Time analysis for temporary gravitational capture - Stable orbits

In a previous work, Vieira Neto & Winter (2001) numerically explored the capture times of particles as temporary satellites of Uranus. The study was made in the framework of the spatial, circular, restricted three-body problem. Regions of the initial condition space whose trajectories are apparently stable were determined. The criterion adopted was that the trajectories do not escape from the planet during an integration of 10(5) years. These regions occur for a wide range of orbital initial inclinations (i). In the present work it is studied the reason for the existence of such stable regions. The stability of the planar retrograde trajectories is due to a family of simple periodic orbits and the associated quasi-periodic orbits that oscillate around them. These planar stable orbits had already been studied (Henon 1970; Huang & Innanen 1983). Their results are reviewed using Poincare surface of sections. The stable non-planar retrograde trajectories, 110 degrees less than or equal to i < 180, are found to be tridimensional quasi-periodic orbits around the same family of periodic orbits found for the planar case (i = 180 degrees). It was not found any periodic orbit out of the plane associated to such quasi-periodic orbits. The largest region of stable prograde trajectories occurs at i = 60 degrees. Trajectories in such region are found to behave as quasi-periodic orbits evolving similarly to the stable retrograde trajectories that occurs at i = 120 degrees.

Distant stable direct orbits around the Moon

In the present work we explore regions of distant direct stable orbits around the Moon. First, the location and size of apparently stable regions are searched for numerically, adopting the approach of temporary capture time presented in Vieira Neto & Winter (2001). The study is made in the framework of the planar, circular, restricted three-body problem, Earth-Moon-particle. Regions of the initial condition space whose trajectories are apparently stable are determined. The criterion adopted was that the trajectories do not escape from the Moon during an integration period of 10(4) days. Using Poincare surface of sections the reason for the existence of the two stable regions found is studied. The stability of such regions proved to be due to two families of simple periodic orbits, h1 and h2, and the associated quasi-periodic orbits that oscillate around them. The robustness of the stability of the larger region, h2, is tested with the inclusion of the solar perturbation. The size of the region decreases, but it is still significant in size and can be useful in spacecraft missions.

Numerical study of low-cost alternative orbits around the Moon

In this paper, we have investigated a region of direct stable orbits around the Moon, whose stability is related to the H2 Family of periodic orbits and to the quasi-periodic orbits that oscillate around them. The stability criteria adopted was that the path did not escape from the Moon during an integration period of 1000 days (remaining with negative two-body Moon-probe orbital energy during this period). Considering the three-dimensional four-body Sun-Earth-Moon-probe problem, we investigated the evolution of the size of the stability region, taking into account the eccentricity of the Earth's orbit, the eccentricity and inclination of the Moon's orbit, and the solar radiation pressure on the probe. We also investigated the evolution of the region's size and its location by varying the inclination of the probe's initial osculating orbit relative to the Moon's orbital plane between 0 degrees and 180 degrees. The size of the stability region diminishes; nevertheless, it remains significant for 0 <= i <= 25 degrees and 35 degrees <= i <= 45 degrees. The orbits of this region could be useful for missions by space vehicles that must remain in orbit around the Moon for periods of up to 1000 days, requiring low maintenance costs. (c) 2005 COSPAR. Published by Elsevier Ltd. All rights reserved.

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.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A simplified Fermi Accelerator Model under quadratic frictional force

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

Numerical study about natural escape and capture routes by the Moon via Lagrangian points L1 and L2

The lunar sphere of influence, whose radius is some 66,300 km, has regions of stable orbits around the Moon and also regions that contain trajectories which, after spending some time around the Moon, escape and are later recaptured by lunar gravity. Both the escape and the capture occur along the Lagrangian equilibrium points L1 and L2. In this study, we mapped out the region of lunar influence considering the restricted three-body Earth-Moon-particle problem and the four-body Sun-Earth-Moon-particle (probe) problem. We identified the stable trajectories, and the escape and capture trajectories through the L I and L2 in plots of the eccentricity versus the semi-major axis as a function of the time that the energy of the osculating lunar trajectory in the two-body Moon-particle problem remains negative. We also investigated the properties of these routes, giving special attention to the fact that they supply a natural mechanism for performing low-energy transfers between the Earth and the Moon, and can thus be useful on a great number of future missions. (C) 2007 Published by Elsevier Ltd on behalf of COSPAR.

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)

Análise da estabilidade da região externa do sistema Plutão-Caronte após a descoberta dos novos satélites NIX e HIDRA: aplicação à sonda new horizons

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

Estabilidade de órbitas congeladas em torno de satélites planetários utilizando o sistema hamiltoniano na forma normal

Pós-graduação em Física - FEG

Planet formation in a triple stellar system: implications of the third star's orbital inclination

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

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Stable retrograde orbits around the triple system 2001 SN263

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

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◦