A real-time 2D gravitational simulation written in C using raylib. Bodies attract each other under Newtonian gravity, merge on collision, and accrete into larger bodies over time.
- Newtonian gravity with softening to prevent force singularities
- Leapfrog (Störmer-Verlet) symplectic integration for long-term orbital stability
- Body merging with conservation of momentum and mass
- Particle sparks on collision
- Glow rendering with layered alpha falloff
- Color scales with body mass (dim red → white)
- Follow cam — click any body to track it
- Simulation speed control
- Pan and zoom
Most simple simulations use Euler integration — add velocity to position, add acceleration to velocity, repeat. It's first-order and bleeds energy over time, causing orbits to slowly spiral inward or outward.
This simulation uses leapfrog integration, which staggers velocity and position updates by a half-timestep. Leapfrog is symplectic — it conserves a quantity that behaves like energy indefinitely, keeping orbits stable over millions of steps. The cost is identical to Euler; the accuracy over long timescales is dramatically better.
Force calculations use a softening parameter in the denominator (r² + ε²) to prevent the force from blowing up when two bodies get very close.
Bodies are initialized in a rotating disk with tangential velocities derived from the circular orbit formula v = √(GM/r), giving each body the exact speed needed for a stable orbit at its radius.
Requires raylib installed on your system.
git clone https://github.com/UniquePython/n-body-sim
cd n-body-sim
make > /dev/null && bin/n-body| Input | Action |
|---|---|
↑ / ↓ |
Increase / decrease simulation speed |
Scroll |
Zoom in / out |
Left drag |
Pan camera |
Right click (body) |
Follow body |
Right click (empty) |
Unfollow |
Key constants in nbody.c you can tune:
| Constant | Default | Effect |
|---|---|---|
N_BODIES |
15 | Number of bodies at start |
G |
1000.0 | Gravitational constant |
SUN_MASS |
3000.0 | Mass of central body |
MIN/MAX_ORBIT_DIST |
80–350 | Initial orbital radius range |
EPS |
5.0 | Softening length |
K |
1.0 | Visual radius scale factor |