Multisutra Scientific Series — Module: Orbital Dynamics & Astrophysics
The Challenge of the N-Body Problem
One of classical mechanics’ deepest challenges is predicting the trajectories of three or
more massive objects interacting solely through gravity. The two-body problem has a clean analytic
solution (Kepler’s ellipses), but adding a third body produces a chaotic, non-linear system
with no general closed form — only numerical integration can track it.
Newtonian Gravitational Foundation
Our simulation engine implements Newton’s Universal Law of Gravitation:
where G = 6.674×10-11 N m2 kg-2 is
the gravitational constant, m1 and m2 are the body
masses, and r is their separation. At each integration step the net force on body
i from all others is:
Energy Conservation Telemetry (v2.0 HUD)
The total mechanical energy of a conservative gravitational system is the Hamiltonian:
Our leapfrog integrator keeps drift in H below 0.1 % over 10,000 steps.
The v2.0 HUD displays this live so you can watch energy conservation in real time.
What You Get
- Python (Pygame): Fully commented source with orbital-decay trails, mass sliders, and HUD.
- HTML version: Runs in any browser with zero installation.
- Authentic GIF preview generated directly from the simulation.
- README with setup guide and physics notes.