10,912 research outputs found
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 numerical investigation of coorbital stability and libration in three dimensions
Motivated by the dynamics of resonance capture, we study numerically the
coorbital resonance for inclination180 >=I>=0 in the circular restricted
three-body problem. We examine the similarities and differences between planar
and three dimensional coorbital resonance capture and seek their origin in the
stability of coorbital motion at arbitrary inclination. After we present
stability maps of the planar prograde and retrograde coorbital resonances, we
characterize the new coorbital modes in three dimensions. We see that
retrograde mode I (R1) and mode II (R2) persist as we change the relative
inclination, while retrograde mode III (R3) seems to exist only in the planar
problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue
to an horseshoe-orbit. The Kozai-Lidov resonance is active for retrograde
orbits as well as prograde orbits and plays a key role in coorbital resonance
capture. Stable coorbital modes exist at all inclinations, including retrograde
and polar obits. This result confirms the robustness the coorbital resonance at
large inclination and encourages the search for retrograde coorbital companions
of the solar system's planets.Comment: accepted for publication in Celestial Mechanics and Dynamical
Astronom
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
STRUCTURAL CHANGE IN THE BRAZILIAN DEMAND FOR IMPORTS: A regime switching approach
The aim of the present paper is to apply a Markov Switching model to check the characteristics of the Brazilian demand for imports equation based on annual data from 1947 to 2002 and on quarterly data from 1978:I to 2002:II. The results show that this model satisfactorily describes the structural and conjunctural characteristics of Brazilian foreign trade in the last decades. The longterm analysis, based on annual data, allowed for the identification of cyclic periods of trade closure and openness that coincide with the historical events of Brazilian economy. The conjunctural analysis, based on quarterly data, indicates different elasticities for a regime with rise and fall in importsMarkov Switching, Error Correction Mechanism, Demand for Imports, Trade Elasticities, Co-integration.
A new data reduction scheme to obtain the mode II fracture properties of Pinus Pinaster wood
In this work a numerical study of the End Notched Flexure (ENF) specimen was performed
in order to obtain the mode II critical strain energy released rate (GIIc) of a Pinus pinaster wood in the RL crack propagation system. The analysis included interface finite elements and a progressive damage
model based on indirect use of Fracture Mechanics.
The difficulties in monitoring the crack length during an experimental ENF test and the inconvenience of performing separate tests in order to obtain the elastic properties are well known. To avoid these
problems, a new data reduction scheme based on the equivalent crack concept was proposed and validated. This new data reduction scheme, the Compliance-Based Beam Method (CBBM), does not require crack measurements during ENF tests and additional tests to obtain elastic properties.FCT - POCTI/EME/45573/200
Finite element analysis of the ECT test on mode III interlaminar fracture of carbon-epoxy composite laminates
In this work a parametric study of the Edge Crack Torsion (ECT) specimen was performed
in order to maximize the mode III component (GIII) of the strain energy release rate for carbon-epoxy laminates.
A three-dimensional finite element analysis of the ECT test was conducted considering a
[90/0/(+45/-45)2/(-45/+45)2/0/90]S lay-up. The main objective was to define an adequate geometry to obtain an almost pure mode III at crack front. The geometrical parameters studied were specimen dimensions, distance between pins and size of the initial crack.
The numerical results demonstrated that the ratio between the specimen length and the initial crack length had a significant effect on the strain energy release rate distributions. In almost all of the tested
configurations, a mode II component occurred near the edges but it did not interfere significantly with the dominant mode III state.FCT - POCTI/EME/45573/200
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
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