Free program that renders 3d imaginary star system with planets, moons, and retrograde orbits?

I’m working on a project with some friends for a custom campaign setting for a game and some stories we plan on writing, but we aren’t sure if the orbital mechanics we came up with would work. We’re looking for a program that will render the system we have in mind so that we can study the orbital patterns, day/night system, and seasons of a habitable moon.
Any help would be appreciated.

Your answer is Celestia.

http://www.shatters.net/celestia/

This program will let you see the rotations of all the planets, orbits. It even lets you see every star and solar system we’ve ever discovered.

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