70 research outputs found
Analytical and numerical study of the ground-track resonances of Dawn orbiting Vesta
The aim of Dawn mission is the acquisition of data from orbits around two
bodies, (4)Vesta and (1)Ceres, the two most massive asteroids. Due to the low
thrust propulsion, Dawn will slowly cross and transit through ground-track
resonances, where the perturbations on Dawn orbit may be significant. In this
context, to safety go the Dawn mission from the approach orbit to the lowest
science orbit, it is essential to know the properties of the crossed
resonances. This paper analytically investigates the properties of the major
ground-track resonances (1:1, 1:2, 2:3 and 3:2) appearing for Vesta orbiters:
location of the equilibria, aperture of the resonances and period at the stable
equilibria. We develop a general method using an averaged Hamiltonian
formulation with a spherical harmonic approximation of the gravity field. If
the values of the gravity field coefficient change, our method stays correct
and applicable. We also discuss the effect of one uncertainty on the C20 and
C22 coefficients on the properties of the 1:1 resonance. These results are
checked by numerical tests. We determine that the increase of the eccentricity
appearing in the 2:3 resonance is due to the C22 and S22 coefficients.
Our method can be easily adapted to missions similar to Dawn because,
contrarily to the numerical results, the analytical formalism stays the same
and is valid for a wide range of physical parameters of the asteroid (namely
the shape and the mass) as well as for different spacecraft orbits.
Finally we numerically study the probability of the capture in resonance 1:1.
Our paper reproduces, explains and supplements the results of Tricarico and
Sykes (2010).Comment: 34 pages, 9 figures, 10 Table
NIMASTEP: a software to modelize, study and analyze the dynamics of various small objects orbiting specific bodies
NIMASTEP is a dedicated numerical software developed by us, which allows one
to integrate the osculating motion (using cartesian coordinates) in a Newtonian
approach of an object considered as a point-mass orbiting a homogeneous central
body that rotates with a constant rate around its axis of smallest inertia. The
code can be applied to objects such as particles, artificial or natural
satellites or space debris. The central body can be either any terrestrial
planet of the solar system, any dwarf-planet, or even an asteroid. In addition,
very many perturbations can be taken into account, such as the combined
third-body attraction of the Sun, the Moon, or the planets, the direct solar
radiation pressure (with the central body shadow), the non-homogeneous
gravitational field caused by the non-sphericity of the central body, and even
some thrust forces. The simulations were performed using different integration
algorithms. Two additional tools were integrated in the software package; the
indicator of chaos MEGNO and the frequency analysis NAFF. NIMASTEP is designed
in a flexible modular style and allows one to (de)select very many options
without compromising the performance. It also allows one to easily add other
possibilities of use. The code has been validated through several tests such as
comparisons with numerical integrations made with other softwares or with
semi-analytical and analytical studies. The various possibilities of NIMASTEP
are described and explained and some tests of astrophysical interest are
presented. At present, the code is proprietary but it will be released for use
by the community in the near future. Information for contacting its authors and
(in the near future) for obtaining the software are available on the web site
http://www.fundp.ac.be/en/research/projects/page_view/10278201/Comment: Astronomy & Astrophysics - Received: 25 November 2011 / Accepted: 27
February 2012 -- 14 pages, 4 figure
Giant Pulsar Glitches and the Inertia of Neutron-Star Crusts
Giant pulsar frequency glitches as detected in the emblematic Vela pulsar
have long been thought to be the manifestation of a neutron superfluid
permeating the inner crust of a neutron star. However, this superfluid has been
recently found to be entrained by the crust, and as a consequence it does not
carry enough angular momentum to explain giant glitches. The extent to which
pulsar-timing observations can be reconciled with the standard vortex-mediated
glitch theory is studied considering the current uncertainties on dense-matter
properties. To this end, the crustal moment of inertia of glitching pulsars is
calculated employing a series of different unified dense-matter equations of
state.Comment: 11 pages, 6 figures, submitted to PR
Skyrmion and Skyrme-Black holes in de Sitter spacetime
Numerical arguments are presented for the existence of regular and black hole
solutions of the Einstein-Skyrme equations with a positive cosmological
constant. These classical configurations approach asymptotically the de Sitter
spacetime. The main properties of the solutions and the differences with
respect to the asymptotically flat ones are discussed. It particular our
results suggest that, for a positive cosmological constant, the mass evaluated
