Sparky is correct. You don't need large apertures to get star trails. You just get more stars that way, and more of any ambient light. As you stop down, the dimmer stars are "removed" from the picture, and only the brightest ones will appear. This usually makes the pic look much better, in my opinion. Shoot too wide open, and there are a zillion trails clogging up the sky.

Those shooting star fields alone sometimes use fancy tripod heads that track the stars, eliminating the need for hypersensitization and/or pushing.