Principia VS SolarSystem

Principia is extremely impressive, they document all their math here: https://github.com/mockingbirdnest/Principia/tree/master/doc...

One interesting detail is that the source code makes extensive use of non-ASCII identifiers, for mathematical symbols and for the names of mathematicians. One of the two primary contributors is also an active contributor to Unicode

KSP2 is still patched conics. Also here's a free n-body mod made by modders, https://github.com/mockingbirdnest/Principia

Principia - 𝑛-Body and Extended Body Gravitation for Kerbal Space Program

But one should just be aware that KSP simplifies by only tracking the strongest source of gravity. This turns all orbits into actual ellipses. But there is a mod called Principia that replaces it with the proper thing, thus allowing for very chaotic (but cool) flight paths using less thrust.

Principia has n-body

Install Principia and Real Solar System, then try again :P

Theres a mod that changes that to N-body simulation, it's called Principia

I'd suggest looking at their readme: https://github.com/mockingbirdnest/Principia

I also ported it in an opengl project: https://github.com/aromanro/SolarSystem

I've got a lot of physics-related projects on GitHub, most of them use matrices, even if sometimes it's not obvious. For example, this one: https://github.com/aromanro/SolarSystem uses matrices for changing from one coordinate system to another, rotations and so on.

I also have a solar system simulator, it used at first velocity Verlet, then I switched to Verlet since I really didn't need the velocity in it: https://github.com/aromanro/SolarSystem

There are countless of open source programs that do that, you just have to look over the sources. For example, one of my projects: aromanro/SolarSystem: A solar system simulator with velocity Verlet, using OpenGL for displaying. (github.com)