391 research outputs found
Frequency map analysis and quasiperiodic decompositions
Frequency Map Analysis is a numerical method based on refined Fourier
techniques which provides a clear representation of the global dynamics of many
multi-dimensional systems, and which is particularly adapted for systems of
3-degrees of freedom and more. This method relies heavily on the possibility of
making accurate quasiperiodic approximations of of quasiperiodic signal given
in a numerical way. In the present paper, we will describe the basis of the
frequency analysis method, focussing on the quasi periodic approximation
techniques. Application of these methods for the study of the global dynamics
and chaotic diffusion of Hamiltonian systems and symplectic maps in different
domains can be found in (Laskar, 1988, 1990, Laskar and Robutel, 1993, Robutel
and Laskar, 2001, Nesvorny and Ferraz-Mello, 1997) for solar system dynamics,
and in (Papaphilippou and Laskar, 1996, 1998, Laskar, 2000, Wachlin and
Ferraz-Mello, 1998, Valluri and Merritt, 1998, Merritt and Valluri, 1999) for
galactic dynamics. The method has been particularly successful for its
application in particle accelerators (Dumas and Laskar, 1993, Laskar and Robin,
1996, Robin et al., 2000, Comunian et al., 2001, Papaphilippou and Zimmermann,
2002, Steier et al., 2002), and was also used for the understanding of atomic
physics (Milczewski et al., 1997), or more general dynamical system issues
(Laskar et al., 1992, Laskar, 1993, 1999, Chandre et al., 2001).Comment: 13 march 200
Andoyer construction for Hill and Delaunay variables
Andoyer variables are well known for the study of rotational dynamics. These
variables were derived by Andoyer through a procedure that can be also used to
obtain the Hill variables of the Kepler problem. Andoyer construction can also
forecast the Delaunay variables which canonicity is then obtained without the
use of a generating function.Comment: 8 pages, 2 figures, revised versio
Precessional quantities for the Earth over 10 Myr
The insolation parameters of the Earth depend on its orbital parameters and on the precession and obliquity. Until 1988, the usually adopted solution for paleoclimate computation consisted in (Bretagnon, 1974) for the orbital elements of the Earth, which was completed by (Berger, 1976) for the computation of the precession and obliquity of the Earth. In 1988, I issued a solution for the orbital elements of the Earth, which was obtained in a new manner, gathering huge analytical computations and numerical integration (Laskar, 1988). In this solution, which will be denoted La88, the precession and obliquity quantities necessary for paleoclimate computations were integrated at the same time, which insure good consistency of the solutions. Unfortunately, due to various factors, this latter solution for the precession and obliquity was not widely distributed (Berger, Loutre, Laskar, 1988). On the other side, the orbital part of the solution La88 for the Earth, was used in (Berger and Loutre, 1991) to derive another solution for precession and obliquity, aimed to climate computations. I also issued a new solution (La90) which presents some slight improvements with respect to the previous one (Laskar, 1990). As previously, this solution contains orbital, precessional, and obliquity variables. The main features of this new solution are discussed
AMD-stability and the classification of planetary systems
We present here in full detail the evolution of the angular momentum deficit
(AMD) during collisions as it was described in (Laskar, PRL,2000). Since then,
the AMD has been revealed to be a key parameter for the understanding of the
outcome of planetary formation models. We define here the AMD-stability
criterion that can be easily verified on a newly discovered planetary system.
We show how AMD-stability can be used to establish a classification of the
multiplanet systems in order to exhibit the planetary systems that are
long-term stable because they are AMD-stable, and those that are AMD-unstable
which then require some additional dynamical studies to conclude on their
stability. The AMD-stability classification is applied to the 131 multiplanet
systems from The Extrasolar Planet Encyclopaedia database (exoplanet.eu) for
which the orbital elements are sufficiently well known.Comment: 18 pages, 13 figures, A&A in pres
Tidal Evolution of Exoplanets
Tidal effects arise from differential and inelastic deformation of a planet
by a perturbing body. The continuous action of tides modify the rotation of the
planet together with its orbit until an equilibrium situation is reached. It is
often believed that synchronous motion is the most probable outcome of the
tidal evolution process, since synchronous rotation is observed for the
majority of the satellites in the Solar System. However, in the 19th century,
Schiaparelli also assumed synchronous motion for the rotations of Mercury and
Venus, and was later shown to be wrong. Rather, for planets in eccentric orbits
synchronous rotation is very unlikely. The rotation period and axial tilt of
exoplanets is still unknown, but a large number of planets have been detected
close to the parent star and should have evolved to a final equilibrium
situation. Therefore, based on the Solar System well studied cases, we can make
some predictions for exoplanets. Here we describe in detail the main tidal
effects that modify the secular evolution of the spin and the orbit of a
planet. We then apply our knowledge acquired from Solar System situations to
exoplanet cases. In particular, we will focus on two classes of planets,
"Hot-Jupiters" (fluid) and "Super-Earths" (rocky with atmosphere).Comment: 30 pages, 19 figures. Chapter in Exoplanets, ed. S. Seager, to be
published by University of Arizona Pres
Speed limit on Neptune migration imposed by Saturn tilting
In this Letter, we give new constraints on planet migration. They were
obtained under the assumption that Saturn's current obliquity is due to a
capture in resonance with Neptune's ascending node. If planet migration is too
fast, then Saturn crosses the resonance without being captured and it keeps a
small obliquity. This scenario thus gives a lower limit on the migration time
scale tau. We found that this boundary depends strongly on Neptune's initial
inclination. For two different migration types, we found that tau should be at
least greater than 7 Myr. This limit increases rapidly as Neptune's initial
inclination decreases from 10 to 1 degree. We also give an algorithm to know if
Saturn can be tilted for any migration law.Comment: 5 pages, 4 figures, published in ApJ
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