Long Periodic Terms in the Solar System

The long period variations of the first eight planets in the solar system are studied. First, the Lagrangian solution is calculated and then the long period terms with fourth order eccentricities and inclinations are introduced into the perturbation function. A second approximation was made taking into account the short period terms' contribution, namely the perturbations of first order with respect to the masses. Special attention was paid to the determination of the integration constants. The relative importance of the different contributions is shown. It is useless, for example, to introduce the long period terms of fifth order if no account has been taken of the short period terms. Meanwhile, the terms that have been neglected would not introduce large changes in the integration constants. Even so, the calculation should be repeated with higher order short period terms and fifth order long periods

Three-body resonance in meteoroid streams

Mean-motion resonances play an important role in the evolution of various meteoroid streams. Previous works have studied the effects of two-body resonances in different comets and streams. These already established two-body resonances were mainly induced either by Jovian or Saturnian effects but not both at the same time. Some of these resonances have led to spectacular meteor outbursts and storms in the past. In this work, we find a new resonance mechanism involving three bodies -- i.e. meteoroid particle, Jupiter and Saturn, in the Perseid meteoroid stream. Long-term three-body resonances are not very common in real small bodies in our solar system although they can mathematically exist at many resonant sweet spots in an abstract sense in any dynamical system. This particular resonance combination in the Perseid stream is such that it is close to the ratio of 1:4:10 if the orbital periods of Perseid particle, Saturn and Jupiter are considered respectively. These resonant Perseid meteoroids stay resonant for typically about 2 kyr. Highly compact dust trails due to this unique resonance phenomenon are present in our simulations. Some past and future years are presented where three-body resonant meteoroids of different sizes (or subject to different radiation pressures) are computed to come near the Earth. This is the first theoretical example of an active and stable three-body resonance mechanism in the realm of meteoroid streams.Comment: 12 pages, 12 figures, 3 tables; Accepted in MNRA

Polar motions equivalent to high frequency nutations for a nonrigid Earth with anelastic mantle

The coefficients of polar motions of the rigid/nonrigid Earth in frequency bands other than the retrograde diurnal one are systematically computed using general expressions, derived here for the first time, for the prograde and retrograde torques exerted on the Earth by lunisolar potentials of arbitrary spherical harmonic type. Taken together with the already known coefficients of low frequency nutations and UT1 variations, they provide a complete characterization, with high precision, of the motions of the pole of the terrestrial reference frame in space; this is needed for high precision studies in astronomy and space geodesy. The inputs used for our computations are a table of tidal amplitudes, and values of the geopotential coefficients of degrees up to 4 and of other relevant basic Earth parameters. General relations which connect the coefficients of high frequency nutations to those of the equivalent polar motions are established and used for deducing the former. The Chandler resonance plays a significant role in low frequency polar motions. In this context, the role of mantle anelasticity and the nature of the Earth's deformational response to zero frequency forcing are given special consideration. The free core nutation (FCN) resonance of low frequency nutations is shown to affect the prograde semidiurnal nutations through the coupling produced between the nutations in the two frequency bands by triaxiality terms in the angular momenta of the whole Earth and of its fluid core. It is shown in a transparent fashion that the effect of the core triaxiality arises almost exclusively from the huge FCN-related resonance in the wobble of the core. The magnitude of the effect is found to be a few times smaller than reported in a recent paper; it is also found, unlike in that paper, that the changes in the eigenfrequencies due to trixiality are only of the second order in the triaxiality parameter. Numerical results for the polar motions of the nonrigid Earth in different frequency bands, as well as for the elliptical nutations of the rigid Earth, are tabulated and compared with available numbers from earlier works

Proper initial conditions for long-term integrations of the solar system

An optimization program is used to re-adjust the initial conditions, in order to reproduce as closely as possible the predictions of a complete ephemeris by using simplified equations of motion in the numerical integration. The adjustment of the initial conditions is illustrated in the transition from the DE406 complete long-range ephemeris to a Newtonian model considering only the Sun and the four major planets. It is also used to best reproduce this same DE406 ephemeris, based on post-Newtonian equations for a system of mass points and including the Moon and asteroids, by using a Newtonian calculation corrected by the Schwarzschild effects of the Sun and restricted to the ten major bodies of the solar system.Comment: 14 pages, accepted for publication in A&A. v2: TeX file instead of PS generated from word proc. as befor

Spin-Exchange Interaction in ZnO-based Quantum Wells

Wurtzitic ZnO/(Zn,Mg)O quantum wells grown along the (0001) direction permit unprecedented tunability of the short-range spin exchange interaction. In the context of large exciton binding energies and electron-hole exchange interaction in ZnO, this tunability results from the competition between quantum confinement and giant quantum confined Stark effect. By using time-resolved photoluminescence we identify, for well widths under 3 nm, the redistribution of oscillator strengths between the A and B excitonic transitions, due to the enhancement of the exchange interaction. Conversely, for wider wells, the redistribution is cancelled by the dominant effect of internal electric fields, which dramatically reduce the exchange energy.Comment: 14 pages, 3 figure

