escaping clump holds at least half the impactor mass while Mlr is within -15%/+12% of Mt; merger if Mlr ≥ 0.9 Mtot (with debris disk if the disk is ≥ 1.2% of Mtot); grazing capture if the target is intact (Mlr within 3% of Mt) and the impactor is still bound and returning; partial accretion if Mlr > 1.03 Mt; erosion if the target lost mass but Mlr > Mtot/2; otherwise catastrophic disruption. Thresholds in the style of Leinhardt & Stewart (2012) and Genda et al. (2012) but chosen for this toy model.
Assets. Cutaway planet, impactor, rock-chunk particle mesh, cratered moon and disk guide were modelled in Blender 5.2 with Cycles-baked procedural textures; the physics runs in plain JavaScript on top of Three.js r160.