Numerical integration methods solve the differential equations governing spacecraft motion through gravitational fields:
- Euler Method: First-order method. Fast computation but accumulates errors rapidly. Best for short simulations or learning.
- Runge-Kutta 4th Order: Fourth-order method with excellent accuracy-to-cost ratio. Industry standard for most simulations.
- Verlet Integration: Symplectic integrator that conserves energy over long periods. Ideal for orbital mechanics.
- Leapfrog Method: Second-order symplectic method. Stable and energy-conserving for gravitational N-body problems.
Performance Trade-offs: Higher-order methods require more computational steps per iteration but provide significantly better long-term accuracy.