On the co-orbital motion of two planets in quasi-circular orbits

We develop an analytical Hamiltonian formalism adapted to the study of the motion of two planets in co-orbital resonance. The Hamiltonian, averaged over one of the planetary mean longitudes, is expanded in power series of eccentricities and inclinations. The model, which is valid in the entire co-orbital region, possesses an integrable approximation modeling the planar and quasi-circular motions. First, focusing on the fixed points of this approximation, we highlight relations linking the eigenvectors of the associated linearized differential system and the existence of certain remarkable orbits like the elliptic Eulerian Lagrangian configurations, the anti-Lagrange (Giuppone et al. in MNRAS 407:390–398, 2010) orbits and some second sort orbits discovered by Poincaré. Then, the variational equation is studied in the vicinity of any quasi-circular periodic solution. The fundamental frequencies of the trajectory are deduced and possible occurrence of low order resonances are discussed. Finally, with the help of the construction of a Birkhoff normal form, we prove that the elliptic Lagrangian equilateral configurations and the anti-Lagrange orbits bifurcate from the same fixed point $L_4$ L 4 .     

On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited

In the framework of the planar and circular restricted three-body problem, we consider an asteroid that orbits the Sun in quasi-satellite motion with a planet. A quasi-satellite trajectory is a heliocentric orbit in co-orbital resonance with the planet, characterized by a nonzero eccentricity and a resonant angle that librates around zero. Likewise, in the rotating frame with the planet, it describes the same trajectory as the one of a retrograde satellite even though the planet acts as a perturbator. In the last few years, the discoveries of asteroids in this type of motion made the term “quasi-satellite” more and more present in the literature. However, some authors rather use the term “retrograde satellite” when referring to this kind of motion in the studies of the restricted problem in the rotating frame. In this paper, we intend to clarify the terminology to use, in order to bridge the gap between the perturbative co-orbital point of view and the more general approach in the rotating frame. Through a numerical exploration of the co-orbital phase space, we describe the quasi-satellite domain and highlight that it is not reachable by low eccentricities by averaging process. We will show that the quasi-satellite domain is effectively included in the domain of the retrograde satellites and neatly defined in terms of frequencies. Eventually, we highlight a remarkable high eccentric quasi-satellite orbit corresponding to a frozen ellipse in the heliocentric frame. We extend this result to the eccentric case (planet on an eccentric motion) and show that two families of frozen ellipses originate from this remarkable orbit.     

THz photometers for solar flare observations from space

The search for the still unrevealed spectral shape of the mysterious THz solar flare emissions is one of the current most challenging research issues. The concept, fabrication and performance of a double THz photometer system, named SOLAR-T, is presented. Its innovative optical setup allows observations of the full solar disk and the detection of small burst transients at the same time. The detecting system was constructed to observe solar flare THz emissions on board of stratospheric balloons. The system has been integrated to data acquisition and telemetry modules for this application. SOLAR-T uses two Golay cell detectors preceded by low-pass filters made of rough surface primary mirrors and membranes, 3 and 7 THz band-pass filters, and choppers. Its photometers can detect small solar bursts (tens of solar flux units) with sub second time resolution. Tests have been conducted to confirm the entire system performance, on ambient and low pressure and temperature conditions. An artificial Sun setup was developed to simulate performance on actual observations. The experiment is planned to be on board of two long-duration stratospheric balloon flights over Antarctica and Russia in 2014–2016.     

Genericity of the non-periodic solutions of the central force problem

We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI _h is foliated by the invariant toriI _hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI _hc is conjugated to a linear flow of rotation number _h (c).A well-known result asserts that if we require _h (c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2) _h (c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2.     

The Fresnel space imager as a disk evolution watcher

The Fresnel Diffractive Imaging Arrays form high resolution images by diffraction with low radiometric efficiencies. They are extremely good devices to make high resolution imaging and integral field spectroscopy of bright sources. Thirty meter arrays will provide a spatial resolution of 0.8 mas at Lyman-?? that will open a completely new field of research: the study of matter distribution around disks and their gravitational drives. In this contribution, the potentials of the 3.6 m precursors (or probes) for astrophysical disks and jets research, are described. Main emphasis is made on young planetary disks.     

Slope-control on the aspect ratio of river basins

Although it is traditionally thought that drainage basins are geometrically similar, we present new results which indicate that the aspect ratio of weakly dissected river basins at large scales (10–10³ km²) depends on the surface slope: steeper surfaces develop narrower and lengthier basins whereas more gently dipping surfaces develop more equant and wider basins. This relationship is interpreted to be related to the nature of water flow over rough surfaces, with steeper slopes causing less flow convergence and lengthier and narrower basins. We derive an empirical relationship that can be used to infer the slope of a surface on which a river basin acquired its geometry based solely on a measure of its basin form. This relation provides a unique means of inferring the relative chronology of river basin development with respect to surface tilting and therefore provides a direct link between river basin morphology and tectonics.     

Spatial and Seasonal Patterns of Salinity in a Large and Shallow Tropical Estuary of the Western Caribbean

Salinity profiles and meteorological data were analyzed during February, May, and September 2006 in Chetumal Bay, a large, shallow estuary of the Western Caribbean. Local meteorological conditions revealed three seasons: (1) a dry season (March–May); (2) a wet season (June–October); and (3) the nortes season, with northerly wind events (October–February). During the nortes and wet seasons, salinity ranged between 13 and 16 psu, and salinity was highest in the dry season, ranging between 18 and 22 psu over most of the area; a strong stratification and a significant contribution of salty water characterized this season. Strong horizontal gradients were observed near Rio Hondo during the three seasons. Deep and narrow peculiar bathymetric features called the pozas showed a strong stratification and a relatively high salinity. The northern part of Chetumal Bay and probably the entire system are far from being homogeneous.     

Mechanisms of landslides in over-consolidated clays and flysch

In this report, we present the situation in Slovenia, Europe with regard to natural hazards, emphasizing land-sliding problems. Furthermore, we shortly present the University of Ljubljana and the Faculty of Civil and Geodetic Engineering as the new member of the ICL that was selected to be the World Center of Excellence on Landslide Risk Reduction for the period of 2008–2013 with the project entitled “Mechanisms of landslides in over-consolidated clays and flysch” in the Activity scale and targeted region as “National.” Some preliminary results of this project are shortly presented at the end.