Electron spin and nuclear spin reduce the anisotropy of photofragments in relatively long-lived levels of the g3Σg+ and i3∏g states of the n = 3 triplet gerade system of molecular hydrogen. The intramolecular forces due to the spin result in a precession of the plane of rotation around the total angular momentum vector. The photofragment anisotropy reveals whether the excited state lifetime allows for this precession to occur, hence whether the fine and hyperfine structure are resolvable. In partially fine structure resolved experiments, using fast beam photofragment spectroscopy, this fine and hyperfine structure depolarization is observed. The theory behind the depolarization is presented as well.