Analytical Approach to the Secular Behaviour of Exoplanetary Systems

We analyse the secular interactions of two coplanar planets which are not in mean motion resonances. The analysis is based on a high order (order 12) expansion of the perturbative potential in powers of the eccentricities. The model depends on only two parameters (the ratio of semi-major axis and the mass ratio of the planets) and can be reduced to a one degree of freedom system, allowing for an exhaustive parametric analysis. Following Pauwels [Pauwels T.: 1983, Celet. Mech. & Dyn. Astro. 30, 229–247] we map the phase space on a sphere, avoiding in this way the artificial singularities introduced by other mappings. We show that the 12 order expansion is able to describe correctly most of the exosolar planetary systems discovered so far, even if the eccentricities of these planets are considerably larger than the eccentricities of our own solar system. The expansion is even able to reproduce, at moderate eccentricities, the secular resonances discovered numerically by Michtchenko and Malhotra [Michtchenko, T. A. and Malhotra, R.: 2004, Icarus 168, 237–248] at moderate to large eccentricities. FNRS Research Fellow.     

Virtual singularities in the artificial satellite theory

When the coordinate system used in perturbation theory presents a geometrical singularity and when the perturbation technique fails to take account of this, the solution developed may present singularities which are no longer easily explained by purely geometrical means. These singularities have been calledvirtual singularities by Deprit and Rom (1970). We propose to demonstrate that virtual singularities can in general be avoided by the use of Lie transforms. In general, it is sufficient to recognize that the original Hamiltonian function presents the d'Alembert characteristic with respect to pairs of action-angle variables and that the averaging operations preserve this characteristic. We then apply this criterion to the artificial satellite theory (for small to moderate eccentricity) showing that all of three possible virtual singularities can be avoided at the same time. A new set of elliptic elements, well suited to the problem at hand, is introduced.     

On Poincaré's second species solutions

A proof of the existence of Poincaré's second species solution in the restricted three body problem is given. It is not based, as Perko's and Guillaume's work, on singular perturbation and asymptotic approximation but rather on topological equivalence between differential systems in the neighborhood of an equilibrium.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Mechanism of differentiation in the Morin Anorthosite complex

The Morin Anorthosite (Grenville province, Canadian shield) occupies the centre of a recrystallised and deformed plutonic complex. Density measurements on selected specimens and density calculations from chemical analysis have shown that such features as layering in basic and intermediate rock, and plagioclase xenocrysts in acidic rocks can be interpreted as having participated in magmatic processes of gravity accumulation and convection currents. Thus, mechanical differentiation in this complex is not basically different from that of well-known layered complexes.The relatively low viscosity that would seem to be required in such processes is in conflict with the high-viscosity type of intrusion that can be deduced from field observations. One way to reconcile these two conflicting concepts is by proposing a model in which the time of consolidation is long enough for gravity accumulation and convection currents to operate, even in a highly viscous magma. This condition can only be attained in catazonal environment. The viscosity of the differentiating magma could be, in this model, of the order of 10¹³ poises.     

The problem of critical inclination combined with a resonance in mean motion in artificial satellite theory

In this paper the two-degree of freedom problem of a geosynchronous artificial satellite orbiting near the critical inclination is studied. First a local approach of this problem is considered. A semi-numerical method, well suited to describe the perturbations of a non-trivial separable system, is then applied such that surfaces of section illustrating the global secular dynamics are obtained. The results are confirmed by numerical integrations of the full Hamiltonian.Research Assistant for the Belgian National Fund for Scientific Research     

Using Laser Beacons for Daytime Adaptive Optics

This article examines the use of Laser Beacons for daytime astronomical observations. There are two potential applications: the diffraction limited observation of (1) the structure in the solar corona at all wavelengths, and (2) non-solar astronomical objects in the thermal infrared part of the spectrum. We examine the brightness of the Laser Beacon required as well as the limitations imposed by the daytime sky brightness and sky/telescope thermal emission on the observable magnitude limits. For both applications the use of Laser Beacon adaptive optics in daytime results in important research opportunities.     

An analysis of the observed contrast of solar surface granulation

The contrast of the solar surface granulation detected in the focal plane of the observing system as well as its relations with the aperture of the observing system, the coherent length of atmospheric turbulence and the sensitivity of the detecting system are analyzed. The results of numerical calculation of the granulation contrast as functions of aperture, coherent length of atmospheric turbulence and sensitivity of the detecting system are presented. Results of a related observation are also given.