Effects of Poynting–Robertson drag on the circular restricted Three-Body Problem with variable masses

Abstract

This paper presents an investigation on the dynamical effect of Poynting–Robertson drag on the circular restricted three-body problem by considering all the masses are variable (primaries as well as infinitesimal body). After determining the equations of motion, the rate of change of the Jacobi constant with time has been evaluated. Further, in the numerical analysis section, the equilibrium points, Poincaré surface of section and Newton–Raphson basins of attraction have been plotted with the effect of Poynting–Robertson drag by Mathematica software. More exactly, we have noted that the equilibrium points are towards the origin, Newton–Raphson basins of attraction shrink and the Poincaré surface of sections, in two planes shrink and in one plane they expand. All these phenomena appear when we increase the effect of Poynting–Robertson drag. Finally, it is shown that the equilibrium points are unstable.

Keywords

• Poynting–Robertson drag
• variation of Jacobi constant
• Poincaré surface of sections
• crooked path
• Newton–Raphson basins of attraction