February 17, 2017

February 11, 2017

N-Body Orbit Simulation with Runge-Kutta

In a previous post I introduced a simple orbital simulation program written in python. In that post we simulated orbits by simply taking the location, and velocities of a set of masses, and computed the force on each body. Then we calculated where all the bodies would end up under that force a small time step into the future. This process was repeated over and over again, and was used to simulate gravitational systems like our solar system giving outputs like you see below.

This technique is called the Euler method. If you're not familiar with using numerical methods to simulate orbits, I'd recommend taking a look there first!

Part 1: Python N Body Simulation


Orbit paths from the previous example




In this post I will be adding a more advanced time stepping technique called the Fourth Order Runge-Kutta method. Kids these days just call it RK4. I'll walk through the logic behind RK4, and share a python implementation. I will also link to a C++ implementation, and do a brief performance comparison.

Fourth Order Runge-Kutta