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RELATIVISTIC N-BODY GRAVITY

Newtonian gravity, relativistic softening, and stable figure-8 celestial choreographies.

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N-BODY GRAVITY HUD

60 FPS

// ORBITAL SCENARIO PRESETS

GRAVITATIONAL CONSTANT G 1.0 G

ORBITAL TRAIL PERSISTENCE 120 pts

[Drag pointer to sling new planets with custom velocity vectors]

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RESEARCH & LEARNING VAULT // Relativistic N-Body Gravity & Orbital Mechanics

Pairwise gravitational summation, stable figure-8 choreography, and black hole accretion.

ACADEMIC & ALGORITHMIC REFERENCE

// HISTORICAL ORIGINS

Poincaré proved in 1887 that the general 3-body problem has no closed-form analytical solution, founding modern chaos theory. In 2000, Chenciner & Montgomery discovered the stable Figure-8 orbit.

// GOVERNING EQUATIONS

\vec{a}_i = \sum_{j \ne i} \frac{G m_j (\vec{r}_j - \vec{r}_i)}{(\|\vec{r}_j - \vec{r}_i\|^2 + \epsilon^2)^{3/2}}

// BROWSER IMPLEMENTATION

Computes pairwise gravitational force vectors with Plummer softening ( $\epsilon$ ), tracking velocity vectors across sub-stepped leapfrog Euler timeframes.

// GUIDED EXPERIMENTS TO TRY IN THIS SANDBOXNORMAL

1Figure-8 Chaos Perturbation

🎯 Action:Load 'Figure-8 3-Body' and click with mouse to inject a small 4th asteroid.

✨ Observe:Watch the delicately balanced 3-body loop suddenly undergo chaotic resonance and eject celestial bodies into deep space.

2Black-Hole Slingshot Assist

🎯 Action:Load the black-hole preset, then drag a slingshot vector from far away so it grazes the event horizon and release.

✨ Observe:The probe whips around the black hole on a hyperbolic bend, stealing orbital energy for a gravity assist.

// CURATED PAPERS, RFCS & RESOURCES

A Remarkable Periodic Solution of the Three-Body Problem in the Case of Equal Massespaper

By Alain Chenciner & Richard Montgomery (Annals of Mathematics, 2000)

The mathematical proof and discovery of the stable zero-angular-momentum figure-8 choreography.

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RELATIVISTIC N-BODY GRAVITY

RESEARCH & LEARNING VAULT // Relativistic N-Body Gravity & Orbital Mechanics