On the Structure of Symplectic Mappings. The Fast Lyapunov Indicator: a Very Sensitive Tool

It is already known (Froeschlé, Lega and Gonczi, 1997) that the Fast Lyapunov Indicator (FLI), that is the computation on a relatively short time of the largest Lyapunov indicator, allows to discriminate between ordered and weak chaotic motion. We have found that, under certain conditions, the FLI also discriminates between resonant and non-resonant orbits, not only for two-dimensional symplectic mappings but also for higher dimensional ones. Using this indicator, we present an example of the Arnold web detection for four and six-dimensional symplectic maps. We show that this method allows to detect the global transition of the system from an exponentially stable Nekhoroshevs like regime to the diffusive Chirikovs one.     

The Universe behind the Milky Way

Summary. Due to the foreground extinction of the Milky Way, galaxies appear increasingly fainter the closer they lie to the Galactic Equator, creating a “zone of avoidance” of about 25% in the distribution of optically visible galaxies. A “whole-sky” map of galaxies is essential, however, for understanding the dynamics in our local Universe, in particular the peculiar velocity of the Local Group with respect to the Cosmic Microwave Background and velocity flow fields such as in the Great Attractor region. Various dynamically important structures behind the Milky Way have only recently been made “visible” through dedicated deep surveys at various wavelengths. The wide range of observational searches (optical, near infrared, far infrared, radio and X-ray) for galaxies in the Zone of Avoidance are reviewed, including a discussion on the limitations and selection effects of these partly complementary approaches. The uncovered and suspected large-scale structures are summarized. Reconstruction methods of the density field in the Zone of Avoidance are described and the resulting predictions compared with observational evidence. The comparison between reconstructed density fields and the observed galaxy distribution allow derivations of the density and biasing parameters and b. Received 4 April 2000 / Published online 18 July 2000     

Rotational Properties of Cometary Nuclei

We review several techniques used to retrieve rotational parameters from observations. The spin period of a dozen of comets retrieved with these techniques are summarized. We describe how the spin period of comet Hale-Bopp (C/1995 O1) has been calculated with a high accuracy (11.30–11.34 h). Although several authors converged to a spin axis orientation at (α,δ) = (275 ± 15°, -55 ± 5°), detailed studies indicate that the dust jets morphology in 1996–1997 may be incompatible with this orientation. Comet 19P/Borrelly has been recently observed by the Deep Space 1 spacecraft. At the same time, its spin axis orientation and period have been determined by several authors to be respectively (α,δ) = (225 ± 15°, -10 ± 10°)and 26h. These two comets are likely to be in (or close to) a principal axis spin state. We discuss new modeling of the spin state of comet 46P/Wirtanen, the target of the Rosetta mission. The model involves a three-dimensional shape and thermal model, from which the torque of the non gravitational force is calculated at each time step. The moments of inertia are computed for each irregular shape. The results from numerical integrations show that this comet can remain in a principal axis spin state during more than 10 orbits if the spin period does not get above～6 h. If the spin period increases, its nucleus gets rapidly into excited spin states. It shows that even small and very active short-period comets are not necessarily in non principal axis spin states. In the last section, the consequences of recent observations and modeling of the rotational parameters of comet nuclei are discussed, and unsolved problems are presented.     

Eclipse monitoring of eccentric binary systems

The observation of apsidal motions in eclipsing binaries is a very rewarding area of research which requires only moderate or small telescopes equipped with a photoelectric photometer. Important contributions can be made to the study of stellar internal structure through these observations, as well as the verification of the theory of general relativity using the equations of orbital motion. The main objectives of such an observational effort are described, together with a list of candidate binary systems. An appeal to photometrists with small telescopes around the world is made to observe these eccentric and well-detached eclipsing binaries.     

A 20 cm2 CCD mosaic camera for a dark matter search part I : Mechanics,optics and cryogeny

A 20cm ² CCD mosaic camera has been especially built to search for dark galactic halo objects by the gravitational microlensing effect. The sensitive area is made of 16 edge-buttable CCDs developped by Thomson-CTS, with 23×23 µm ² pixels. The 35 kg camera housing and mechanical equipment is presented. The associated electronics and data acquisition system are described in a separate paper. The camera resides at the focal plane of a 40 cm, f/10, Ferson reflector. The instrument has been in operation since December 1991 at the La Silla Observatory (ESO).     

The Scattered Disk Population and the Oort Cloud

The trans-Neptunian belt has been subject to a strong depletion that has reduced its primordial population by a factor of one hundred over the solar system's age. One by-product of such a depletion process is the existence of a scattered disk population in transit from the belt to other places, such as the Jupiter zone, the Oort cloud or interstellar space. We have integrated the orbits of the scattered disk objects (SDOs) so far discovered by 2500 Myr to study their dynamical time scales and the probability of falling in each of the end states mentioned above, paying special attention to their contribution to the Oort cloud. We found that their dynamical half-time is close to 2.5 Gyr and that about one third of the SDOs end up in the Oort cloud.     

Hα Photometry of Two Contact Binaries

We carried out optical and Hα photometry of two contact binaries (V861 Herculis, EQ Tauri). The light curve modeling revealed stellar spots in both contact systems and strong Hα excess in the position of the observed stellar spots. A correlation was found between the V−R and R−H_α colour indices of V861 Her.     

Use of the Geometric Elements in Numerical Simulations

We derive the transformations to convert the state vector in cartesian coordinates into geometric orbital elements (and conversely the geometric elements into the state vector) for a test particle moving around an oblate planet. These transformations arise from the epicyclic theory and are accurate to second order in eccentricity and inclination. This paper is written to be directly used for computational purposes, such as the numerical study of ring dynamics.     

Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity. We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis, inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations or librations around an equilibrium point.     

Symmetric horseshoe periodic orbits in the general planar three-body problem

We present some families of horseshoe periodic orbits in the general planar three-body problem for the case of two equal masses. The considered system is a symmetric version of the one formed by Saturn, Janus and Epimetheus. We use a mass ratio equal to 35×10⁻⁵, corresponding to 10⁵ times the Saturn-Janus mass parameter of the restricted case; for this mass ratio the satellites have a significantly bigger influence on the planet than in the classical Saturn, Janus and Epimetheus system. To obtain periodic orbits, we search those horseshoe orbits passing through two reversible configurations. A particular kind of periodic orbits where the minor bodies follow the same path is discussed.