by @tlehman

• Euclidean space (no curvature)
• Newtonian gravity is the only force
• All bodies are spheres

• Existence of an NVIDIA GPU
• Computer runs Linux
• OpenGL is present

Each of the $n$ bodies will have a mass $m$ and a position $x(t)$ that is a 3-vector like $(0.1, -0.2, 3.1)$

The bodies need to be initialized with:

• masses
• positions and
• velocities

Once initialized, the simulation loop will take over.

The state of the universe is an array of length $n$, each cell of the array is the state of a body:

typedef struct body {
    float r; // radius
    float m; // mass
    float x,y,z;    // position
    float vx,vy,vz; // velocity
    float fx,fy,fz; // force on object (added up each sim loop)
} body;

To update the state of the universe, each unique pair of bodies needs to be selected to calculate it's mutual gravitational attraction. So with $n$ bodies, this runs at $O(n^2)$.

We can pass in the $n$ bodies into GPU memory, and then divide the CUDA kernels up to compute the force vectors in parallel.