96 research outputs found
The Janus head of the HD 12661 planetary system
In this work we perform a global analysis of the radial velocity curve of the
HD 12661 system. Orbital fits that are obtained by the genetic and gradient
algorithms of minimization reveal the proximity of the system to the 6:1 mean
motion resonance. The orbits are locked in the secular resonance with apsidal
axes librating about 180 deg with the full amplitude . Our
solution incorporates the mutual interaction between the companions. The
stability analysis with the MEGNO fast indicator shows that the system is
located in an extended stable zone of quasi-periodic motions. These results are
different from those obtained on the basis of the orbital fit published by
Fischer et al. (2003)Comment: 7 pages, 5 figures, manuscript submitted to ApJ Letters, revised
versio
Non-integrability of the problem of a rigid satellite in gravitational and magnetic fields
In this paper we analyse the integrability of a dynamical system describing
the rotational motion of a rigid satellite under the influence of gravitational
and magnetic fields. In our investigations we apply an extension of the Ziglin
theory developed by Morales-Ruiz and Ramis. We prove that for a symmetric
satellite the system does not admit an additional real meromorphic first
integral except for one case when the value of the induced magnetic moment
along the symmetry axis is related to the principal moments of inertia in a
special way.Comment: 39 pages, 4 figures, missing bibliography was adde
Orbital configurations and dynamical stability of multi-planet systems around Sun-like stars HD 202206, 14 Her, HD 37124 and HD 108874
We perform a dynamical analysis of the recently published radial velocity
(RV) measurements of a few solar type stars which host multiple Jupiter-like
planets. In particular, we re-analyze the data for HD 202206, 14 Her, HD 37124
and HD 108874. We derive dynamically stable configurations which reproduce the
observed RV signals using our method called GAMP (an acronym of the Genetic
Algorithm with MEGNO Penalty). The GAMP relies on the N-body dynamics and makes
use of genetic algorithms merged with a stability criterion. For this purpose,
we use the maximal Lyapunov exponent computed with the dynamical fast indicator
MEGNO. Through a dynamical analysis of the phase-space in a neighborhood of the
obtained best-fit solutions, we derive meaningful limits on the parameters of
the planets. We demonstrate that GAMP is especially well suited for the
analysis of the RV data which only partially cover the longest orbital period
and/or correspond to multi-planet configurations involved in low-order mean
motion resonances (MMRs). In particular, our analysis reveals a presence of a
second Jupiter-like planet in the 14 Her system (14 Her c) involved in a 3:1 or
6:1 MMR with the known companion b. We also show that the dynamics of the HD
202206 system may be qualitatively different when coplanar and
mutually-inclined orbits of the companions are considered. We demonstrate that
the two outer planets in the HD 37124 system may reside in a close neighborhood
of the 5:2 MMR. Finally, we found a clear indication that the HD 108874 system
may be very close to, or locked in an exact 4:1 MMR.Comment: Contains 7 pages (text), 17 figures (some in low resolution suitable
for astro-ph), 1 table. Submitted to ApJ. The manuscript with high-resolution
figures is available from http://www.astri.uni.torun.pl/~chris/ms64109.ps.g
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