Solar System planetary orbital motions and dark matter

In this paper we explicitly work out the effects that a spherically symmetric distribution of dark matter with constant density would induce on the Keplerian orbital elements of the Solar System planets and compare them with the latest results in planetary orbit determination from the EPM2004 ephemerides. It turns out that the longitudes of perihelia and the mean longitudes are affected by secular precessions. The resulting upper bounds on dark matter density, obtained from the EPM2004 formal errors in the determined mean longitude shifts over 90 years, lie in the range 10^-19-10^-20 g cm^-3 with a peak of 10^-22 g cm^-3 for Mars. Suitable combinations of the planetary mean longitudes and perihelia, which cancel out the aliasing impact of some of the unmodelled or mismodelled forces of the dynamical models of EPM2004, yield a global upper bound of 7 10^-20 g cm^-3 and 4 10^-19 g cm^-3, respectively.Comment: Latex, 8 pages, 2 tables, no figures, 8 references. Revised version with improved analysi

Density of dark matter in Solar system and perihelion precession of planets

Direct relation is pointed out between the secular perihelion precession of a planet and the density of dark matter at its orbit. It is valid under the only assumption that the density is spherically-symmetric, with the center coinciding with the Sun. This relation, combined with the observational data on perihelion precession of planets, results in upper limits on local values of the dark matter density in the Solar system.Comment: 4 pages; some explanations on derivation of master formula adde

The impact of the new CHAMP and GRACE Earth gravity models on the measurement of the general relativistic Lense--Thirring effect with the LAGEOS and LAGEOS II satellites

Among the effects predicted by the General Theory of Relativity for the orbital motion of a test particle, the post-Newtonian gravitomagnetic Lense-Thirring effect is very interesting and, up to now, there is not yet an undisputable experimental direct test of it. To date, the data analysis of the orbits of the existing geodetic LAGEOS and LAGEOS II satellites has yielded a test of the Lense-Thirring effect with a claimed accuracy of 20%-30%. According to some scientists such estimates could be optimistic. Here we wish to discuss the improvements obtainable in this measurement, in terms of reliability of the evaluation of the systematic error and reduction of its magnitude, due to the new CHAMP and GRACE Earth gravity models.Comment: LaTex2e, 6 pages, no figures, no tables. Paper presented at 2nd CHAMP science meeting, Potsdam, 1-4 September 200

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

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

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

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

Will the recently approved LARES mission be able to measure the Lense-Thirring effect at 1%?

After the approval by the Italian Space Agency of the LARES satellite, which should be launched at the end of 2009 with a VEGA rocket and whose claimed goal is a about 1% measurement of the general relativistic gravitomagnetic Lense-Thirring effect in the gravitational field of the spinning Earth, it is of the utmost importance to reliably assess the total realistic accuracy that can be reached by such a mission. The observable is a linear combination of the nodes of the existing LAGEOS and LAGEOS II satellites and of LARES able to cancel out the impact of the first two even zonal harmonic coefficients of the multipolar expansion of the classical part of the terrestrial gravitational potential representing a major source of systematic error. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be placed at an altitude of 1450 km. Thus, it will be sensitive to much more even zonals than LAGEOS and LAGEOS II. Their corrupting impact \delta\mu has been evaluated by using the standard Kaula's approach up to degree L=70 along with the sigmas of the covariance matrices of eight different global gravity solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, JEM01-RL03B, ITG-Grace02s, ITG-Grace03, EGM2008) obtained by five institutions (GFZ, CSR, JPL, IGG, NGA) with different techniques from long data sets of the dedicated GRACE mission. It turns out \delta\mu about 100-1000% of the Lense-Thirring effect. An improvement of 2-3 orders of magnitude in the determination of the high degree even zonals would be required to constrain the bias to about 1-10%.Comment: Latex, 15 pages, 1 table, no figures. Final version matching the published one in General Relativity and Gravitation (GRG

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

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