Perturbed Restricted Three-Body Problem with Elongated Primary and Secondary Having Modified Newtonian Potential

This study investigates the dynamic motion properties of a variable-mass test particle under the effects of the gravitational forces of the elongated line-segment primary and secondary with modified Newtonian potential. The equations of motion, quasi-Jacobian integral, and perturbed mean motion of the system are evaluated with the use of the Jeans law and Meshcherskii space–time transformations. After this, an analytical study is presented on the existence and stability of stationary points. Then, we numerically illustrate the projections of potential surfaces, the locations of stationary points, their stability, and the attracting domain. This study provides valuable insights into the effects of various perturbations on the motion of a test particle within the system, thereby contributing to a deeper understanding of celestial dynamics and motivating further research into celestial mechanics and astrodynamics.