Depth test problems in large environments

Hello, I'm developing an application that models flight dynamics around the Earth, and because of this, I have a rather large environment (I define my near clipping plane to be 0.1 and my far to be 35,000,000). I use gluLookAt to follow the plane(s) around, however there are often cases where the depth test seems to be malfunctioning; if I place a sphere in place of the Earth and place a texture map on the sphere, often times (usually depending on the location of the camera) I see the opposite side of the texture map. If I *don't* use a texture map, and instead use a LINE polygon mode when rendering the sphere, sometimes the lines appear on the *outside* of the plane, even though the plane is "above" the earth. None of these problems occur, however, when the objects are smaller-- and it may have nothing to do with the size of the environment at all, but rather the size of the sphere that I'm using. Does anyone have any clue why a sphere (of radius > 6,000,000) would have these depth-test issues? Or is it maybe not a depth test issue at all? Thanks in advance! Rick