How to make first-person work in zero-G with planets?

As my first project with Unity, I’m trying to make a 3D star system that you can fly around in first-person. I’m not too worried about planetary gravity, but my real problem is that you can only get so close to the planet before you just stop. I’d like to be able to just fly up to a planet and skim the surface (before you ask, no, I don’t need anything on the surface other than textures) without being locked on one altitude or being kept a certain distance from each planet.

I guess what I’m trying to ask is, how do I make the camera go straight forward, with little to no regard for collisions or physics in general?

I’m building a space game similar to what you’re talking about. I just have the camera with a small box collider on it and then rigid bodies with gravity disabled and sphere colliders on the planets.