Measuring the relativistic perigee advance with Satellite Laser Ranging

One of the most famous classical tests of General Relativity is the gravitoelectric secular advance of the pericenter of a test body in the gravitational field of a central mass. In this paper we explore the possibility of performing a measurement of the gravitoelectric pericenter advance in the gravitational field of the Earth by analyzing the laser-ranged data to some existing, or proposed, laser-ranged geodetic satellites. At the present level of knowledge of various error sources, the relative precision obtainable with the data from LAGEOS and LAGEOS II, suitably combined, is of the order of $10^{\rm -3}$. Nevertheless, these accuracies could sensibly be improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available. The use of the perigee of LARES (LAser RElativity Satellite), in the context of a suitable combination of orbital residuals including also LAGEOS II, should further raise the precision of the measurement. As a secondary outcome of the proposed experiment, with the so obtained value of \ppn and with \et=4\beta-\gamma-3 from Lunar Laser Ranging it could be possible to obtain an estimate of the PPN parameters $\gamma$ and $\beta$ at the $10^{-2}-10^{-3}$ level.Comment: LaTex2e, 14 pages, no figures, 2 tables. To appear in Classical and Quantum Gravit

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 critical approach to the concept of a polar, low-altitude LARES satellite

According to very recent developments of the LARES mission, which would be devoted to the measurement of the general relativistic Lense--Thirring effect in the gravitational field of the Earth with Satellite Laser Ranging, it seems that the LARES satellite might be finally launched in a polar, low--altitude orbit by means of a relatively low--cost rocket. The observable would be the node only. In this letter we critically analyze this scenario.Comment: LaTex2e, 11 pages, 4 figures, 1 table. Accepted for publication in Classical and Quantum Gravit

LARES/WEBER-SAT and the equivalence principle

It has often been claimed that the proposed Earth artificial satellite LARES/WEBER-SAT-whose primary goal is, in fact, the measurement of the general relativistic Lense-Thirring effect at a some percent level-would allow to greatly improve, among (many) other things, the present-day (10^-13) level of accuracy in testing the equivalence principle as well. Recent claims point towards even two orders of magnitude better, i.e. 10^-15. In this note we show that such a goal is, in fact, unattainable by many orders of magnitude being, instead, the achievable level of the order of 10^-9.Comment: LaTex, 4 pages, no figures, no tables, 26 references. Proofs corrections included. To appear in EPL (Europhysics Letters

Gravitomagnetism in the Kerr-Newman-Taub-NUT spacetime

We study the motion of test particles and electromagnetic waves in the Kerr-Newman-Taub-NUT spacetime in order to elucidate some of the effects associated with the gravitomagnetic monopole moment of the source. In particular, we determine in the linear approximation the contribution of this monopole to the gravitational time delay and the rotation of the plane of the polarization of electromagnetic waves. Moreover, we consider "spherical" orbits of uncharged test particles in the Kerr-Taub-NUT spacetime and discuss the modification of the Wilkins orbits due to the presence of the gravitomagnetic monopole.Comment: 12 pages LaTeX iopart style, uses PicTex for 1 Figur

On the possibility of measuring relativistic gravitational effects with a LAGEOS-LAGEOS II-OPTIS-mission

In this paper we wish to preliminary investigate if it would be possible to use the orbital data from the proposed OPTIS mission together with those from the existing geodetic passive SLR LAGEOS and LAGEOS II satellites in order to perform precise measurements of some general relativistic gravitoelectromagnetic effects, with particular emphasis on the Lense-Thirring effect.Comment: Abridged version. 16 pages, no figures, 1 table. First results from the GGM01C Earth gravity model. GRACE data include

An alternative derivation of the gravitomagnetic clock effect

The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same circular orbit but in opposite directions in orthogonal electric and magnetic fields and show that the particles take different times in describing a full orbit. The expression for the time difference is completely analogous to that of the general relativistic gravitomagnetic clock effect in the weak-field and slow-motion approximation. The latter is obtained by considering the gravitomagnetic force as a small classical non-central perturbation of the main central Newtonian monopole force. A general expression for the clock effect is given for a spherical orbit with an arbitrary inclination angle. This formula differs from the result of the general relativistic calculations by terms of order c^{-4}.Comment: LaTex2e, 11 pages, 1 figure, IOP macros. Submitted to Classical and Quantum Gravit

Spinning test particles and clock effect in Schwarzschild spacetime

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson-Papapetrou equations of motion we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ are not parallel four-vectors. These orbits are shown to exist because the spin induced tidal forces provide the required acceleration no matter what supplementary condition we select. Of course, in the limit of a small spin the particle's orbit is close of being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting both spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum gravity, 200

Quantum statistical properties of the radiation field in a cavity with a movable mirror

A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve in principle as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standard quantum limit. We also study the effect of the nonlinear interaction between the moving mirror and the radiation pressure on the quadrature fluctuations of the initially coherent cavity field.Comment: REVTeX, 9 pages, 5 figures. More info on http://www.ligo.caltech.edu/~cbrif/science.htm

An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging

We deal with the attempts to measure the Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES spacecraft.The first issue addressed here is: are the so far published evaluations of the systematic uncertainty induced by the bad knowledge of the even zonal harmonic coefficients J_L of the multipolar expansion of the Earth's geopotential reliable and realistic? Our answer is negative. Indeed, if the differences Delta J_L among the even zonals estimated in different Earth's gravity field global solutions from the dedicated GRACE mission are assumed for the uncertainties delta J_L instead of using their covariance sigmas sigma_JL, it turns out that the systematic uncertainty \delta\mu in the Lense-Thirring test with the nodes Omega of LAGEOS and LAGEOS II may be up to 3 to 4 times larger than in the evaluations so far published ($5-10$) based on the use of the sigmas of one model at a time separately. The second issue consists of the possibility of using a different approach in extracting the relativistic signature of interest from the LAGEOS-type data. The third issue is the possibility of reaching a realistic total accuracy of 1% with LAGEOS, LAGEOS II and LARES, which should be launched in November 2009 with a VEGA rocket. While LAGEOS and LAGEOS II fly at altitudes of about 6000 km, LARES will be likely 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 has been evaluated with the standard Kaula's approach up to degree L=60 by using Delta J_L and sigma_JL; it turns out that it may be as large as some tens percent.Comment: LaTex, 19 pages, 1 figure, 12 tables. Invited and refereed contribution to The ISSI Workshop, 6-10 October 2008, on The Nature of Gravity Confronting Theory and Experiment in Space To appear in Space Science Review