Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

Abstract

The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. In our setup, three primaries lay at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

Cuencas de salida para el límite clásico de una perturbación exacta de agujero negro tipo Hénon-Heiles

“…18 (1) o raíces de las funciones. En general, es necesario recurrir a métodos numéricos, pues las ecuaciones son no lineales y el sistema (14) no puede resolverse analíticamente. En el presente trabajo usaremos un método gráfico para comparar y confirmar los resultados obtenidos con el método de Newton-Raphson.…”

“…El cálculo de los puntos fijos puede hacerse en sistemas simples a través de la solución de sistemas de ecuaciones algebraicas, o recurriendo a métodos numéricos más elaborados cuando de sistemas altamente no lineales se trata. Este último enfoque ha sido utilizado en otros contextos astrofísicos para determinar los puntos fijos de algunas versiones del problema restringido de tres cuerpos [11], el problema de cuatro cuerpos restringido [12], el problema de cinco cuerpos restringido [13] y problemas de gravedad con presencia de radiación y arrastre de las primarias [14], entre otros.…”

Unpredictable basin boundaries in restricted six-body problem with square configuration

“…We can determine various aspects of dynamical system with the help of N-R BoA. Recently, few researchers have applied N-R method in various dynamical system including different perturbing terms in the effective potential ( [16], [22], [23], [24] and [25],). We have applied N-R iterative scheme (multivariate form) to study the BoA associated with the libration points.…”

“…In our case, we need the multivariate form of the N-R scheme. While going through recent articles on the applications of N-R method ( [16], [22] and [25]), we note that some initial conditions converge very quickly, some of them need more number of iterations, some of them even do not converge to any of the libration points. Thus, the study of the convergence of initial conditions is also a crucial aspect of the investigation.…”