Low temperature reflectivity study of ZnO/(Zn,Mg)O quantum wells grown on M-plane ZnO substrates

We report growth of high quality ZnO/Zn0.8Mg0.2O quantum well on M-plane oriented ZnO substrates. The optical properties of these quantum wells are studied by using reflectance spectroscopy. The optical spectra reveal strong in-plane optical anisotropies, as predicted by group theory, and marked reflectance structures, as an evidence of good interface morphologies. Signatures ofc onfined excitons built from the spin-orbit split-off valence band, the analog of exciton C in bulk ZnO are detected in normal incidence reflectivity experiments using a photon polarized along the c axis of the wurtzite lattice. Experiments performed in the context of an orthogonal photon polarization, at 90^{\circ}; of this axis, reveal confined states analogs of A and B bulk excitons. Envelope function calculations which include excitonic interaction nicely account for the experimental report

Precession, nutation, and space geodetic determination of the Earth's variable gravity field

Precession and nutation of the Earth depend on the Earth's dynamical flattening, H, which is closely related to the second degree zonal coefficient, J2 of the geopotential. A small secular decrease as well as seasonal variations of this coefficient have been detected by precise measurements of artificial satellites (Nerem et al. 1993; Cazenave et al. 1995) which have to be taken into account for modelling precession and nutation at a microarcsecond accuracy in order to be in agreement with the accuracy of current VLBI determinations of the Earth orientation parameters. However, the large uncertainties in the theoretical models for these J2 variations (for example a recent change in the observed secular trend) is one of the most important causes of why the accuracy of the precession-nutation models is limited (Williams 1994; Capitaine et al. 2003). We have investigated in this paper how the use of the variations of J2 observed by space geodetic techniques can influence the theoretical expressions for precession and nutation. We have used time series of J2 obtained by the "Groupe de Recherches en G\'eod\'esie spatiale" (GRGS) from the precise orbit determination of several artificial satellites from 1985 to 2002 to evaluate the effect of the corresponding constant, secular and periodic parts of H and we have discussed the best way of taking the observed variations into account. We have concluded that, although a realistic estimation of the J2 rate must rely not only on space geodetic observations over a limited period but also on other kinds of observations, the monitoring of periodic variations in J2 could be used for predicting the effects on the periodic part of the precession-nutation motion

High quality factor nitride-based optical cavities: microdisks with embedded GaN/Al(Ga)N quantum dots

We compare the quality factor values of the whispery gallery modes of microdisks incorporating GaN quantum dots (QDs) grown on AlN and AlGaN barriers by performing room temperature photoluminescence (PL) spectroscopy. The PL measurements show a large number of high Q factor (Q) resonant modes on the whole spectrum which allows us to identify the different radial mode families and to compare them with simulations. We report a considerable improvement of the Q factor which reflect the etching quality and the relatively low cavity loss by inserting QDs into the cavity. GaN/AlN QDs based microdisks show very high Q values (Q > 7000) whereas the Q factor is only up to 2000 in microdisks embedding QDs grown on AlGaN barrier layer. We attribute this difference to the lower absorption below bandgap for AlN barrier layers at the energies of our experimental investigation

Transport of indirect excitons in ZnO quantum wells

We report on spatially- and time-resolved emission measurements and observation of transport of indirect excitons in ZnO/MgZnO wide single quantum wells

A precise modeling of Phoebe's rotation

Although the rotation of some Saturn's satellites in spin-orbit has already been studied by several authors, this is not the case of the rotation of Phoebe, which has the particularity of being non resonant. The purpose of the paper is to determine for the first time and with precision its precession-nutation motion. We adopt an Hamiltonian formalism of the motion of rotation of rigid celestial body set up by Kinoshita (1977) based on Andoyer variables and canonical equations. First we calculate Phoebe's obliquity at J2000,0 from available astronomical data as well as the gravitational perturbation due to Saturn on Phoebe rotational motion. Then we carry out a numerical integration and we compare our results for the precession rate and the nutation coefficients with pure analytical model. Our results for Phoebe obliquity (23{\deg}95) and Phoebe precession rate (5580".65/cy) are very close to the respective values for the Earth. Moreover the amplitudes of the nutations (26" peak to peak for the nutaton in longitude and 8" for the nutation in obliquity) are of the same order as the respective amplitudes for the Earth. We give complete tables of nutation, obtained from a FFT analysis starting from the numerical signals. We show that a pure analytical model of the nutation is not accurate due to the fact that Phoebe orbital elements e, M and Ls are far from having a simple linear behaviour. The precession and nutation of Phoebe have been calculated for the first time in this paper. We should keep on the study in the future by studying the additional gravitational effects of the Sun, of the large satellites as Titan, as well as Saturn dynamical ellipticity.Comment: 11 pages,15 figures, accepted for publication in A&