If I wanted to accurately simulate and orbit of some non-existing celestials that orbit around one object, what free program should I use?

The developer for this game I play (www.aberoth.com) builds a lot of his stuff using physics. When the solar system in the game has certain orbs orbiting a candle line up in a specific way special events occur. However he is very secretive as to how it works exactly, but I have gathered data on their radius's and speeds and was wondering if there was a good program I could use to simulate the simple orbit to accurately predict future events In order to gain an edge on the other players using science.