Periodic Solution of the Two-Body Problem by KB Averaging Method Within Frame of the Modified Newtonian Potential

In this paper, the Newtonian potential is modified by using the continued fraction potential. A simple formula for the modified potential is constructed, which is easy and powerful in practical uses. We investigate that the new parameter of the modified potential may play the same role of the zonal harmonic coefficients in the potential of an oblate body. The periodic solution of the two-body problem within frame of the central body has the modified potential is found by KB averaging method. The difference of the perigee vectors is also estimated at subsequent orbits. We underline that the model studied in this work could be used to obtain a harmony between the theoretical predictions and the observational evidences.