A loose and non-technical breakdown of how PISES generates random but realistic orbital hierarchies and geometries for multiple-star solar systems.
For the past few months, we have been working on generating an orbital hierarchy of a solar system. We then took this abstract hierarchy and ascribed it with a set of Keplerian Orbital Elements. Finally, we used these orbital elements to build up hard position and velocity data for our orbital bodies. We now have everything we need in order to render and propagate these orbital bodies in Unity Gaming Engine.
In our final step before visualization, we must actually generate a series of positions and velocities for these orbital bodies, so we can draw them to screen and animate them. At this point, we have all the data we need.
We have managed to generate an abstract simplex solar hierarchy. This abstract hierarchy contains no geometric data, only a binary tree of orbital nodes. We wish now to translate this abstract tree into a series of legitimate Orbital Elements, whose ellipses we want to render to screen.
In order to ascribe actual orbital data to the various stars and barycenters of a solar system, we will need a way to describe orbits in PISES. In this post, we'll get spun up on the 6 Keplerian Orbital Elements and what their limitations are.
In this post we will create a system which produces random, abstract simplex solar hierarchies for an N-ary solar system. We emphasize abstract here because these orbital hierarchies will contain no information about the actual Keplerian elements of the various solar bodies they describe: only their hierarchical arrangement.
The "Solar Hierarchy" of a solar system in PISES describes how the various stars of an N-ary solar system arrange themselves. If this seems like it might be an unsolvable, n-body gravitational problem that would require warehouses full of supercomputers to model with even vague realism, it absolutely is. However, it turns out that most N-ary solar systems arrange themselves in such a way that can be simplified to a series of very manageable, idealistic 2-body problems.