1,831 research outputs found
HD60532, a planetary system in a 3:1 mean motion resonance
In a recent paper it was reported a planetary system around the star HD60532,
composed by two giant planets in a possible 3:1 mean motion resonance, that
should be confirmed within the next decade. Here we show that the analysis of
the global dynamics of the system allows to confirm this resonance. The present
best fit to data already corresponds to this resonant configuration and the
system is stable for at least 5Gry. The 3:1 resonance is so robust that
stability is still possible for a wide variety of orbital parameters around the
best fit solution and also if the inclination of the system orbital plane with
respect to the plane of the sky is as small as 15 deg. Moreover, if the
inclination is taken as a free parameter in the adjustment to the observations,
we find an inclination ~ 20 deg, which corresponds to M_b =3.1 M_Jup and M_c =
7.4 M_Jup for the planetary companions.Comment: 4 Pages, 4 Figures, accepted by A&
La2010: A new orbital solution for the long term motion of the Earth
We present here a new solution for the astronomical computation of the
orbital motion of the Earth spanning from 0 to -250 Myr. The main improvement
with respect to the previous numerical solution La2004 (Laskar et al. 2004) is
an improved adjustment of the parameters and initial conditions through a fit
over 1 Myr to a special version of the high accurate numerical ephemeris
INPOP08 (Fienga et al. 2009). The precession equations have also been entirely
revised and are no longer averaged over the orbital motion of the Earth and
Moon. This new orbital solution is now valid over more than 50 Myr in the past
or in the future with proper phases of the eccentricity variations. Due to
chaotic behavior, the precision of the solution decreases rapidly beyond this
time span, and we discuss the behavior of various solutions beyond 50 Myr. For
paleoclimate calibrations, we provide several different solutions that are all
compatible with the most precise planetary ephemeris. We have thus reached the
time where geological data are now required to discriminate among planetary
orbital solutions beyond 50 Myr.Comment: 17 pages, 14 figure
High order symplectic integrators for perturbed Hamiltonian systems
We present a class of symplectic integrators adapted for the integration of
perturbed Hamiltonian systems of the form . We give a
constructive proof that for all integer , there exists an integrator with
positive steps with a remainder of order ,
where is the stepsize of the integrator. The analytical expressions of
the leading terms of the remainders are given at all orders. In many cases, a
corrector step can be performed such that the remainder becomes
. The performances of these integrators
are compared for the simple pendulum and the planetary 3-Body problem of
Sun-Jupiter-Saturn.Comment: 24 pages, 6 figurre
Tidal dissipation and the formation of Kepler near-resonant planets
Multi-planetary systems detected by the Kepler mission present an excess of
planets close to first-order mean-motion resonances (2:1 and 3:2) but with a
period ratio slightly higher than the resonant value. Several mechanisms have
been proposed to explain this observation. Here we provide some clues that
these near-resonant systems were initially in resonance and reached their
current configuration through tidal dissipation. The argument that has been
opposed to this scenario is that it only applies to the close-in systems and
not to the farthest ones for which the tidal effect is too weak. Using the
catalog of KOI of the Kepler mission, we show that the distributions of period
ratio among the most close-in planetary systems and the farthest ones differ
significantly. This distance dependent repartition is a strong argument in
favor of the tidal dissipation scenario.Comment: 3 pages, 3 figures, submitted for publicatio
Chaotic diffusion of the Vesta family induced by close encounters with massive asteroids
We numerically estimate the semi-major axis chaotic diffusion of the Vesta
family asteroids induced by close encounters with 11 massive main belt
asteroids : (1) Ceres, (2) Pallas, (3) Juno, (4) Vesta, (7) Iris, (10) Hygiea,
(15) Eunomia, (19) Fortuna, (324) Bamberga, (532) Herculina, (704) Interamnia.
We find that most of the diffusion is due to Ceres and Vesta. By extrapolating
our results, we are able to constrain the global effect of close encounters
with all the main belt asteroids. A comparison of this drift estimate with the
one expected for the Yarkovsky effect shows that for asteroids whose diameter
is larger than about 40 km, close encounters dominate the Yarkovsky effect.
