A new solution to the Main Problem of Lunar Theory

A new solution for the Main Problem on Lunar Theory is given. This solution maintains the advantages of an analytical solution and should be more accurate than previous analytical or numerical solutions. It contains the effects of the mass ratios which are often neglected in the definition of the Main Problem.     

On a perturbation theory using Lie transforms

Kamel has recently extended to non-Hamiltonian equations a perturbation theory using Lie transforms. We show here how Kamel's extension can be approached from an intrinsic viewpoint, which reformulation leads to a simpler algorithm. Then we complete Kamel's contribution by establishing the rules for inverting the transformation generated by the perturbation theory, and for composing two such transformations.     

The line response function of stellar atmospheres and the effective depth of line formation

The response function defines the response of line profiles to a depth variation of such atmospheric parameters as velocity, magnetic field and turbulence. The properties of this function are derived and compared with the so-called contribution function.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Normalisation des systèmes linéaires canoniques et application au problème restreint des trois corps

An algorithm is given for normalizing conservative linear Hamiltonian systems. This one generalizes Siegel's method to the cases where the eigenvalues are multiple. We obtain by a canonical transformation a normal form of two blocks, one of which is the upper Jordan form, and the other, the lower Jordan form. We select real solutions from the solutions of these equations, and we apply the result to the restricted three body problem in the vicinity of the triangular points for Routh's critical mass ratio.

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_n est la matrice unité d'ordren,O _n est la matrice nulle d'ordren.     

Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control

Dissolution and precipitation rates of brucite (Mg(OH)₂) were measured at 25°C in a mixed-flow reactor as a function of pH (2.5 to 12), ionic strength (10⁻⁴ to 3 M), saturation index (−12 < log Ω < 0.4) and aqueous magnesium concentrations (10⁻⁶ to 5·10⁻⁴ M). Brucite surface charge and isoelectric point (pH_IEP) were determined by surface titrations in a limited residence time reactor and electrophoretic measurements, respectively. The pH of zero charge and pH_IEP were close to 11. A two-pK, one site surface speciation model which assumes a constant capacitance of the electric double layer (5 F/m²) and lack of dependence on ionic strength predicts the dominance of >MgOH₂⁺ species at pH < 8 and their progressive replacement by >MgOH° and >MgO⁻ as pH increases to 10-12. Rates are proportional to the square of >MgOH₂⁺ surface concentration at pH from 2.5 to 12. In accord with surface speciation predictions, dissolution rates do not depend on ionic strength at pH 6.5 to 11. Brucite dissolution and precipitation rates at close to equilibrium conditions obeyed TST-derived rate laws. At constant saturation indices, brucite precipitation rates were proportional to the square of >MgOH₂⁺ concentration. The following rate equation, consistent with transition state theory, describes brucite dissolution and precipitation kinetics over a wide range of solution composition and chemical affinity:

     

Heliocentric evolution of the degradation of polyoxymethylene: Application to the origin of the formaldehyde (H2CO) extended source in Comet C/1995 O1 (Hale-Bopp)

The H₂CO production rates measured in Comet C/1995 O1 (Hale-Bopp) from radio wavelength observations [Biver, N., and 22 colleagues, 2002a. Earth Moon Planets 90, 5-14] showed a steep increase with decreasing heliocentric distance. We studied the heliocentric evolution of the degradation of polyoxymethylene (formaldehyde polymers: (CH₂O)_n, also called POM) into gaseous H₂CO. POM decomposition can indeed explain the H₂CO density profile measured in situ by Giotto spacecraft in the coma of Comet 1P/Halley, which is not compatible with direct release from the nucleus [Cottin, H., Bénilan, Y., Gazeau, M.-C., Raulin, F., 2004. Icarus 167, 397-416]. We show that the H₂CO production curve measured in Comet C/1995 O1 (Hale-Bopp) can be accurately reproduced by this mechanism with a few percents by mass of solid POM in grains. The steep heliocentric evolution is explained by the thermal degradation of POM at distances less than 3.5 AU. This study demonstrates that refractory organics present in cometary dust can significantly contribute to the composition of the gaseous coma. POM, or POM-like polymers, might be present in cometary grains. Other molecules, like CO and HNC, might also be produced by a similar process.     

TNOs are Cool: A Survey of the Transneptunian Region

Over one thousand objects have so far been discovered orbiting beyond Neptune. These trans-Neptunian objects (TNOs) represent the primitive remnants of the planetesimal disk from which the planets formed and are perhaps analogous to the unseen dust parent-bodies in debris disks observed around other main-sequence stars. The dynamical and physical properties of these bodies provide unique and important constraints on formation and evolution models of the Solar System. While the dynamical architecture in this region (also known as the Kuiper Belt) is becoming relatively clear, the physical properties of the objects are still largely unexplored. In particular, fundamental parameters such as size, albedo, density and thermal properties are difficult to measure. Measurements of thermal emission, which peaks at far-IR wavelengths, offer the best means available to determine the physical properties. While Spitzer has provided some results, notably revealing a large albedo diversity in this population, the increased sensitivity of Herschel and its superior wavelength coverage should permit profound advances in the field. Within our accepted project we propose to perform radiometric measurements of 139 objects, including 25 known multiple systems. When combined with measurements of the dust population beyond Neptune (e.g. from the New Horizons mission to Pluto), our results will provide a benchmark for understanding the Solar debris disk, and extra-solar ones as well.