N-Body Spacetime Gravity

Symplectic Verlet Integrator

Theory & Scientific Principles

Newtonian Gravitation: Softened Plummer Potential prevents infinite divergence during close encounters:

F_ij = G · (m_i · m_j) / (r_ij² + ε²)^(3/2) · r_ij

1. Symplectic Velocity Verlet: Conserves phase-space volume and maintains long-term orbital energy stability without artificial decay.

2. Inelastic Coalescence: Merging bodies conserve linear momentum: p = m₁v₁ + m₂v₂ and volume: R = (r₁³ + r₂³)¹/³.

3. Conservation Laws: Tracks kinetic (E_k), potential (E_p), and angular momentum (L) in real time.

Usage: Click & drag to launch bodies with velocity vector. Scroll to zoom, right-drag to pan.

Gravitational Constant G (N·m²/kg²)

Plummer Softening ε (px)

Time Step dt (seconds/frame)

Spawn Mass (kg)

Orbital Trail Length (steps)

Body Coalescence (Merge):

Active Bodies (N): 0

Total Kinetic (E_k): 0.00 J

Potential Energy (E_p): 0.00 J

Total Energy (E_tot): 0.00 J

Angular Momentum: 0.00

Spacetime Gravity Stage

Left Drag: Launch Body | Right Drag: Pan | Scroll: Zoom