I'm wondering if the long shadows of late afternoon keep more and more light from being reflected from the ground toward the satellite, resulting in a gradually increasing darkening even though the sun is still visible to thee and me.
I imagine with no atmosphere and a billiard-ball smooth surface, the terminator would approach a sharp line except for diffraction and the fact that the sun is not a point source.
Right now, you can see the terminator swoop across the state.