144 research outputs found
The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits
We present families of symmetric and asymmetric periodic orbits at the 1/1
resonance, for a planetary system consisting of a star and two small bodies, in
comparison to the star, moving in the same plane under their mutual
gravitational attraction. The stable 1/1 resonant periodic orbits belong to a
family which has a planetary branch, with the two planets moving in nearly
Keplerian orbits with non zero eccentricities and a satellite branch, where the
gravitational interaction between the two planets dominates the attraction from
the star and the two planets form a close binary which revolves around the
star. The stability regions around periodic orbits along the family are
studied. Next, we study the dynamical evolution in time of a planetary system
with two planets which is initially trapped in a stable 1/1 resonant periodic
motion, when a drag force is included in the system. We prove that if we start
with a 1/1 resonant planetary system with large eccentricities, the system
migrates, due to the drag force, {\it along the family of periodic orbits} and
is finally trapped in a satellite orbit. This, in principle, provides a
mechanism for the generation of a satellite system: we start with a planetary
system and the final stage is a system where the two small bodies form a close
binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast
On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets
We study the dynamics of planetary systems with two planets moving in the
same plane, when frictional forces act on the two planets, in addition to the
gravitational forces. The model of the general three-body problem is used.
Different laws of friction are considered. The topology of the phase space is
essential in understanding the evolution of the system. The topology is
determined by the families of stable and unstable periodic orbits, both
symmetric and non symmetric. It is along the stable families, or close to them,
that the planets migrate when dissipative forces act. At the critical points
where the stability along the family changes, there is a bifurcation of a new
family of stable periodic orbits and the migration process changes route and
follows the new stable family up to large eccentricities or to a chaotic
region. We consider both resonant and non resonant planetary systems. The 2/1,
3/1 and 3/2 resonances are studied. The migration to larger or smaller
eccentricities depends on the particular law of friction. Also, in some cases
the semimajor axes increase and in other cases they are stabilized. For
particular laws of friction and for special values of the parameters of the
frictional forces, it is possible to have partially stationary solutions, where
the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom
Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)
The theory of diffusion in many-dimensional Hamiltonian system is applied to
asteroidal dynamics. The general formulations developed by Chirikov is applied
to the Nesvorn\'{y}-Morbidelli analytic model of three-body (three-orbit)
mean-motion resonances (Jupiter-Saturn-asteroid system). In particular, we
investigate the diffusion \emph{along} and \emph{across} the separatrices of
the (5,-2,-2) resonance of the (490) Veritas asteroidal family and their
relationship to diffusion in semi-major axis and eccentricity. The estimations
of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type
sympletic map and numerical integrations for times up to years.Comment: 27 pages, 6 figure
Dynamics of two planets in co-orbital motion
We study the stability regions and families of periodic orbits of two planets
locked in a co-orbital configuration. We consider different ratios of planetary
masses and orbital eccentricities, also we assume that both planets share the
same orbital plane. Initially we perform numerical simulations over a grid of
osculating initial conditions to map the regions of stable/chaotic motion and
identify equilibrium solutions. These results are later analyzed in more detail
using a semi-analytical model. Apart from the well known quasi-satellite (QS)
orbits and the classical equilibrium Lagrangian points L4 and L5, we also find
a new regime of asymmetric periodic solutions. For low eccentricities these are
located at , where \sigma is
the difference in mean longitudes and \Delta\omega is the difference in
longitudes of pericenter. The position of these Anti-Lagrangian solutions
changes with the mass ratio and the orbital eccentricities, and are found for
eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation
to one of the planets, and analyzed its effect on an initially asymmetric
periodic orbit. We found that the resonant solution is preserved as long as the
mass variation is adiabatic, with practically no change in the equilibrium
values of the angles.Comment: 9 pages, 11 figure
Elliptical motions of stars in close binary systems
Motions of stars in close binary systems with a conservative mass exchange
are examined. It is shown that Paczynski-Huang model widely used now for
obtaining the semi-major axis variation of a relative stars orbit is incorrect,
because it brings about large mistakes. A new model suitable for elliptical
orbits of stars is proposed. Both of reactive and attractive forces between
stars and a substance of the flowing jet are taken into account. A possibility
of a mass exchange at presence of accretion disk is considere
Computation of an MRI brain atlas from a population of Parkinsonâs disease patients
Abstract Parkinsonâs Disease (PD) is a degenerative disorder of the brain. This study presents an MRI-based brain atlas of PD to characterize associated alterations for diagnostic and interventional purposes. The atlas standardizes primarily the implicated subcortical regions such as the globus pallidus (GP), substantia nigra (SN), subthalamic nucleus (STN), caudate nucleus (CN), thalamus (TH), putamen (PUT), and red nucleus (RN). The data were 3.0 T MRI brain images from 16 PD patients and 10 matched controls. The images used were T1-weighted ( T 1 w ), T2-weighted ( T 2 w ) images, and Susceptibility Weighted Images (SWI). The T1w images were the reference for the inter-subject non-rigid registration available from 3DSlicer. Anatomic labeling was achieved with BrainSuite and regions were refined with the level sets segmentation of ITK-Snap. The subcortical centers were analyzed for their volume and signal intensity. Comparison with an age-matched control group unravels a significant PD-related T1w signal loss in the striatum (CN and PUT) centers, but approximately a constant volume. The results in this study improve MRI based PD localization and can lead to the development of novel biomarkers
Planetary Migration and Extrasolar Planets in the 2/1 Mean-Motion Resonance
We analyze the possible relationship between the current orbital elements
fits of known exoplanets in the 2/1 mean-motion resonance and the expected
orbital configuration due to migration. It is found that, as long as the
orbital decay was sufficiently slow to be approximated by an adiabatic process,
all captured planets should be in apsidal corotations. In other words, they
should show a simultaneous libration of both the resonant angle and the
difference in longitudes of pericenter.
We present a complete set of corotational solutions for the 2/1
commensurability, including previously known solutions and new results.
Comparisons with observed exoplanets show that current orbital fits of three
known planetary systems in this resonance are either consistent with apsidal
corotations (GJ876 and HD82943) or correspond to bodies with uncertain orbits
(HD160691).
Finally, we discuss the applicability of these results as a test for the
planetary migration hypothesis itself. If all future systems in this
commensurability are found to be consistent with corotational solutions, then
resonance capture of these bodies through planetary migration is a working
hypothesis. Conversely, If any planetary pair is found in a different
configuration, then either migration did not occur for those bodies, or it took
a different form than currently believed.Comment: Submitted to MNRA
Low thrust propulsion in a coplanar circular restricted four body problem
This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model
Energy management and control of photovoltaic and storage systems in active distribution grids
The evolution of power distribution grids from passive to active systems creates reliability and efficiency challenges to the distribution system operators. In this paper, an energy management and control scheme for managing the operation of an active distribution grid with prosumers is proposed. A multi-objective optimization model to minimize (i) the prosumers electricity cost and (ii) the cost of the grid energy losses, while guaranteeing safe and reliable grid operation is formulated. This is done by determining the active and reactive power set-points of the photovoltaic and storage systems integrated in the grid buildings. The resulting optimization model is non-convex, thus a convex second-order cone program is developed by appropriately relaxing the non-convex constraints which yields optimal results in most operating conditions. The convexified model is further utilized to develop an algorithm that yields feasible solutions to the non-convex problem under any operating conditions. Moreover, a second novel algorithm to find the operating point that provides fairness between the prosumers and the grid costs is proposed. Simulation results demonstrate the effectiveness and superiority of the proposed scheme in managing an industrial distribution grid compared to a self-consumption approach
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