This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 ≤ μ < μcrit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case μ = μcrit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness.

The linear stability of libration points of the photogravitational restricted three-body problem when the smaller primary is an oblate spheroid

In this paper we use the planar circular restricted three-body problem where one of the primary bodies is an oblate spheroid or an emitter of radiation in order to determine the basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the values of the mass ratio $\mu $
 , the oblateness coefficient $A_{1}$
 , and the radiation pressure factor $q$
 vary in predefined intervals. The regions on the configuration $(x,y)$
 plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson method. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed in order to obtain the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation demonstrating how the dynamical quantities $\mu $
 , $A_{1}$
 , and $q$
 influence the basins of attractions. Our results suggest that the mass ratio and the radiation pressure factor are the most influential parameters, while on the other hand the structure of the basins of convergence are much less affected by the oblateness coefficient.

Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

This paper investigates the stability of triangular equilibrium points (L
 4,5) in the elliptic restricted three-body problem (ER3BP), when both oblate primaries emit light energy simultaneously. The positions of the triangular points are seen to shift away from the line joining the primaries than in the classical case on account of the introduction of the eccentricity, semi-major axis, radiation and oblateness factors of both primaries. This is shown for the binary systems Achird, Luyten 726-8, Kruger 60, Alpha Centauri AB and Xi Bootis. We found that motion around these points is conditionally stable with respect to the parameters involved in the system dynamics. The region of stability increases and decreases with variability in eccentricity, oblateness and radiation pressures.

On the stability of triangular points in the elliptic R3BP under radiating and oblate primaries

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors), in the planar circular restricted five-body problem (CR5BP). The evolution of the position and the linear stability of the equilibrium points is determined, as a function of the value of the mass parameter. The attracting regions, on several types of two dimensional planes, are revealed by using the multivariate version of the classical Newton-Raphson iterative method. We perform a systematic investigation in an attempt to understand how the mass parameter affects the geometry as well as the degree of fractality of the basins of attraction. The regions of convergence are also related with the required number of iterations and also with the corresponding probability distributions.

Basins of attraction of equilibrium points in the planar circular restricted five-body problem

This paper introduces a new approach to the study of artificial equilibrium points in the circular restricted three-body problem for propulsion systems with continuous and purely radial thrust. The propulsion system is described by means of a general mathematical model that encompasses the behavior of different systems like a solar sail, a magnetic sail and an electric sail. The proposed model is based on the choice of a coefficient related to the propulsion type and a performance parameter that quantifies the system technological complexity. The propulsion system is therefore referred to as generalized sail. The existence of artificial equilibrium points for a generalized sail is investigated. It is shown that three different families of equilibrium points exist, and their characteristic locus is described geometrically by varying the value of the performance parameter. The linear stability of the artificial points is also discussed.

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Artificial Equilibrium Points for a Generalized Sail in the Circular Restricted Three-Body Problem

In the case where the mass of the radiating body (such as the sun) is much smaller than the mass of the other main gravitating body (such as the galactic nucleus), the triangular libration points in the plane photogravitational restricted circular three-body problem will be Lyapunov-stable almost everywhere within the region in which the necessary stability conditions are satisfied Instability will, however, occur on the curves corresponding to the inner third- and fourth-order resonances

A. A. Perezhogin

Papers

Stability of the triangular libration points in the photogravitational restricted circular three-body problem