Pseudo-Newtonian planar circular restricted 3-body problem

Abstract

We study the dynamics of the planar circular restricted three-body problem in the context of a pseudo-Newtonian approximation. By using the Fodor-HoenselaersPerjés procedure, we perform an expansion in the mass potential of a static massive spherical source up to the first non-Newtonian term, giving place to a gravitational potential that includes first-order general relativistic effects. With this result, we model a system composed by two pseudo-Newtonian primaries describing circular orbits around their common center of mass, and a test particle orbiting the system in the equatorial plane. The dynamics of the new system of equations is studied in terms of the Poincaré section method and the Lyapunov exponents, where the introduction of a new parameter ǫ, allows us to observe the transition from the Newtonian to the pseudo-Newtonian regime. We show that when the Jacobian constant is fixed, a chaotic orbit in the Newtonian regime can be either chaotic or regular in the pseudo-Newtonian approach. As a general result, we find that most of the pseudo-Newtonian configurations are less stable than their Newtonian equivalent.

Orbital dynamics in the photogravitational restricted four-body problem: Lagrange configuration

“…From Eqs. (1)(2)(3)(4)(5)(6), the location of the primaries (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ), are respectively…”

“…Until today, the study of the dynamics in the restricted three-body problem is still an active field of research (see e.g. [3][4][5][6][7]).…”

Unveiling the basins of convergence in the pseudo-Newtonian planar circular restricted four-body problem

“…A series of research papers (e.g., [23]; [12]; [14]) are available on the 1 st order post-Newtonian equations of motion for the restricted problem of three bodies which are deduced by using the Einstein-Infeld-Hoffmann theory (e.g., [19], [18]). [17] studied the dynamics of the planar circular restricted problem of three-bodies in the context of a pseudo-Newtonian approximation by using the Fodor-Hoenselaers-Perjé procedure, while [20] examined the influence of the separation between the primaries. It is concluded that the post-Newtonian dynamics substantially differ from the corresponding classical Newtonian dynamics provided the distance between the primaries is sufficiently small.…”

“…When the value of the transition parameter ∈ (0, 0.67752839], the libration points L 11,12,13,14 , L 15,16,17,18 and L 19,20,21,22 move away from the centers of the primaries P 1 , P 2 , and P 3 , respectively, while on the other hand the libration points L 2,7,8 move towards the centers of the primaries P 1 , P 2 , and P 3 , respectively. In particular, L 1,3,5,6,9 and L 10 , move towards the central libration point L 4 .…”

Orbit classification in a pseudo-Newtonian Copenhagen problem with Schwarzschild-like primaries

“…On the other hand, the study of the motion of test particles around binary black hole systems based on reduced three-body problem approaches (Roche approximations) is a relatively recent line of research (see e.g., Dubeibe et al 2017). In point of fact, in a recent paper, some of us have given a general theoretical framework based on the Paczyński & Wiita potential for describing the gravitational field of two non-Newtonian primaries (Zotos et al 2018).…”