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Physics Engine

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SpaceEngineerSS edited this page Dec 18, 2025 · 2 revisions

🔬 Physics Engine

CosmoRisk uses a scientifically accurate physics simulation based on established celestial mechanics.

Integrator

We use the Velocity Verlet algorithm for numerical integration:

x(t+dt) = x(t) + v(t)·dt + ½·a(t)·dt²
v(t+dt) = v(t) + ½·(a(t) + a(t+dt))·dt

Why Velocity Verlet?

  • Symplectic (conserves energy)
  • 2nd order accuracy
  • Stable for orbital mechanics
  • Used by NASA/JPL

Gravitational Model

N-Body Gravity

F = G · m₁ · m₂ / r²

Where:

  • G = 6.67430 × 10⁻¹¹ m³/(kg·s²)
  • m₁, m₂ = masses of bodies
  • r = distance between centers

Included Perturbations

Effect Description
Solar Gravity Central force from Sun
Earth Gravity For lunar/geocentric objects
Moon Gravity Close Earth approach perturbations
Jupiter Perturbation Major asteroid belt influence
Mars Perturbation Inner solar system effects
J2 Oblateness Earth's equatorial bulge
Solar Radiation Pressure Light momentum transfer
Yarkovsky Effect Thermal recoil from anisotropic emission
Poynting-Robertson Radiation drag on small particles

MOID Calculation

Minimum Orbit Intersection Distance is calculated using:

  • 72×72 point orbital sampling
  • Full Keplerian rotation matrices (Ω, i, ω)
  • Comparison between asteroid and Earth orbits

Constants

Constant Value Unit
G (Gravitational) 6.67430 × 10⁻¹¹ m³/(kg·s²)
AU (Astronomical Unit) 1.495978707 × 10¹¹ m
Solar Mass 1.98892 × 10³⁰ kg
Earth Mass 5.972 × 10²⁴ kg
Speed of Light 299792458 m/s

Orbital Elements

Asteroids are defined using Keplerian orbital elements:

Element Symbol Description
Semi-major axis a Orbit size
Eccentricity e Orbit shape (0=circle, 1=parabola)
Inclination i Tilt from ecliptic
Longitude of Ascending Node Ω Orientation of ascending point
Argument of Perihelion ω Orientation of closest approach
Mean Anomaly M Position in orbit

Kepler's Equation

To convert orbital elements to position:

E - e·sin(E) = M

Solved using Newton-Raphson iteration.

Torino Scale

CosmoRisk implements energy-based Torino Scale assessment:

Level Color Meaning
0 White No hazard
1 Green Normal discovery
2-4 Yellow Meriting attention
5-7 Orange Threatening
8-10 Red Certain collision

Energy thresholds (Megatons TNT):

  • < 1 kt: Burns up (Level 0)
  • 1 kt - 1 MT: Local damage
  • 1 - 100 MT: Regional damage
  • 100 - 1000 MT: National scale
  • > 1000 MT: Global effects

📖 See Torino Scale for complete methodology.

References

  1. NASA JPL Solar System Dynamics
  2. Velocity Verlet: Swope et al. (1982)
  3. Orbital Mechanics: Vallado (2007)
  4. Asteroid Densities: Carry (2012)
  5. Torino Scale: Morrison et al. (2004)

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