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## 6. Environmental Context

### Earth, Moon, and Planets (2006) 98: 205-245 , October 27, 2006

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On Earth, the Archaean aeon lasted from 4.0 to 2.5 Ga; it corresponds to a relatively stable period. Compared with today, internal Earth heat production was several times greater resulting in high geothermal flux that induced the genesis of rocks such as komatiites and TTG suites, which are no more generated on Earth since 2.5 Ga. Similarly, the details of plate tectonic modalities (plate size, plate motion rate, plate thickness, tectonic style, irregular crustal growth, etc...) were different of modern plate tectonics. Both atmosphere and ocean compositions have been progressively modified and the greater heat production favoured the development of hydrothermalism and therefore created niches potentially favourable for the development of some forms of life. Catastrophic events such as giant meteorite falls or world-sized glaciations drastically and suddenly changed the environment of Earth surface, thus being able to strongly affect development of life. Even if specialists still debate about the age of the oldest indubitable fossil trace of life, Archaean can be considered as having been extremely favourable for life development and diversification.

## The post-RLOF structure of the secondary components in close binary systems, with an application to masses of Wolf-Rayet stars

### Astrophysics and Space Science (1984) 104: 83-109 , September 01, 1984

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The post-RLOF structure of the secondary after relaxation towards thermal equilibrium is calculated for a large grid of massive close binaries evolving through an early case*B* of mass transfer. The initial primary masses range between 15 and 30*M*_{o}, the initial mass ratio between 0.3 and 0.9. The possibility that matter leaves the system during RLOF is included using an additional free parameter β. The calculations are based on the accretion and relaxation properties of massive accretion stars. Conclusions on the post-RLOF secondaries are presented in function of β, M1i, and*q*_{i}, in the form of tables and figures on the post-RLOF positions in the HR diagram, the final masses, mass ratios, chemical profiles and the remaining core-hydrogen burning lifetime. It is found that all systems starting from initial conditions in the grid specified above evolve sequentially, i.e. the primary evolves into a supernova before the end of core H burning of the secondary. No WR+WR systems are encountered. The results are used to determine the masses of ten double lined spectroscopic WR+OB binaries. Most of the WR masses are in the range 8–14*M*_{o}, although the sample is subject to some important selection effects. One WR+OB binary has a WR mass between 4 and 5*M*_{o}. It is argued that mass determinations based only on the spectral type of the secondary yield WR masses that are too high up to a factor two.

## Extended Schubart Averaging

### Celestial Mechanics & Dynamical Astronomy (1994) 60: 173-186 , September 01, 1994

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The purpose of this paper is the presentation of an integrator for the average motion of an asteroid in mean motion commensurability with Jupiter. The program is valid for any (*p+q*)/*p* mean motion commensurability (except when*q*=0) and uses a double precision version of DE (Shampine and Gordon 1975) as propagator. The averaged equations of motion of the asteroid are evaluated in a non-singular way for any value of the eccentricities and the inclinations and the orbit of Jupiter is described by the most important terms in Longstop 1B (Nobili*et al.* 1989). This integrator can be considered as an extension of the well known Schubart Averaging (Schubart 1978) in which Jupiter is moving on a fixed ellipse.

## Regularization of the two body problem with variable mass

### Celestial Mechanics (1974) 10: 141-149 , October 01, 1974

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Using Levi Civita's regularization, we put the two body problem with variable mass (x=−*M*x*r*^{−3}) into a form which can be solved analytically on computer. Two particular cases are discussed: 1.
$$\dot M$$
=*C*^{te}; 2.
$$\dot M$$
÷*M*^{α} (α unspecified).

## Mode identification of pulsating stars from line profile variations with the moment method

### The Atmospheres of Early-Type Stars (1992) 401: 163-166 , January 01, 1992

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The moment method seems to be suitable for determining the pulsation parameters of early-type stars but line profile variations are by no means staightforward to interpret (Waelkens and Aerts, this volume). It is clear that we have used only part of the information contained in the moments. A future development will be the construction of a discriminant which includes all significant information given by the moments and does not rely only upon a few leading terms.

## Surfaces of section in the Miranda-Umbriel 3:1 inclination problem

### Celestial Mechanics & Dynamical Astronomy (1994) 59: 129-148 , June 01, 1994

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The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermott*et al.* (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical landscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 3:1 inclination resonance between Miranda and Umbriel is analysed.

## CLÉS, Code Liégeois d’Évolution Stellaire

### Astrophysics and Space Science (2008) 316: 83-91 , August 27, 2008

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CLÉS is an evolution code recently developed to produce stellar models meeting the specific requirements of studies in asteroseismology. It offers the users a lot of choices in the input physics they want in their models and its versatility allows them to tailor the code to their needs and implement easily new features. We describe the features implemented in the current version of the code and the techniques used to solve the equations of stellar structure and evolution. A brief account is given of the use of the program and of a solar calibration realized with it.

## Planetary perturbations on the Libration of the Moon

### Celestial Mechanics (1984) 34: 263-273 , September 01, 1984

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A theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field, was recently built (Moons, 1982). The Lie transforms method was used to reduce the Hamiltonian of the main problem of the libration of the Moon and to produce the usual libration series p_{1}, p_{2} and τ. This main problem takes into account the perturbations due to the Sun and the Earth on the rotation of a rigid Moon about its center of mass. In complement to this theory, we have now computed the planetary effects on the libration, the planetary terms being added to the mean Hamiltonian of the main problem before a last elimination of the angles. For the main problem, as well as for the planetary perturbations, the motion of the center of mass of the Moon is described by the ELP 2000 solution (Chapront and Chapront-Touze, 1983).

## The reducing transformation and Apocentric Librators

### Celestial Mechanics (1986) 38: 335-344 , April 01, 1986

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We propose a canonical transformation reducing the averaged planar planetary problem near resonance to a one degree of freedom problem when the perturbation is truncated at the first order in the eccentricities.

This reducing transformation leads to a very simple explanation of the puzzling behaviour of the Apocentric Librators, a class of asteroids identified by Franklin*et al.* (1975).

An exploration of the phase space of the average problem with the use of the mapping technique shows that the alternation of two libration mechanism is a common feature for initial conditions near, but not inside, the deep resonance region.

## Spiral Shocks in an Inviscid Simulation of Accretion Flow in a Close Binary System

### Astrotomography (2001) 573: 88-93 , January 01, 2001

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We perform 2D and 3D numerical simulations of an accretion disc in a close binary with a mass ratio of 0.5, corresponding to the dwarf nova IP Pegasi. We do not include artificial nor α-viscosity and supply gas from the inner L1 point. We construct Doppler maps and artificial trailed spectrograms. In the 2D calculation, the results agree very well with those observed in IP Peg. In the 3D calculations, the stream from the L1 point penetrates into the accretion disc. The resulting flow pattern, therefore, is different from the 2D results.