Third-body perturbation in the case of elliptic orbits for the disturbing body

This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed. Copyright (C) 2008 R. C. Domingos et al.

Third body perturbation using a single averaged model considering elliptic orbits for the disturbing body

In the present work, we expanded the study done by Solorzanol(1) including the eccentricity of the perturbing body. The assumptions used to develop the single-averaged analytical model are the same ones of the restricted elliptic three-body problem. The disturbing function was expanded in Legendre polynomials up to fourth-order. After that, the equations of motion are obtained from the planetary equations and we performed a set of numerical simulations. Different initial eccentricities for the perturbing and perturbed body are considered. The results obtained perform an analysis of the stability of a near-circular orbits and investigate under which conditions this orbit remain near-circular.

Third-body perturbation in the case of elliptic orbits for the disturbing body

In the present work it is presented a semi-analytical and a numerical study of the perturbation caused in a spacecraft by a third body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second-order. The important reason for this procedure is to eliminate the terms due to the short time periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. It is presented an analysis of the stability of a near-circular orbit and a study to know under which conditions this orbit remains near-circular. A study of the equatorial orbits is also performed.

Optimal low-cost transfer to L4 and L5 lagrangian points based on G-family of periodic orbits

An alternative transfer strategy to send spacecrafts to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around LI is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecrafts in elliptic orbits around L4 and L5 are analysed considering the Restricted Three-Body Problem Earth- Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth. Copyright© (2012) by the International Astronautical Federation.

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)

Dynamical capture in the Pluto-Charon system

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

Effects of the eccentricity on the primames in the gravitational capture phenomenon

Gravitational capture is a characteristic of some dynamical systems in celestial mechanics, as in the elliptic restricted three-body problem that is considered in this paper. The basic idea is that a spacecraft (or any particle with negligible mass) can change a hyperbolic orbit with a small positive energy around a celestial body into an elliptic orbit with a small negative energy without the use of any propulsive system. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third body involved in the dynamics. In this way, this force is used as a zero cost control, equivalent to a continuous thrust applied in the spacecraft. One of the most important applications of this property is the construction of trajectories to the Moon. The objective of the present paper is to study in some detail the effects of the eccentricity of the primaries in this maneuver.

Strategies for plane change of Earth orbits using lunar gravity and derived trajectories of family G

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

3D stability orbits close to 433 Eros using an effective polyhedral model method

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dynamics of classical particles in oval or elliptic billiards with a dispersing mechanism

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

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

FROZEN ORBITS AROUND EUROPA

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

Low-altitude, near-polar and near-circular orbits around Europa

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

Artificial satellites orbits in 2:1 resonance: GPS constellation

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

GPS Satellites Orbits: Resonance

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)