as timelike infinity in infinite. Special emphasis is set to De Sitter black
holes Skyrmions which display two horizons.Comment: 11 pages, 4 figure
Interesting dynamics at high mutual inclination in the framework of the Kozai problem with an eccentric perturber
We study the dynamics of the 3-D three-body problem of a small body moving
under the attractions of a star and a giant planet which orbits the star on a
much wider and elliptic orbit. In particular, we focus on the influence of an
eccentric orbit of the outer perturber on the dynamics of a small highly
inclined inner body. Our analytical study of the secular perturbations relies
on the classical octupole hamiltonian expansion (third-order theory in the
ratio of the semi-major axes), as third-order terms are needed to consider the
secular variations of the outer perturber and potential secular resonances
between the arguments of the pericenter and/or longitudes of the node of both
bodies. Short-period averaging and node reduction (Laplace plane) reduce the
problem to two degrees of freedom. The four-dimensional dynamics is analyzed
through representative planes which identify the main equilibria of the
problem. As in the circular problem (i.e. perturber on a circular orbit), the
"Kozai-bifurcated" equilibria play a major role in the dynamics of an inner
body on quasi-circular orbit: its eccentricity variations are very limited for
mutual inclination between the orbital planes smaller than ~40^{\deg}, while
they become large and chaotic for higher mutual inclination. Particular
attention is also given to a region around 35^{\deg} of mutual inclination,
detected numerically by Funk et al. (2011) and consisting of long-time stable
and particularly low eccentric orbits of the small body. Using a 12th-order
Hamiltonian expansion in eccentricities and inclinations, in particular its
action-angle formulation obtained by Lie transforms in Libert & Henrard (2008),
we show that this region presents an equality of two fundamental frequencies
and can be regarded as a secular resonance. Our results also apply to binary
star systems where a planet is revolving around one of the two stars.Comment: 12 pages, 9 figures, accepted for publication in MNRA
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
Dual Spaces of Resonance In Thick Branes
In this work we consider form fields in a brane embedded in a
space-time. The membrane is generated by a domain wall in a
Randall-Sundrum-like scenario. We study conditions for localization of zero
modes of these fields. The expression agrees and generalizes the one found for
the zero, one, two and three-forms in a brane. By a generalization we mean
that our expression is valid for any form in an arbitrary dimension with
codimension one. We also point out that, even without the dilaton coupling,
some form fields are localized in the membrane. The massive modes are
considered and the resonances are calculated using a numerical method. We find
that different spaces have identical resonance structures, which we call dual
spaces of resonances(DSR).Comment: 15 page
Charged-rotating black holes and black strings in higher dimensional Einstein-Maxwell theory with a positive cosmological constant
We present arguments for the existence of charged, rotating black holes in
dimensions, with with a positive cosmological constant.
These solutions posses both, a regular horizon and a cosmological horizon of
spherical topology and have equal-magnitude angular momenta. They approach
asymptotically the de Sitter spacetime background. The counterpart equations
for are investigated, by assuming that the fields are independant of
the extra dimension , leading to black strings solutions. These solutions
are regular at the event horizon. The asymptotic form of the metric is not the
de Sitter form and exhibit a naked singularity at finite proper distance.Comment: 21 pages, 9 figure
Enthalpy and the Mechanics of AdS Black Holes
We present geometric derivations of the Smarr formula for static AdS black
holes and an expanded first law that includes variations in the cosmological
constant. These two results are further related by a scaling argument based on
Euler's theorem. The key new ingredient in the constructions is a two-form
potential for the static Killing field. Surface integrals of the Killing
potential determine the coefficient of the variation of the cosmological
constant in the first law. This coefficient is proportional to a finite,
effective volume for the region outside the AdS black hole horizon, which can
also be interpreted as minus the volume excluded from a spatial slice by the
black hole horizon. This effective volume also contributes to the Smarr
formula. Since the cosmological constant is naturally thought of as a pressure,
the new term in the first law has the form of effective volume times change in
pressure that arises in the variation of the enthalpy in classical
thermodynamics. This and related arguments suggest that the mass of an AdS
black hole should be interpreted as the enthalpy of the spacetime.Comment: 21 pages; v2 references adde
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