Retrograde resonance in the planar three-body problem

We continue the investigation of the dynamics of retrograde resonances initiated in Morais & Giuppone (2012). After deriving a procedure to deduce the retrograde resonance terms from the standard expansion of the three-dimensional disturbing function, we concentrate on the planar problem and construct surfaces of section that explore phase-space in the vicinity of the main retrograde resonances (2/-1, 1/-1 and 1/-2). In the case of the 1/-1 resonance for which the standard expansion is not adequate to describe the dynamics, we develop a semi-analytic model based on numerical averaging of the unexpanded disturbing function, and show that the predicted libration modes are in agreement with the behavior seen in the surfaces of section.Comment: Celestial Mechanics and Dynamical Astronomy, in pres

Asteroids in retrograde resonance with Jupiter and Saturn

We identify a set of asteroids among Centaurs and Damocloids, that orbit contrary to the common direction of motion in the Solar System and that enter into resonance with Jupiter and Saturn. Their orbits have inclinations I >= 140 deg and semi-major axes a < 15 AU. Two objects are currently in retrograde resonance with Jupiter: 2006 BZ8 in the 2/-5 resonance and 2008 SO218 in the 1/-2 resonance. One object, 2009 QY6, is currently in the 2/-3 retrograde resonance with Saturn. These are the first examples of Solar System objects in retrograde resonance. The present resonant configurations last for several thousand years. Brief captures in retrograde resonance with Saturn are also possible during the 20,000 years integration timespan, particularly in the 1/-1 resonance (2006 BZ8) and the 9/-7 resonance (1999 LE31).Comment: 6 pages, 7 figures, accepted for publication in MNRAS Letter

Stellar wobble caused by a nearby binary system: eccentric and inclined orbits

Most extrasolar planets currently known were discovered by means of an indirect method that measures the stellar wobble caused by the planet. We previously studied a triple system composed of a star and a nearby binary on circular coplanar orbits. We showed that although the effect of the binary on the star can be differentiated from the stellar wobble caused by a planet, because of observational limitations the two effects may often remain indistinguishable. Here, we develop a model that applies to eccentric and inclined orbits. We show that the binary's effect is more likely to be mistaken by planet(s) in the case of coplanar motion observed equator-on. Moreover, when the orbits are eccentric, the magnitude of the binary's effect may be larger than in the circular case. Additionally, an eccentric binary can mimic two planets with orbital periods in the ratio 2/1. However, when the star's orbit around the binary's center of mass has a high eccentricity and a reasonably well-constrained period, it should be easier to distinguish the binary's effect from a planet.Comment: 10 pages, 9 figures, 2 table

A semi-empirical stability criterion for real planetary systems

We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet systems quite well. In addition, we show that elliptical orbits can remain stable even for regions where the apocenter distance of the inner orbit is larger than the pericenter distance of the outer orbit, as long as the initial orbits are aligned. The analytical expressions provided here can be used to put rapid constraints on the stability zones of multi-planetary systems. As a byproduct of this research, we further show that the amplitude variations of the eccentricity can be used as a fast-computing stability indicator.Comment: 11 pages, 11 figures. MNRAS accepte

Tidal damping of the mutual inclination in hierachical systems

Hierarchical two-planet systems, in which the inner body's semi-major axis is between 0.1 and 0.5 AU, usually present high eccentricity values, at least for one of the orbits. As a result of the formation process, one may expect that planetary systems with high eccentricities also have high mutual inclinations. However, here we show that tidal effects combined with gravitational interactions damp the initial mutual inclination to modest values in timescales that are shorter than the age of the system. This effect is not a direct consequence of tides on the orbits, but it results from a secular forcing of the inner planet's flattening. We then conclude that these hierarchical planetary systems are unlikely to present very high mutual inclinations, at least as long as the orbits remain outside the Lidov-Kozai libration areas. The present study can also be extended to systems of binary stars and to planet-satellite systems.Comment: 16 pages, 13 figure

The population of Near Earth Asteroids in coorbital motion with Venus

We estimate the size and orbital distributions of Near Earth Asteroids (NEAs) that are expected to be in the 1:1 mean motion resonance with Venus in a steady state scenario. We predict that the number of such objects with absolute magnitudes H<18 and H<22 is 0.14±0.03 and 3.5±0.7, respectively. We also map the distribution in the sky of these Venus coorbital NEAs and we see that these objects, as the Earth coorbital NEAs studied in a previous paper, are more likely to be found by NEAs search programs that do not simply observe around opposition and that scan large areas of the sky.http://www.sciencedirect.com/science/article/B6WGF-4KMYG2W-2/1/a7a3dcf3c98ddc8cf0d2d1cdbde6853

Local density of states of electron-crystal phases in graphene in the quantum Hall regime

We calculate, within a self-consistent Hartree-Fock approximation, the local density of states for different electron crystals in graphene subject to a strong magnetic field. We investigate both the Wigner crystal and bubble crystals with M_e electrons per lattice site. The total density of states consists of several pronounced peaks, the number of which in the negative energy range coincides with the number of electrons M_e per lattice site, as for the case of electron-solid phases in the conventional two-dimensional electron gas. Analyzing the local density of states at the peak energies, we find particular scaling properties of the density patterns if one fixes the ratio nu_N/M_e between the filling factor nu_N of the last partially filled Landau level and the number of electrons per bubble. Although the total density profile depends explicitly on M_e, the local density of states of the lowest peaks turns out to be identical regardless the number of electrons M_e. Whereas these electron-solid phases are reminiscent to those expected in the conventional two-dimensional electron gas in GaAs heterostructures in the quantum Hall regime, the local density of states and the scaling relations we highlight in this paper may be, in graphene, directly measured by spectroscopic means, such as e.g. scanning tunneling microscopy.Comment: 8 pages, 7 figures; minor correction

Precession due to a close binary system: An alternative explanation for {\nu}-Octantis?

