Cactus is a general, modular, parallel environment for solving systems of partial differential equations. The code has been developed over many years by a large international collaboration of numerical relativity and computational science research groups and can be used to provide a portable platform for solving any system of partial differential equations.
Xplanet was inspired by Xearth, which renders an image of the earth into the X root window. All of the major planets and most satellites can be drawn, similar to JPL's Solar System Simulator. A number of different map projections are also supported, including azimuthal, Mercator, Mollweide, orthographic, and rectangular.
SaVi is satellite visualization software that lets you create, run, examine, and modify satellite orbits in two and three dimensions. Simulations of Iridium, Globalstar, Galileo, GPS, and other satellite constellations are included. SaVi requires Tcl and Tk on a system with Unix libraries. SaVi works well with the 3D renderer Geomview. Geomview is optional, though recommended for its 3D rendering capabilities.
Planets is a fun, interactive program for many-body gravity simulations. The emphasis is on play: it's easy to add in planets, zoom in and out, change the physical constants, save and load configurations, etc. It's designed to be easy enough for a kid to enjoy, but that hardly precludes adults.