Equilibrium points and basins of convergence in the triangular restricted four-body problem with a radiating body
arXiv:1812.08641 · doi:10.1142/S0218127420300037
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.
arXiv comment15 pages, 10 figures, Preprint submitted to Elsevier
References in corpus (9)
- Basin entropy: a new tool to analyze uncertainty in dynamical systems
- Revealing the basins of convergence in the planar equilateral restricted four-body problem
- Chaotic dynamics and fractal structures in experiments with cold atoms
- Equilibrium Points and Zero Velocity Surfaces in the Restricted Four Body Problem with Solar Wind Drag
- Equilibrium points and basins of convergence in the linear restricted four-body problem with angular velocity
- On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem
- Orbital dynamics in the post-Newtonian planar circular Sun-Jupiter system
- Basins of convergence of equilibrium points in the generalized Henon-Heiles system
- Basins of convergence of equilibrium points in the generalized Hill problem