Photogravitational magnetic-binary problem with oblateness and belt of material points

Abstract

We study the motion of a charged particle in the framework of magnetic-binary problem where the bigger primary is the source of radiation and the smaller primary is the oblate body; and they are enclosed by a homogeneous circular truss of material points centered at the center of mass of the system. We have determined the equations of motion that govern the motion of a charged particle. The coordinates of collinear and non-collinear equilibrium points and their linear stability have been calculated. Numerical results reveal that the ratio of magnetic moment λ has a huge impact on the location, stability and orbital dynamics of the problem. We observed that there exists eight, eleven and thirteen equilibrium points for different values of mass parameter μ and the ratio of magnetic moment λ. Further, we observed that all non-collinear equilibrium points are unstable in the Lyapunov sense. But the collinear points L4 and L6 show a stable behavior for some values of μ and λ, while other collinear equilibrium points are unstable. The geometric configuration of zero velocity curves of the charged particle is numerically simulated and addressed. Moreover, first order approximations to a Lyapunov and Lissajous orbits are summarized near the collinear equilibrium points under the effect of λ.