  A novel approximation method in studying the perihelion precession and
planetary orbits in general relativity is to use geodesic deviation equations
of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic
deviation approach, we generalize the calculation of orbital precession and the
elliptical trajectory of neutral test particles to Kerr$-$Newman space-times.
One of the advantage of this method is that, for small eccentricities, one
obtains trajectories of planets without using Newtonian and post-Newtonian
approximations for arbitrary values of quantity ${G M}/{R c^2}$.
