Yes, perhaps is it because of the far setting of the depth buffer this happens. Just setting a bigger value should fix it but probably leads to new problems since the precision gets worse. You see far object suddenly disappering in many games.
It’s Z-buffer artifacts that appear when the near to far ratio is too big. Move the near clipping plane as far away as possible. Because the bigger the near to far ratio (value of far divided by the value of near) is, the more precision you loose in your depthbuffer.
If you have z-buffer problems on spheres, than enable back face culling.
Another reason could be wrong mipmaps. Far away objects use minification with lower levels of detail textures. Maybe some are broken.
This isn’t an image of the day forum but I felt like commenting. The first pic looks good but you have stars appearing infront of the planet which is wrong.
Actually Tim, it’s not a star, if you download the program and move around, you will notice that those are little dust particles that fade in and out around the ship. In a still picture it looks like a star since the dust particles are simply points but it’s not an error. To remove the dust particles simply set the dustfield to 0 in the demo.sol file.