I remember spending a lot of time playing with a planets-and-gravity simulator on the Mac when i was a kid. I wrote a crappy clone of it as an applet for one of my first jobs!
This is the best web-based equivalent i found with a quick search:
I played with a simple program like that for the Amiga when I was younger, and then I discovered that there was an O(n log n) algorithm[1] rather than the obvious O(n^2) one. Never was up to writing a program to use it.
https://en.wikipedia.org/wiki/Barnes%E2%80%93Hut_simulation