962 research outputs found
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
Symplectic integration of space debris motion considering several Earth's shadowing models
In this work, we present a symplectic integration scheme to numerically
compute space debris motion. Such an integrator is particularly suitable to
obtain reliable trajectories of objects lying on high orbits, especially
geostationary ones. Indeed, it has already been demonstrated that such objects
could stay there for hundreds of years. Our model takes into account the
Earth's gravitational potential, luni-solar and planetary gravitational
perturbations and direct solar radiation pressure. Based on the analysis of the
energy conservation and on a comparison with a high order non-symplectic
integrator, we show that our algorithm allows us to use large time steps and
keep accurate results. We also propose an innovative method to model Earth's
shadow crossings by means of a smooth shadow function. In the particular
framework of symplectic integration, such a function needs to be included
analytically in the equations of motion in order to prevent numerical drifts of
the energy. For the sake of completeness, both cylindrical shadows and penumbra
transitions models are considered. We show that both models are not equivalent
and that big discrepancies actually appear between associated orbits,
especially for high area-to-mass ratios
Stellar Dynamics of Extreme-Mass-Ratio Inspirals
Inspiral of compact stellar remnants into massive black holes (MBHs) is
accompanied by the emission of gravitational waves at frequencies that are
potentially detectable by space-based interferometers. Event rates computed
from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due
to uncertaintities about the rate coefficients. Here we present results from
direct integration of the post-Newtonian N-body equations of motion descrbing
dense clusters of compact stars around Schwarzschild MBHs. These simulations
embody an essentially exact (at the post-Newtonian level) treatment of the
interplay between stellar dynamical relaxation, relativistic precession, and
gravitational-wave energy loss. The rate of capture of stars by the MBH is
found to be greatly reduced by relativistic precession, which limits the
ability of torques from the stellar potential to change orbital angular
momenta. Penetration of this "Schwarzschild barrier" does occasionally occur,
resulting in capture of stars onto orbits that gradually inspiral due to
gravitational wave emission; we discuss two mechanisms for barrier penetration
and find evidence for both in the simulations. We derive an approximate formula
for the capture rate, which predicts that captures would be strongly disfavored
from orbits with semi-major axes below a certain value; this prediction, as
well as the predicted rate, are verified in the N-body integrations. We discuss
the implications of our results for the detection of extreme-mass-ratio
inspirals from galactic nuclei with a range of physical properties.Comment: 28 pages, 16 figures. Version 2 is significantly revised to reflect
new insights into J and Q effects, to be published late
Baltic Ecological Recycling Agriculture and Society (BERAS project) - a case of Juva milk system
The aim of the study was to determine the potential, impact and prerequisites of localization and enhanced recycling in a rural food system, illustrated by the case of Juva milk. An interdisciplinary scenario based on the increase of local, organic milk to 50 % of milk comsumption was created and the sustainability was compared, on the basis of the statistics and data collected from the actors, with the present milk system
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