We model the secular evolution of a star's orbit when it has a nearby binary system. We assume a hierarchical triple system where the inter-binary distance is small in comparison with the distance to the star. We show that the major secular effect is precession of the star's orbit around the binary system's centre of mass. We explain how we can obtain this precession rate from the star's radial velocity data, and thus infer the binary system's parameters. We show that the secular effect of a nearby binary system on the star's radial velocity can sometimes mimic a planet. We analyze the radial velocity data for {\nu}-octantis A which has a nearby companion ({\nu}-octantis B) and we obtain retrograde precession of (-0.86 \pm 0.02)\degree/yr. We show that if {\nu}-octantis B was itself a double star, it could mimic a signal with similarities to that previously identified as a planet of {\nu}-octantis A. Nevertheless, we need more observations in order to decide in favor of the double star hypothesis

Estudo da viabilidade de construção de pontes em arco

As pontes de alvenaria em arco são o testemunho do engenho a nível de concepção, método construtivo e carácter estético. Existem inúmeros exemplos de pontes em alvenaria de pedra que atravessaram vários séculos até aos nossos dias, continuando a cumprir as suas funções com um nível de desempenho adequado. Actualmente é rara a construção desta tipologia de pontes. As reconhecidas dificuldades associadas à construção de pontes em arco, agravado pelo surgimento de novos materiais, justificam o declínio desta solução estrutural. As vantagens associadas ao comportamento estrutural deste tipo de pontes e a estética da construção em alvenaria, motivou o desenvolvimento de novos processos para uma construção mais simples e sobretudo mais rápida. Neste trabalho estudou-se a viabilidade de construção de pontes em arco com recurso a blocos maciços de betão. A não inclusão de qualquer tipo de armadura nesta solução traduzse numa maior durabilidade, eliminando os problemas associados ao destacamento de betão e à corrosão. De referir ainda que na produção dos blocos para a solução proposta poderão ser incorporados resíduos de construção e demolição. Propõe-se uma solução em arco para a construção de passagens inferiores, agrícolas e hidráulicas ou para aplicações com vãos até 12 metros. Foram avaliadas numericamente três modulações correspondendo a 4, 9 e 12 metros de vão. Em cada caso, o número de aduelas é definido em função de critérios que facilitem o seu transporte. Com a solução proposta pretende-se justificar a viabilidade de construção de pontes em arco recorrendo a métodos de construção simples, de rápida execução, contribuindo para a utilização desta tipologia estrutural, com a qualidade e durabilidade que caracterizam as pontes de alvenaria

Avaliação da segurança sísmica de pontes e reforço com FRP´s

A avaliação da segurança e a conservação das pontes têm vindo a suscitar interesse crescente nos últimos anos. O reforço destas estruturas para a acção sísmica é importante, uma vez que são infra-estruturas fundamentais para a intervenção das equipas de socorro em acções pós-sismo, mas também pelas consequências económicas e sociais associadas a eventuais danos severos ou colapso destas obras. O reforço sísmico passa pela aplicação de sistemas que permitam atenuar e controlar os efeitos produzidos pelas acções dos sismos. Actualmente, com o aparecimento de nova regulamentação, como os Eurocódigos e outras guidelines, e de novos materiais como os polímeros reforçados com fibras (FRP – Fiber Reinforced Polymer), o reforço de pontes existentes é mais viável, tecnicamente e economicamente. As vantagens da utilização de sistemas de FRP’s na reabilitação e reforço de pontes resultam das suas propriedades mecânicas, dado que possuem elevada resistência mecânica, reduzido peso dos materiais e elevada resistência à corrosão, aliada à facilidade de aplicação e à disponibilidade de uma grande diversidade de sistemas de FRP’s no mercado. Neste trabalho procedeu-se à análise de um viaduto corrente existente, simulandose, com recurso a um modelo numérico, o seu comportamento estrutural, identificando e localizando as zonas críticas. Com base nos resultados da avaliação, estudou-se e propôs-se uma solução de reforço sísmico com base nas indicações do Boletim FIB 14, e de acordo com a filosofia adoptada pelos Eurocódigos. Desse modo, procedeuse à recolha de informação relativa à obra de arte em estudo e à simulação numérica da estrutura. Inicialmente procedeu-se à calibração do modelo numérico com recurso a medições das suas frequências fundamentais. De seguida, desenvolveu-se a verificação da segurança estrutural ao nível dos elementos. E, por fim desenvolveu-se uma proposta de reforço sísmico com recurso a sistemas de FRP’s de modo a garantir a capacidade exigida aos elementos onde a segurança não foi verificada para a acção sísmica