I've created and run simulations of satellite constellations using SaVi, the Satellite Visualization software that was originally written at the Geometry Center. I began contributing to SaVi while studying at the Centre for Communication Systems Research. Now you can run SaVi, too, on Linux, FreeBSD, Solaris, SGI Irix, on Mac OS X, on Cygwin for Microsoft Windows, and even on a Raspberry Pi.
My SaVi releases include the constellation simulation scripts I've written, as well as enhanced resizeable coverage and fisheye displays.
SaVi is introduced in a SourceForge interview and a short paper. SaVi's features are described in the SaVi user manual. Satellite constellations are introduced in a tutorial using SaVi.
For real-time 3D animations, SaVi can use Geomview, also originally written at The Geometry Center. These videos, interactive java animations and renderings of constellations will quickly give you a quick idea of what Geomview can offer.