The relativistic precession of the orbits

The relativistic precession can be quickly inferred from the nonlinear polar orbit equation without actually solving it.Comment: Accepted for publication in Astrophysics & Space Scienc

On the perspectives of testing the Dvali-Gabadadze-Porrati gravity model with the outer planets of the Solar System

The multidimensional braneworld gravity model by Dvali, Gabadadze and Porrati was primarily put forth to explain the observed acceleration of the expansion of the Universe without resorting to dark energy. One of the most intriguing features of such a model is that it also predicts small effects on the orbital motion of test particles which could be tested in such a way that local measurements at Solar System scales would allow to get information on the global properties of the Universe. Lue and Starkman derived a secular extra-perihelion \omega precession of 5\times 10^-4 arcseconds per century, while Iorio showed that the mean longitude \lambda is affected by a secular precession of about 10^-3 arcseconds per century. Such effects depend only on the eccentricities e of the orbits via second-order terms: they are, instead, independent of their semimajor axes a. Up to now, the observational efforts focused on the dynamics of the inner planets of the Solar System whose orbits are the best known via radar ranging. Since the competing Newtonian and Einsteinian effects like the precessions due to the solar quadrupole mass moment J2, the gravitoelectric and gravitomagnetic part of the equations of motion reduce with increasing distances, it would be possible to argue that an analysis of the orbital dynamics of the outer planets of the Solar System, with particular emphasis on Saturn because of the ongoing Cassini mission with its precision ranging instrumentation, could be helpful in evidencing the predicted new features of motion. In this note we investigate this possibility in view of the latest results in the planetary ephemeris field. Unfortunately, the current level of accuracy rules out this appealing possibility and it appears unlikely that Cassini and GAIA will ameliorate the situation.Comment: LaTex, 22 pages, 2 tables, 10 figures, 27 references. Reference [17] added, reference [26] updated, caption of figures changed, small change in section 1.

Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test

We deal with the test of the general relativistic gravitomagnetic Lense-Thirring effect currently ongoing in the Earth's gravitational field with the combined nodes \Omega of the laser-ranged geodetic satellites LAGEOS and LAGEOS II. One of the most important source of systematic uncertainty on the orbits of the LAGEOS satellites, with respect to the Lense-Thirring signature, is the bias due to the even zonal harmonic coefficients J_L of the multipolar expansion of the Earth's geopotential which account for the departures from sphericity of the terrestrial gravitational potential induced by the centrifugal effects of its diurnal rotation. The issue addressed here is: are the so far published evaluations of such a systematic error reliable and realistic? The answer is negative. Indeed, if the difference \Delta J_L among the even zonals estimated in different global solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, ITG-Grace02, ITG-Grace03s, JEM01-RL03B, EGM2008, AIUB-GRACE01S) is assumed for the uncertainties \delta J_L instead of using their more or less calibrated covariance sigmas \sigma_{J_L}, it turns out that the systematic error \delta\mu in the Lense-Thirring measurement is about 3 to 4 times larger than in the evaluations so far published based on the use of the sigmas of one model at a time separately, amounting up to 37% for the pair EIGEN-GRACE02S/ITG-Grace03s. The comparison among the other recent GRACE-based models yields bias as large as about 25-30%. The major discrepancies still occur for J_4, J_6 and J_8, which are just the zonals the combined LAGEOS/LAGOES II nodes are most sensitive to.Comment: LaTex, 12 pages, 12 tables, no figures, 64 references. To appear in Central European Journal of Physics (CEJP

On the effects of the Dvali-Gabadadze-Porrati braneworld gravity on the orbital motion of a test particle

In this paper we explicitly work out the secular perturbations induced on all the Keplerian orbital elements of a test body to order O(e^2) in the eccentricity e by the weak-field long-range modifications of the usual Newton-Einstein gravity due to the Dvali-Gabadadze-Porrati (DGP) braneworld model. The Gauss perturbative scheme is used. It turns out that the argument of pericentre and the mean anomaly are affected by secular rates which are independent of the semimajor axis of the orbit of the test particle. The first nonvaishing eccentricity-dependent corrections are of order O(e^2). For circular orbits the Lue-Starkman (LS) effect on the pericentre is obtained. Some observational consequences are discussed for the Solar System planetary mean longitudes lambda which would undergo a 1.2\cdot 10^-3 arcseconds per century braneworld secular precession. According to recent data analysis over 92 years for the EPM2004 ephemerides, the 1-sigma formal accuracy in determining the Martian mean longitude amounts to 3\cdot 10^-3 milliarcseconds, while the braneworld effect over the same time span would be 1.159 milliarcseconds. The major limiting factor is the 2.6\cdot 10^-3 arcseconds per century systematic error due to the mismodelling in the Keplerian mean motion of Mars. A suitable linear combination of the mean longitudes of Mars and Venus may overcome this problem. The formal, 1-sigma obtainable observational accuracy would be \sim 7%. The systematic error due to the present-day uncertainties in the solar quadrupole mass moment, the Keplerian mean motions, the general relativistic Schwarzschild field and the asteroid ring would amount to some tens of percent.Comment: LaTex2e, 23 pages, 5 tables, 1 figure, 37 references. Second-order corrections in eccentricity explicitly added. Typos corrected. References update

