Impact of a Disc and Drag Forces on the Existence Linear Stability of Equilibrium Points and Newton-Raphson Basins of Attraction

Abstract

This paper presents a study of zero velocity curves, linear stability analysis and basins of attraction corresponding to the equilibrium points in the Sun-Jupiter system with asteroid belt and β-Pictoris system with dust belt, respectively under the influence of perturbing factors in the form of Poynting-Robertson drag (P-R drag), solar wind drag and a disc, which is rotating about the common center of mass of the system. Zero velocity curves are obtained and it is observed that in the presence of perturbing factors, the prohibited regions of the motion of infinitesimal mass get disturbed. Again, linear stability and effects of perturbing factors are analyzed for the triangular equilibrium points. It is noticed that because of P-R drag, triangular equilibrium points become unstable within the stability range. Finally, the Newton-Raphson basins of attraction corresponding to the equilibrium points are computed and it is found that in the presence of the disc, geometry of the basins of attraction gets change, whereas the effects of remaining perturbing factors on the structure of basins of attraction are very small.