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.     

The influence of tropical Pacific forcing on the Arctic Oscillation

The potential role of tropical Pacific forcing in driving the seasonal variability of the Arctic Oscillation (AO) is explored using both observational data and a simple general circulation model (SGCM). A lead–lag regression technique is first applied to the monthly averaged sea surface temperature (SST) and the AO index. The AO maximum is found to be related to a negative SST anomaly over the tropical Pacific three months earlier. A singular value decomposition (SVD) analysis is then performed on the tropical Pacific SST and the sea level pressure (SLP) over the Northern Hemisphere. An AO-like atmospheric pattern and its associated SST appear as the second pair of SVD modes. Ensemble integrations are carried out with the SGCM to test the atmospheric response to different tropical Pacific forcings. The atmospheric response to the linear fit of the model’s empirical forcing associated with the SST variability in the second SVD modes strongly projects onto the AO. Idealized thermal forcings are then designed based on the regression of the seasonally averaged tropical Pacific precipitation against the AO index. Results indicate that forcing anomalies over the western tropical Pacific are more effective in generating an AO-like response while those over the eastern tropical Pacific tend to produce a Pacific-North American (PNA)-like response. The physical mechanisms responsible for the energy transport from the tropical Pacific to the extratropical North Atlantic are investigated using wave activity flux and vorticity forcing formalisms. The energy from the western tropical Pacific forcing tends to propagate zonally to the North Atlantic because of the jet stream waveguide effect while the transport of the energy from the eastern tropical Pacific forcing mostly concentrates over the PNA area. The linearized SGCM results show that nonlinear processes are involved in the generation of the forced AO-like pattern.