Families of periodic horseshoe orbits in the restricted three-body problem

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found.We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of 17◦

Caustics of the restricted three-body problem

Trajectories of the planar, circular, restricted three-body problem are given in the configuration space through the caustics associated to the invariant tori of quasi-periodic orbits. It is shown that the caustics of trajectories librating in any particular resonance display some features associated to that resonance. This method can be considered complementary to the Poincare surface of section method, because it provides information not accessible by the other method.

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Exact solution for a three-dimensional three-body problem with harmonic interactions

The three-dimensional three-body problem with non-equal masses interacting through pairwise harmonic forces of non-equal strengths is analysed. It is shown that the Jacobi coordinates per se do not decouple this problem but lead to the problem of two coupled three-dimensional harmonic oscillators which becomes exactly soluble through the use of an additional coordinate set.

The Three Body Problem and the Runge-Lenz Equivalent Constant of the Motion

The Runge-Lenz equivalent for the Hydrogen Molecular Cation (and the Earth, Moon and Sun) problem is obtained

Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

On the periodic orbits and the integrability of the regularized Hill lunar problem

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantum propagator for some classes of three-dimensional three-body systems

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally, the energy spectrum and the eigenfunctions are recovered from the propagators. © 2005 Elsevier Inc. All rights reserved.

Irregular satellites of Jupiter: Three-dimensional study of binary-asteroid captures

Among the hidden pieces of the giant puzzle, which is our Solar system, the origins of irregularsatellites of the giant planets stand to be explained, while the origins of regular satellites arewell explained by the in situ formation model through matter accretion. Once they are notlocally formed, the most acceptable theory predicts that they had been formed elsewhere andbecame captured later, most likely during the last stage of planet formation. However, underthe restricted three-body problem theory, captures are temporary and there is still no assistedcapture mechanism which is well established. In a previous work, we showed that the capturemechanism of a binary asteroid under the co-planar four-body scenario yielded permanentcaptured objects with an orbital shape which is very similar to those of the actual progradeirregular Jovian satellites. By extending our previous study to a 3D case, here we demonstratethat the capture mechanism of a binary asteroid can produce permanent captures of objects byitself which have very similar orbits to irregular Jovian satellites. Some of the captured objectswithout aid of gas drag or other mechanisms present a triplet: semi-major axis, eccentricityand inclination, which is comparable to the already known irregular Jovian objects. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Contact parameters in two dimensions for general three-body systems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Natural formations at the Earth-Moon triangular point in perturbed restricted problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the evection resonance and its connection to the stability of outer satellites

In terms of stability around the primary, it is widely known that the semimajor axis of the retrograde satellites is much larger than the corresponding semimajor axis of the prograde satellites. Usually this conclusion is obtained numerically, since precise analytical derivation is far from being easy, especially, in the case of two or more disturbers. Following the seminal idea that what is unstable in the restricted three-body problem is also unstable in the general N-body problem, we present a simplified model which allows us to derive interesting resonant configurations. These configurations are responsible for cumulative perturbations which can give birth to strong instability that may cause the ejection of the satellite. Then we obtain, analytically, approximate bounds of the stability of prograde and retrograde satellites. Although we recover quite well previous results of other authors, we comment very briefly some weakness of these bounds. Copyright (c) 2008 Tadashi Yokoyama et al.

Exploring S-type orbits in the Pluto-Charon binary system

This work generates, through a sample of numerical simulations of the restricted three-body problem, diagrams of semimajor axis and eccentricity which defines stable and unstable zones for particles in S-type orbits around Pluto and Charon. Since we consider initial conditions with 0 <= e <= 0.99, we found several new stable regions. We also identified the nature of each one of these newly found stable regions. They are all associated to families of periodic orbits derived from the planar circular restricted three-body problem. We have shown that a possible eccentricity of the Pluto-Charon system slightly reduces, but does not destroy, any of the stable regions.