Projection from inside a sphere

Hi all,

I have a projector and a sphere with a hole at the bottom to let a fisheye lens in. Of course I’d like to project planets onto it for an exhibit.

I haven’t been able to deform the projection properly so that the junction of the two grids meet at the equator. In real life, it looks more or less like this picture.

So I’d like to shift the whole thing down but if I fiddle with the FOV Angle of the Projection TOP, I’m loosing pixels at the pole. So what would be the right approach to achieve the right deformation?