Is infinity that far? A Bayesian nonparametric perspective of finite mixture models

Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. Following a Bayesian nonparametric perspective, we introduce a new class of priors: the Normalized Independent Point Process. We investigate the probabilistic properties of this new class and present many special cases. In particular, we provide an explicit formula for the distribution of the implied partition, as well as the posterior characterization of the new process in terms of the superposition of two discrete measures. We also provide consistency results. Moreover, we design both a marginal and a conditional algorithm for finite mixture models with a random number of components. These schemes are based on an auxiliary variable MCMC, which allows handling the otherwise intractable posterior distribution and overcomes the challenges associated with the Reversible Jump algorithm. We illustrate the performance and the potential of our model in a simulation study and on real data applications

Weyl Symmetry and the Liouville Theory

Flat-space conformal invariance and curved-space Weyl invariance are simply related in dimensions greater than two. In two dimensions the Liouville theory presents an exceptional situation, which we here examine.Comment: 8 pages, no figure

LAGEOS-type Satellites in Critical Supplementary Orbit Configuration and the Lense-Thirring Effect Detection

In this paper we analyze quantitatively the concept of LAGEOS--type satellites in critical supplementary orbit configuration (CSOC) which has proven capable of yielding various observables for many tests of General Relativity in the terrestrial gravitational field, with particular emphasis on the measurement of the Lense--Thirring effect.Comment: LaTex2e, 20 pages, 7 Tables, 6 Figures. Changes in Introduction, Conclusions, reference added, accepted for publication in Classical and Quantum Gravit

A uniform treatment of the orbital effects due to a violation of the Strong Equivalence Principle in the gravitational Stark-like limit

We analytically work out several effects which a violation of the Strong Equivalence Principle (SEP) induces on the orbital motion of a binary system constituted of self-gravitating bodies immersed in a constant and uniform external field. We do not restrict to the small eccentricity limit. Moreover, we do not select any specific spatial orientation of the external polarizing field. We explicitly calculate the SEP-induced mean rates of change of all the osculating Keplerian orbital elements of the binary, the perturbation of the projection of the binary orbit onto the line-of-sight, the shift of the radial velocity, and the range and range-rate signatures and as well. We find that the ratio of the SEP precessions of the node and the inclination of the binary depends only on and the pericenter of the binary itself, being independent on both the magnitude and the orientation of the polarizing field, and on the semimajor axis, the eccentricity and the node of the binary. Our results, which do not depend on any particular SEP-violating theoretical scheme, can be applied to quite general astronomical and astrophysical scenarios. They can be used to better interpret present and future SEP experiments, especially when several theoretical SEP mechanisms may be involved, and to suitably design new dedicated tests.Comment: LaTex2e, 14 pages, no figures, no tables, 42 references. To appear in Classical and Quantum Gravity (CQG

On the Possibility of Measuring the Gravitomagnetic Clock Effect in an Earth Space-Based Experiment

In this paper the effect of the post-Newtonian gravitomagnetic force on the mean longitudes $l$ of a pair of counter-rotating Earth artificial satellites following almost identical circular equatorial orbits is investigated. The possibility of measuring it is examined. The observable is the difference of the times required to $l$ in passing from 0 to 2$\pi$ for both senses of motion. Such gravitomagnetic time shift, which is independent of the orbital parameters of the satellites, amounts to 5$\times 10^{-7}$ s for Earth; it is cumulative and should be measured after a sufficiently high number of revolutions. The major limiting factors are the unavoidable imperfect cancellation of the Keplerian periods, which yields a constraint of 10$^{-2}$ cm in knowing the difference between the semimajor axes $a$ of the satellites, and the difference $I$ of the inclinations $i$ of the orbital planes which, for $i\sim 0.01^\circ$, should be less than $0.006^\circ$. A pair of spacecrafts endowed with a sophisticated intersatellite tracking apparatus and drag-free control down to 10$^{-9}$ cm s$^{-2}$ Hz$^{-{1/2}}$ level might allow to meet the stringent requirements posed by such a mission.Comment: LaTex2e, 22 pages, no tables, 1 figure, 38 references. Final version accepted for publication in Classical and Quantum Gravit

Nonlinear electrodynamics and the Pioneer 10/11 spacecraft anomaly

The occurrence of the phenomenon known as photon acceleration is a natural prediction of nonlinear electrodynamics (NLED). This would appear as an anomalous frequency shift in any modeling of the electromagnetic field that only takes into account the classical Maxwell theory. Thus, it is tempting to address the unresolved anomalous, steady; but time-dependent, blueshift of the Pioneer 10/11 spacecrafts within the framework of NLED. Here we show that astrophysical data on the strength of the magnetic field in both the Galaxy and the local (super)cluster of galaxies support the view on the major Pioneer anomaly as a consequence of the phenomenon of photon acceleration. If confirmed, through further observations or lab experiments, the reality of this phenomenon should prompt to take it into account in any forthcoming research on both cosmological evolution and origin and dynamical effects of primordial magnetic fields, whose seeds are estimated to be very weak.Comment: Final version accepted for publication in Europhysics Letters, uses EPL style, 7 page