On a new observable for measuring the Lense-Thirring effect with Satellite Laser Ranging

In this paper we present a rather extensive error budget for the difference of the perigees of a pair of supplementary SLR satellites aimed to the detection of the Lense-Thirring effect.Comment: LaTex2e, 14 pages, 1 table, no figures. Some changes and additions to the abstract, Introduction and Conclusions. References updated, typos corrected. Equation corrected. To appear in General Relativity and Gravitatio

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 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.

On the possibility of measuring the Earth's gravitomagnetic force in a new laboratory experiment

In this paper we propose, in a preliminary way, a new Earth-based laboratory experiment aimed to the detection of the gravitomagnetic field of the Earth. It consists of the measurement of the difference of the circular frequencies of two rotators moving along identical circular paths, but in opposite directions, on a horizontal friction-free plane in a vacuum chamber placed at South Pole. The accuracy of our knowledge of the Earth's rotation from VLBI and the possibility of measuring the rotators'periods over many revolutions should allow for the feasibility of the proposed experiment.Comment: Latex2e, 8 pages, no figures, no tables, accepted for publication by Classical and Quantum Gravity. Typo corrected in the formula of the error in the difference of the orbital period

Super-ASTROD: Probing primordial gravitational waves and mapping the outer solar system

Super-ASTROD (Super Astrodynamical Space Test of Relativity using Optical Devices or ASTROD III) is a mission concept with 3-5 spacecraft in 5 AU orbits together with an Earth-Sun L1/L2 spacecraft ranging optically with one another to probe primordial gravitational-waves with frequencies 0.1 microHz - 1 mHz, to test fundamental laws of spacetime and to map the outer solar system. In this paper we address to its scientific goals, orbit and payload selection, and sensitivity to gravitational waves.Comment: 7 pages, 1 figure, presented to 7th International LISA Symposium, 16-20 June 2008, Barcelona; submitted to Classical and Quantum Gravity; presentation improve

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

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

Gravitomagnetic time-varying effects on the motion of a test particle

We study the effects of a time-varying gravitomagnetic field on the motion of test particles. Starting from recent results, we consider the gravitomagnetic field of a source whose spin angular momentum has a linearly time-varying magnitude. The acceleration due to such a time-varying gravitomagnetic field is considered as a perturbation of the Newtonian motion, and we explicitly evaluate the effects of this perturbation on the Keplerian elements of a closed orbit. The theoretical predictions are compared with actual astronomical and astrophysical scenarios, both in the solar system and in binary pulsars systems, in order to evaluate the impact of these effects on real systems.Comment: 8 pages, RevTeX; revised to match the version accepted for publication in General Relativity and Gravitatio

Constraining the relative inclinations of the planets B and C of the millisecond pulsar PSR B1257+12

We investigate on the relative inclination of the planets B and C orbiting the pulsar PSR B1257+12 in connection with potential violations of the equivalence principle (Abridged).Comment: LaTex2e, 10 pages, 1 table, 3 figures, 17 references. Small stylistic changes. Version to appear in Journal of Astrophysics and Astronomy (JAA

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