Stability of the celestial body orbits under the influence of Yukawa potential

Abstract

The famous Yukawa-type potential was very often used for explaining a great variety of recent observed astronomical phenomena which range from the solar-system scale to cosmological distances. In this paper we tackle the two-body problem in the Yukawa post-Newtonian field from the particular standpoint of orbits stability. Starting from the equations of motion and first integrals written in standard polar coordinates, we apply McGehee-type transformations of the second kind. Then we depict the phase-space structure considering the foliations by the energy constant and the angular momentum constant. Various stability regions are found for each case. The problem presents interesting features, such as: cases when all trajectories (maybe except for a separatrix) are stable; cases when there exist totally different types of orbits, both stable and unstable, for the same values of the energy constant and the angular momentum constant; the existence of stable motion for nonnegative energy levels; positive Lebesgue measure for initial data leading to quasiperiodic and noncircular periodic orbits; the key role of the angular momentum.