After nearly a month of tinkering with code, nearly giving up twice, and realizing that I was going to actually need to relearn my linear algebra to get a real solution, I managed to create this graph.  It is the position of the moons of Jupiter relative to the planet as seen from earth.

Thanks to Thor for helping me get to the realization that straight up geometry wasn’t going to be good enough, and help boot strap my relearning of vector math.  Once I started using real linear algebra I didn’t even have to cheat on generating the sign.  Next step… JNI.