STARCLUSTER
N-BODY 60 FPS
Gravitational N-Body & Cosmic Logistics

10,000-Star Sublight Relativistic Orbital Simulator

Experience symplectic Velocity-Verlet orbital integration across dense globular clusters, Keplerian planetary disks, and relativistic trade networks with real-time velocity distributions and economic throughput telemetry.

Active Stellar Bodies
2,500 Stars
Total System Mass
14,850 M☉
Virial Equilibrium (2K/|U|)
0.984
Interstellar Trade Volume
8.42 kTLy/hr

N-Body Orbital Simulator

Symplectic Integrator
Zoom: 1.0x | Center: (0, 0) AU | Mode: PAN/DRAG
Interactive Cursor Tool
Orbital Architecture Presets
Gravitational Dynamics
Gravity Constant ($G$) 1.00x
Time Step ($\Delta t$) 1.00x
Star Count ($N$) 2,500
Optics & Rendering
Orbital Trail Length Medium

Velocity Distribution ($N(v)$ vs $v$)

Interstellar Trade Volume (kTLy/hr)

Astrodynamics Diagnostics

  • Kinetic Energy ($K$): 3.41 × 10⁴⁶ J
  • Potential Energy ($U$): -6.88 × 10⁴⁶ J
  • Energy Drift ($\Delta E/E_0$): < 0.002%
  • Max Lorentz Factor ($\gamma_{\text{max}}$): 1.024
  • Center of Mass ($\Delta R$): 0.012 AU
  • Integrator Clock: 0.00 Kyr
Astrodynamics & Classical Gravitation

Symplectic Velocity-Verlet Integration & Plummer Softening

The N-body gravitational problem solves the mutual interactions of $N$ point masses under Newtonian gravity modified by a Plummer softening parameter $\epsilon$ to eliminate singular close-encounter force divergence:

$$\mathbf{a}_i = \frac{d^2\mathbf{r}_i}{dt^2} = -G \sum_{j \ne i}^N \frac{m_j (\mathbf{r}_i - \mathbf{r}_j)}{\left( |\mathbf{r}_i - \mathbf{r}_j|^2 + \epsilon^2 \right)^{3/2}}$$
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Symplectic Invariance

The Velocity-Verlet numerical scheme preserves phase space volume (Liouville's theorem) and exhibits zero secular energy drift over millions of orbital cycles, making it vastly superior to Standard Euler or Runge-Kutta for long-term orbital stability.

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Virial Theorem Equilibrium

For a self-gravitating cluster in statistical equilibrium, the time-averaged kinetic and potential energies satisfy $2\langle K \rangle + \langle U \rangle = 0$. Deviations indicate ongoing core collapse, tidal stripping, or cluster evaporation.

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Doppler Velocity Shift

Stellar colors dynamically shift based on projected line-of-sight velocity: approaching stars undergo relativistic blue shift ($z < 0$), while receding stars undergo red shift ($z > 0$), providing instant orbital kinematics visualization.

Cosmic Logistics

Sublight Interstellar Trade & Commodity Routing

Across colonized star systems, automated sublight freighters travel along gravitational corridors to exchange antimatter propellant, rare earth elements, and bio-dome agricultural surpluses.

Gravitational Slingshots

Freighter routes leverage Oberth-effect slingshots around central supermassive cores, boosting freight velocity to $0.15c$ without expending reaction mass.

Relativistic Market Lag

Commodity pricing indices update with light-speed communication delays $\tau = d/c$, generating orbital price arbitrage opportunities between inner core worlds and outer rim outposts.

Dynamic Topological Routing

Trade corridors dynamically reconfigure as planetary systems orbit, minimizing relativistic transit time and shielding ships from coronal mass ejections.

System State JSON

Live Orbital System Manifest

Export or inspect the real-time astrophysical parameters of the active star cluster:

{ "system_id": "STARCLUSTER-NGC-7006", "canonical_url": "https://jirnyak.github.io/starcluster/", "integrator": "Symplectic Velocity-Verlet 2nd Order", "central_body": { "name": "Sagittarius Core Alpha", "type": "Supermassive Compact Core", "mass_solar": 10000.0, "schwarzschild_radius_au": 0.197 }, "cluster_parameters": { "active_particles": 2500, "gravitational_constant": 1.0, "plummer_softening_au": 0.25, "virial_ratio_2K_U": 0.984, "trade_network_active_nodes": 6 } }