Motion compensation is one of the key technologies enabling the high compression efficiency of modern video coding standards. To allow compression of spherical video content, special mapping functions are required to project the video to the 2D image plane. Distortions inevitably occurring in these mappings impair the performance of classical motion models. In this paper, we propose a novel motion plane adaptive motion modeling technique (MPA) for spherical video that allows to perform motion compensation on different motion planes in 3D space instead of having to work on the - in theory arbitrarily mapped - 2D image representation directly. The integration of MPA into the state-of-the-art H.266/VVC video coding standard shows average Bj{\o}ntegaard Delta rate savings of 1.72\% with a peak of 3.37\% based on PSNR and 1.55\% with a peak of 2.92\% based on WS-PSNR compared to VTM-14.2.