Transfers from the Earth to $$L_2$$ Halo orbits in the Earth–Moon bicircular problem

This paper deals with direct transfers from the Earth to Halo orbits related to the translunar point. The gravitational influence of the Sun as a fourth body is taken under consideration by means of the Bicircular Problem (BCP), which is a periodic time dependent perturbation of the Restricted Three Body Problem (RTBP) that includes the direct effect of the Sun on the spacecraft. In this model, the Halo family is quasi-periodic. Here we show how the effect of the Sun bends the stable manifolds of the quasi-periodic Halo orbits in a way that allows for direct transfers.

Perturbation due to a Circumbinary Disc around L4,5 in the Photogravitational Elliptic Restricted Three-Body Problem

The motion is investigated of dust/gas particles in the elliptic restricted three-body problem (ER3BP) in which the less massive primary is an oblate spheroid and the more massive a luminous body surrounded by a circumbinary disk. The paper has investigated both analytically and numerically the effects of oblateness and radiation pressure of the primaries respectively together with the gravitational potential from a disk on the triangular equilibrium L4,5 of the system, all in the elliptic framework of the restricted problem of three bodies. The important result obtained therein is a move towards the line joining the primaries in the presence of any /all perturbation(s). A significant shift away from the origin as the radiation pressure factor decreases and oblateness of the smaller primary increase is also observed. It is also seen that, all aforementioned parameters in the region of stability have destabilizing tendencies resulting in a decrease in the size of the region of stability except the gravitational potential from the disc. The binary system Ruchbah in the constellation Cassiopeiae is an excellent model for the problem, using the analytic results obtained, the locations of the triangular points and the critical mass parameter are computed numerically.

LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

A SURVEY ON EXTENSIONS OF THE PURE GRAVITY SWING-BY MANEUVER

The present paper surveys the more recent techniques related to the swingby maneuver, where a spacecraft changes its energy and angular momentum by passing close to celestial bodies. It is focused on the literature related to extensions of this maneuver, with emphasis in the powered version, where an impulse is applied to the spacecraft near the closest approach. Several mathematical models are considered, including the patched-conics approximation for analytical studies, and the restricted three-body problem for the numerical simulations. The main goal is to show the models and the main conclusions available in the literature for those maneuvers. Some key results are shown to discuss important aspects of this maneuver, including the analysis of the energy variation of the spacecraft, the behavior of the trajectories and other applications.