Precessions of spherical orbits in the rotating Melvin black hole spacetime and its constraints from the jet of M87*

We investigate precessions of spherical orbits of timelike particles in the background of a rotating black hole immersed in the Melvin magnetic field, and probe effects of the magnetic field on the precession period. Our results show that effects of the magnetic field on the particles' motions gradually decrease with the titled angle and finally vanish as the titled angle tends to $\pi/2$. With the increase of the magnetic field parameter, we find that the precession becomes rapidly. Modelling the spherical orbit to the warp radius in the accretion disk and with the observed precession period from the jet of M87*, we analyze the allowed regions of the black hole parameters and the warp radius in the accretion disk. Especially, we find a novel degenerated phenomenon of precession periods arising from magnetic field for two different spherical orbits, which does not appear in the usual Kerr black hole case. Moreover, we also discuss the possibility of observing effects of the magnetic field on the precession periods of jets for astrophysical black holes. Our study could help to further understand the rotating Melvin black hole and the relationship between magnetic fields and precessions of jets.