Okay looked at your BMP loader and noticed a big problem. I went into one of my full blown BMP loaders and twiddled yours specific to 24-bit RGB bitmaps.

Problem #1 - you were treating header data...

Your palette is flipped!

Red is Blue and Blue is Red. Green is fine!

You're using a 24-bit BMP and those are oriented Blue, Green, Red, however the frame buffer is Red, Green, Blue!

I...

The planets. They're pretty small to make out on screen and making them larger for testing purposes, and making them stationary infront of the viewport.

I normally don't use the glQuad stuff. I use my own meshes, even for sphere's.

I can't examine your code right now, but have you tried increasing your radius to 4.0 or so, stopped the orbits, and rotated in place to see your planets better?

Big possible problem.\
Your textures are not 2^N, and not all square.
Some video cards require square, but most definitely 2^N, with few exceptions. Try stretching the bitmap to 128x128, etc.

You may want to mention it is OpenGL.
I cut in my own textures and Kind of cool, but I only see one blue planet.

Adding your textures would be cool. If you're worried about copy cats, Put a big...