Curving strokes in 3d object

Hey,

I have spent all day trying to figure out a way how to create spinning planet with different locations and curved lines going from one place to another. I have spinning planet which just turns around, also locations on the globe, however couldn't find the way how to curve these lines which has to to be pinned to concrete location. My goal is to offset those lines in animation.  Any suggestions?  Picture is a reference what I am going for.