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&

Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices

We study the fluctuations of the matrix entries of regular functions of Wigner random matrices in the limit when the matrix size goes to infinity. In the case of the Gaussian ensembles (GOE and GUE) this problem was considered by A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are valid provided the off-diagonal matrix entries have finite fourth moment, the diagonal matrix entries have finite second moment, and the test functions have four continuous derivatives in a neighborhood of the support of the Wigner semicircle law.Comment: minor corrections; the manuscript will appear in the Journal of Statistical Physic

An Empirical Explanation of the Anomalous Increases in the Astronomical Unit and the Lunar Eccentricity

Both the recently reported anomalous secular increase of the astronomical unit, of the order of a few cm yr^-1, and of the eccentricity of the lunar orbit e_ = (9+/-3) 10^-12 yr^-1 can be phenomenologically explained by postulating that the acceleration of a test particle orbiting a central body, in addition to usual Newtonian component, contains a small additional radial term proportional to the radial projection vr of the velocity of the particle's orbital motion. Indeed, it induces secular variations of both the semi-major axis a and the eccentricity e of the test particle's orbit. In the case of the Earth and the Moon, they numerically agree rather well with the measured anomalies if one takes the numerical value of the coefficient of proportionality of the extra-acceleration approximately equal to that of the Hubble parameter H0 = 7.3 10^-11 yr^-1.Comment: Latex2e, no figures, no tables, 9 pages, 51 references. Published in The Astronomical Journal (AJ

On universality of local edge regime for the deformed Gaussian Unitary Ensemble

We consider the deformed Gaussian ensemble $H_n=H_n^{(0)}+M_n$ in which $H_n^{(0)}$ is a hermitian matrix (possibly random) and $M_n$ is the Gaussian unitary random matrix (GUE) independent of $H_n^{(0)}$. Assuming that the Normalized Counting Measure of $H_n^{(0)}$ converges weakly (in probability if random) to a non-random measure $N^{(0)}$ with a bounded support and assuming some conditions on the convergence rate, we prove universality of the local eigenvalue statistics near the edge of the limiting spectrum of $H_n$.Comment: 25 pages, 2 figure

The influence of Galactic aberration on precession parameters determined from VLBI observations

The influence of proper motions of sources due to Galactic aberration on precession models based on VLBI data is determined. Comparisons of the linear trends in the coordinates of the celestial pole obtained with and without taking into account Galactic aberration indicate that this effect can reach 20 $\mu$as per century, which is important for modern precession models. It is also shown that correcting for Galactic aberration influences the derived parameters of low-frequency nutation terms. It is therefore necessary to correct for Galactic aberration in the reduction of modern astrometric observations

The empirical Earth rotation model from VLBI observations

AIMS: An alternative to the traditional method for modeling kinematics of the Earth's rotation is proposed. The purpose of developing the new approach is to provide a self-consistent and simple description of the Earth's rotation in a way that can be estimated directly from observations without using intermediate quantities. METHODS: Instead of estimating the time series of pole coordinates, the UT1--TAI angles, their rates, and the daily offsets of nutation, it is proposed to estimate coefficients of the expansion of a small perturbational rotation vector into basis functions. The resulting transformation from the terrestrial coordinate system to the celestial coordinate system is formulated as a product of an a priori matrix of a finite rotation and an empirical vector of a residual perturbational rotation. In the framework of this approach, the specific choice of the a priori matrix is irrelevant, provided the angles of the residual rotation are small enough to neglect their squares. The coefficients of the expansion into the B-spline and Fourier bases, together with estimates of other nuisance parameters, are evaluated directly from observations of time delay or time range in a single least square solution. RESULTS: This approach was successfully implemented in a computer program for processing VLBI observations. The dataset from 1984 through 2006 was analyzed. The new procedure adequately represents the Earth's rotation, including slowly varying changes in UT1--TAI and polar motion, the forced nutations, the free core nutation, and the high frequency variations of polar motion and UT1.Comment: 15 pages, 10 figures, Published in Astronomy and Astrophysics. For numerical tables see http://vlbi.gsfc.nasa.gov/er