Perihelion advance and stability criterion of a spinning charged test particle in Reissner-Nordstrom field: Application in earth orbit

In this study, a new equation of motion of a spinning charged test particle is examined. This equation is a counterpart of Papapetrou equations in Riemannian geometry when the charge of the particle disappears. By using the Lagrangian approach, the equation of motion of the spinning charged particle is derived. Furthermore, the path deviation of the spinning charged particle is achieved by the same Lagrangian function. The equation of motion of the spinning charged test particle, in the Reissner-Nordstrom background is entirely solved. The stability criteria of the spinning motion of the charge test particle are discussed. The Perihelion advance and trajectory of a spinning charged test particle, in the Reissner-Nordstrom space-time, is scrutinized along with two different methods; the first is the perturbation method (Einstein's method) and the second is described by Kerner et al.(14) Moreover, the effect of charge and spin on Perihelion advance are inspected. Additionally, the existing results are matched with the previously cited works. Finally, applications to the Earth's orbit are also analyzed.