Solar System

9 bodies, Newtonian gravity. Distances real (AU), bodies enlarged for visibility.

Planets

View

Speed

simulation speed 1.0 years/s

logarithmic — 1 to 1000 years/s

Visual scale

1× is the default exaggerated size — bodies are inflated relative to orbital distance so they remain visible. The Sun is rendered ≈ 35× wider than at real proportions, planets ≈ 2000× on average. Adjusting these sliders is purely cosmetic and does not affect gravity.

Sun size 1.0× (≈ 35× real)

visual only — does not affect gravity

Planet sizes 1.0× (≈ 2,000× real avg)

gas giants ~900×, rocky planets ~3000× — visual only

KAM stability

KAM (Kolmogorov–Arnold–Moser): a theorem about which orbits in a perturbed gravitational system stay stable. Orbits with irrational period ratios — especially the golden ratio φ — resist perturbations the longest; integer ratios like 2:1 and 3:1 collapse through resonance. The controls below let you push the system past these thresholds and watch what survives.

Distances are given in AU (astronomical units; 1 AU ≈ 149.6 million km, the mean Earth–Sun distance). Jupiter's real orbital distance is 5.20 AU; the presets below pull it inward to specific resonance positions with Earth.

planet masses × 1×

Uniform scale on planetary masses (Sun stays at M=1). At the real Jupiter position (5.20 AU) even ×100 keeps the inner system bounded on visible timescales — destabilisation requires combining high mass with resonant positioning (use the KAM presets below).

eccentricity × 1.0×

Multiplies each planet's initial eccentricity. e=0 is a perfect circle, e=0.5 a strongly elongated ellipse. Re-initialises orbits — physics state resets.

inclinations × 1.0×

Multiplies orbital inclination relative to the ecliptic plane. Real Solar-System inclinations are 0.8°–7° and barely visible in 3D; ×8 makes the layered structure clear without breaking stability.

gas drag 0

Linear drag F = −k·v on every planet, analogous to protoplanetary-disc gas drag. Orbits decay exponentially with timescale τ ≈ 1/(2k); at slider ~90 planets reach the Sun within tens of simulated years.

Presets

Real (5.20 AU) — restores the actual Solar System. No perturbations.
φ — stable — Jupiter at a ≈ 1.376 AU; Jupiter:Earth period ratio = φ (golden ratio). KAM-protected, no collapse on visible timescales.
2:1 → collapse — Jupiter at a ≈ 1.587 AU + masses ×50. Earth–Jupiter mean-motion resonance; inner system ejected within decades. Same mechanism that carves the Kirkwood gap at 3.27 AU in the real belt.
3:1 → collapse — Jupiter at a ≈ 2.08 AU + masses ×30. Weaker MMR than 2:1, slightly slower collapse.
⚠ break KAM — 2:1 position + masses ×800. Jupiter becomes gravitationally stellar-mass (0.76 M⊙); the Sun–Jupiter pair forms a tight binary. Earth and Mars fall inside Jupiter's stellar Hill sphere (R ≈ 1 AU); Mercury and Venus are ejected by the perturbation. Neptune at 30 AU survives and ends up on a circumbinary orbit.
⟳ reset state — restore positions and velocities to the last saved snapshot.

Diagnostics

Real-time metrics. Orbit counters confirm physics is running and show the timescale separation between inner and outer planets. The eccentricity rows are the KAM-stability indicator — they stay near nominal values in a stable system and grow under perturbation. Watch them spike when you apply a collapse preset.

time: 0.0 years

Mercury orbits: 0

Jupiter orbits: 0

Inner planets run ≈ 50× faster than outer ones (Mercury's period 0.24 y vs Jupiter's 11.9 y). Counters increment with simulated time; reset when you apply a preset or click reset state.

Mercury e_max: 0.21

Earth e_max: 0.02

Mars e_max: 0.09

Peak instantaneous eccentricity since last reset, computed via the Laplace–Runge–Lenz vector. Starts at the nominal real-system values (0.206 / 0.017 / 0.093) and stays there in a stable run. Grows past 0.3–1 (planet on a hyperbolic ejection trajectory) when KAM stability breaks. Display caps at 2.

Jupiter–Saturn T_S/T_J = 2.484

Saturn:Jupiter period ratio, computed from osculating semi-major axes (`a` recovered from current position and velocity via vis-viva), so the value reacts to perturbations and to KAM-preset changes in real time. In the real Solar System this equals 2.484 ≈ 5:2 — the Great Inequality, identified by Halley (1695) and Euler (1750s) and quantitatively explained by Laplace in 1785 as a near-5:2 commensurability. It drives oscillations in Jupiter's and Saturn's semi-major axes (amplitudes ≈ 0.002 AU and 0.005 AU respectively) and mean longitudes over a libration period of ≈ 883 years.

consumed by Sun: 0

About scales

Distances from the Sun are real in astronomical units (Mercury 0.387 AU, Neptune 30.07 AU).

Body sizes are exaggerated. Earth's actual diameter is 11,700× smaller than its orbital radius — on screen that would be 0.07 pixels. Use the «Visual scale» panel above to see how much they have been inflated.

Barycenter. In reality the centre of mass of the Sun–Jupiter system lies outside the Sun's surface (at 1.07 solar radii from the centre). With the Sun visually enlarged here, the marker appears inside the Sun's drawn body. Reduce the Sun's visual scale to see the real geometric relation.

Time is accelerated — the speed slider ranges from 1 to 1000 years/s.

Orbital lines are theoretical (Keplerian, two-body). Under strong perturbations planets deviate from them — that is the breakdown of KAM tori.

Asteroid belt is decorative — particles follow fixed Kepler orbits around the Sun's mesh, do not participate in N-body gravity, and rigidly track the Sun's wobble in the inertial frame (rather than orbiting the barycenter independently). It auto-hides when a planet falls into the Sun, so the belt doesn't keep peacefully orbiting through a collapsed system.

drag — rotate · scroll — zoom