Map / surfance separating from 3d ball

I’m about to make an animation where a whole world map separates from globe/ball. Kind of coating/jacket that opens from 3d ball to plain 2d surfance.
Does anyone have any certain technique that could be used for this purpose?

I have done some experiments with page curls that are used in flipping books, basically that is pretty close to what I’m looking for. But still it does the flipping to the wrong side, and it doesn’t look good.