Revisiting dynamical orbits in the planar anisotropic Kepler problem

In this investigation, a novel solving method has been introduced for determining the coordinates of a mass point m2 in orbit around a more massive primary m1 (within the framework of modified version of the restricted two- body problem, R2BP). Such analytical approach describes periodic orbits for the planar anisotropic Kepler problem instead of the classical Kepler's formulation of the R2BP. Simultaneously, a system of equations of motion in polar coordinates has been derived and then successfully explored to identify the quasi-periodic orbits for the planar anisotropic Kepler problem which are proved to be slightly quasi-oscillating along the elliptic classical orbit according to Kepler's law for R2BP. An analytical expression has been obtained for the function of polar radius via elegant procedure of integration (a successful repetitive cascade of changes of appropriate variables). So, solution can be presented via quasi-periodic cycles of oscillations of trajectory of mass point m2 moving around a massive primary m1. MSC classes: 70F15, 70F07.