Quote Originally Posted by thor36 View Post
... I would like to save some sweat, time, nerves and errors with drawing a sphere, since the central point of my project are orbits and physical calculations of spacecraft motion ...
Google gluSphere. It generates all of the vertices and polygons making up a sphere. You have control over the number of lat-lon divisions it generates. Also, if you request, it generates texture coordinates allowing you to wrap a world map image around the sphere without any ugly seams. This is what I use in my sims.

You are smart in the way you're setting your priorities. You are developing a very small application. No need to spend a lot of time worrying about ultra-efficient OpenGL. Doing the graphics simply will allow you to concentrate on the engineering features of your sim.