I have a sphere and I am trying to find out its orientation with respect to ground frame. The sphere is as follows:-

As can be seen from the image, different colors are painted on the sphere with equal thickness of each color along the circumference. I am comparing the sphere with our earth and these colors signify the longitude. The gradually decreasing thickness of each color as one travels towards the poles, is a measure of latitude. Now the angle of the edges (between two colors) with the horizontal of the world frame is what I think to be a measure of tilt somehow (however, the tilt for our earth is fixed at 23.5 degrees with vertical)
My question is that using these images of the sphere captured from a single camera, can I uniquely specify the orientation of the sphere with respect to the ground frame?
I do not know much about complex geometry, so please help.