Overall, our findings confirm the standard scenario for the history of the
Vesta family.Comment: 9 pages, 9 figures, 1 Table, submitte
Dissipation in planar resonant planetary systems
Close-in planetary systems detected by the Kepler mission present an excess
of periods ratio that are just slightly larger than some low order resonant
values. This feature occurs naturally when resonant couples undergo dissipation
that damps the eccentricities. However, the resonant angles appear to librate
at the end of the migration process, which is often believed to be an evidence
that the systems remain in resonance.
Here we provide an analytical model for the dissipation in resonant planetary
systems valid for low eccentricities. We confirm that dissipation accounts for
an excess of pairs that lie just aside from the nominal periods ratios, as
observed by the Kepler mission. In addition, by a global analysis of the phase
space of the problem, we demonstrate that these final pairs are non-resonant.
Indeed, the separatrices that exist in the resonant systems disappear with the
dissipation, and remains only a circulation of the orbits around a single
elliptical fixed point. Furthermore, the apparent libration of the resonant
angles can be explained using the classical secular averaging method. We show
that this artifact is only due to the severe damping of the amplitudes of the
eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&
Determination of the threshold of the break-up of invariant tori in a class of three frequency Hamiltonian systems
We consider a class of Hamiltonians with three degrees of freedom that can be
mapped into quasi-periodically driven pendulums. The purpose of this paper is
to determine the threshold of the break-up of invariant tori with a specific
frequency vector. We apply two techniques: the frequency map analysis and
renormalization-group methods. The renormalization transformation acting on a
Hamiltonian is a canonical change of coordinates which is a combination of a
partial elimination of the irrelevant modes of the Hamiltonian and a rescaling
of phase space around the considered torus. We give numerical evidence that the
critical coupling at which the renormalization transformation starts to diverge
is the same as the value given by the frequency map analysis for the break-up
of invariant tori. Furthermore, we obtain by these methods numerical values of
the threshold of the break-up of the last invariant torus.Comment: 18 pages, 4 figure
A comment on 'Accurate spin axes and solar system dynamics'
In a recent paper, Edvardsson etal (2002) propose a new solution for the spin
evolution of the Earth and Mars. Their results differ significantly with
respect to previous studies, as they found a large contribution on the
precession of the planet axis from the tidal effects of Phobos and Deimos. In
fact, this probably results from the omission by the authors of the torques
exerted on the satellites orbits by the planet's equatorial bulge, as otherwise
the average torque exerted by the satellites on the planet is null.Comment: november 19, 200
Stability analysis of the Martian obliquity during the Noachian era
We performed numerical simulations of the obliquity evolution of Mars during
the Noachian era, at which time the giant planets were on drastically different
orbits than today. For the preferred primordial configuration of the planets we
find that there are two large zones where the Martian obliquity is stable and
oscillates with an amplitude lower than 20. These zones occur at
obliquities below 30 and above 60; intermediate values show
either resonant or chaotic behaviour depending on the primordial orbits of the
terrestrial planets
Dynamical stability analysis of the HD202206 system and constraints to the planetary orbits
Long-term precise Doppler measurements with the CORALIE spectrograph revealed
the presence of two massive companions to the solar-type star HD202206.
Although the three-body fit of the system is unstable, it was shown that a 5:1
mean motion resonance exists close to the best fit, where the system is stable.
We present here an extensive dynamical study of the HD202206 system aiming at
constraining the inclinations of the two known companions, from which we derive
possible ranges of value for the companion masses.
We study the long term stability of the system in a small neighborhood of the
best fit using Laskar's frequency map analysis. We also introduce a numerical
method based on frequency analysis to determine the center of libration mode
inside a mean motion resonance.
We find that acceptable coplanar configurations are limited to inclinations
to the line of sight between 30 and 90 degrees. This limits the masses of both
companions to roughly twice the minimum. Non coplanar configurations are
possible for a wide range of mutual inclinations from 0 to 90 degrees, although
configurations seem to be favored. We also confirm the
5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we
provide a very good stable solution in the resonance, whose does not
differ significantly from the best fit. Using our method to determine the
center of libration, we further refine this solution to obtain an orbit with a
very low amplitude of libration, as we expect dissipative effects to have
dampened the libration.Comment: 14 pages, 18 figure
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