Dynamic behavior of variable mass R4BP with radiating and oblate primaries

This study presents dynamical equations for a variable mass fourth body, accounting for radiation from the first primary body and oblateness in the second and third primary bodies. Our findings reveal that the number and positional evolution of Lagrangian points are highly sensitive to variations in radiation, oblateness, and perturbation parameters in the $uv-$ and $uw-$plane, leading to the emergence of three, eight, or ten Lagrangian points. We employ linear stability analysis, utilizing the Routh–Hurwitz stability criterion, to demonstrate the instability of these Lagrangian points under specific conditions. Additionally, we investigate geometric structures, including zero velocity curves and surfaces at varying system energies, which illustrate an expansion of the potential motion region as system energy decreases. The geometry of the Newton–Raphson basins of attraction is also influenced by changes in radiation parameters and oblateness coefficients. Furthermore, we apply the Lindstedt–Poincaré technique to derive second- and third-order periodic orbits near non-collinear Lagrangian points, revealing distinct characteristics of these orbits through numerical simulations.