Searcharxiv⌕ Search

arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

At least 253 records · Page 14Linked to original sources
arXiv2005

The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense-Thirring effect with a new Earth's artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a=12270 km of the existing LAGEOS and inclination i=70 deg) by inserting the new spacecraft in a relatively low, and cheaper, orbit (a=7500-8000 km, i\sim 70 deg) and suitably combining its node Omega with those of LAGEOS and LAGEOS II in order to cancel out the first even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J_2, J_4 along with their temporal variations. The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to \sim 1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K_1 tidal perturbation, would amount to \sim 10^2 days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.

gr-qc↗
arXiv2005

On the possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test body in a Solar System scenario

The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect it for Mercury at a precision level of 10^-4. This level is mainly set by the unavoidable systematic errors due to the mismodelling in the Keplerian period which could not be reduced by accumulating a large number of orbital revolutions. Future missions like Messenger and BepiColombo should allow to improve it by increasing our knowledge of the Mercury's orbital parameters. The observational accuracy is estimated to be 10^-4 from the knowledge of the International Celestial Reference Frame (ICRF) axes. It could be improved by observing as many planetary transits as possible. It is not possible to measure such an effect in the gravitational field of the Earth by analyzing the motion of artificial satellites or the Moon because of the unavoidable systematic errors related to the uncertainties in the Keplerian periods. In the case of some recently discovered exoplanets the problems come from the observational errors which are larger than the relativistic effect.

gr-qc↗
arXiv2004

How to reach a few percent level in determining the Lense-Thirring effect?

In this paper we discuss and compare a node-only LAGEOS-LAGEOS II combination and a node-only LAGEOS-LAGEOS II-Ajisai-Jason1 combination for the determination of the Lense-Thirring effect. The new combined EIGEN-CG01C Earth gravity model has been adopted. The second combination cancels the first three even zonal harmonics along with their secular variations but introduces the non-gravitational perturbations of Jason1. The first combination is less sensitive to the non-conservative forces but is sensitive to the secular variations of the uncancelled even zonal harmonics of low degree J4 and J6 whose impact grows linearly in time.

gr-qc↗
arXiv2004

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$π$ 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.

gr-qc↗
arXiv2004

Some comments about a recent paper on the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the laser-ranged LAGEOS and LAGEOS II satellites

In this brief note some comments about the observable used in a recently published paper on the measurement of the general relativistic Lense-Thirring in the gravitational field of the Earth are presented. It turns out that, among other things, the authors might have yielded an optimistic evaluation of the error budget because of an underestimation of the impact of the secular variations of the even zonal harmonics of the geopotential. More realistic evaluations point towards a 15-45% error at 1-3sigma level, respectively.

gr-qc↗
arXiv2004

On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging

In this paper we first calculate the post-Newtonian gravitoelectric secular rate of the mean anomaly of a test particle freely orbiting a spherically symmetric central mass. Then, we propose a novel approach to suitably combine the presently available planetary ranging data to Mercury, Venus and Mars in order to determine, simultaneously and independently of each other, the Sun's quadrupole mass moment J_2 and the secular advances of the perihelion and the mean anomaly. This would also allow to obtain the PPN parameters gamma and beta independently. We propose to analyze the time series of three linear combinations of the experimental residuals of the rates of the nodes, the longitudes of perihelia and mean anomalies of Mercury, Venus and Mars built up in order to absorb the secular precessions induced by the solar oblateness and the post-Newtonian gravitoelectric forces. The values of the three investigated parameters can be obtained by fitting the expected linear trends with straight lines, determining their slopes in arcseconds per century and suitably normalizing them. According to the present-day EPM2000 ephemerides accuracy, the obtainable precision would be of the order of 10^-4-10^-5 for the PPN parameters and, more interestingly, of 10^-9 for J_2. The future BepiColombo mission should improve the Mercury's orbit by one order of magnitude.

gr-qc↗
arXiv2004

Is it possible to measure the Lense-Thirring effect on the orbits of the planets in the gravitational field of the Sun?

Here we explore a novel approach in order to try to measure the post-Newtonian 1/c^2 Lense-Thirring secular effect induced by the gravitomagnetic field of the Sun on the planetary orbital motion. Due to the relative smallness of the solar angular momentum J and the large values of the planetary semimajor axes a, the gravitomagnetic precessions, which affect the nodes Omega and the perihelia omega and are proportional to J/a^3, are of the order of 10^-3 arcseconds per century only for, e.g., Mercury. This value lies just at the edge of the present-day observational sensitivity in reconstructing the planetary orbits, although future missions to Mercury like Messenger and BepiColombo could allow to increase it. The major problems come from the main sources of systematic errors. They are the aliasing classical precessions induced by the multipolar expansion of the Sun's gravitational potential and the classical secular N-body precessions which are of the same order of magnitude or much larger than the Lense-Thirring precessions of interest. This definitely rules out the possibility of analyzing only one orbital element of, e.g., Mercury. In order to circumvent these problems, we propose a suitable linear combination of the orbital residuals of the nodes of Mercury, Venus and Mars which is, by construction, independent of such classical secular precessions. A 1-sigma reasonable estimate of the obtainable accuracy yields a 36% error. Since the major role in the proposed combination is played by the Mercury's node, it could happen that the new, more accurate ephemerides available in future thanks to the Messenger and BepiColombo missions will offer an opportunity to improve the present unfavorable situation.

gr-qc↗
arXiv2004

Towards a few-percent measurement of the Lense-Thirring effect with the LAGEOS and LAGEOS II satellites?

Up to now attempts to measure the general relativistic Lense-Thirring effect in the gravitational field of Earth have been performed by analyzing a suitable J_2-J_4-free combination of the nodes Omega of LAGEOS and LAGEOS II and the perigee omega of LAGEOS II with the Satellite Laser Ranging technique. The claimed total accuracy is of the order of 20-30%, but, according to some scientists, it could be an optimistic estimate. The main sources of systematic errors are the mismodelling in the even zonal harmonic coefficients J_l of the multipolar expansion of the gravitational potential of Earth and the non-gravitational perturbations which plague especially the perigee of LAGEOS II and whose impact on the proposed measurement is difficult to be reliably assessed. Here we present some evaluations of the accuracy which could be reached with a different J_2-free observable built up with the nodes of LAGEOS and LAGEOS II in view of the new preliminary 2nd-generation Earth gravity models from the GRACE mission. According to the GRACE-only based EIGEN-GRACE02S solution, a 1-sigma upper bound of 4% for the systematic error due to the even zonal harmonics can be obtained. In the near future it could be possible to perform a reliable measurement of the Lense-Thirring effect by means of the existing LAGEOS satellites with an accuracy of a few percent by adopting a time span of a few years. The choice of a not too long observational temporal interval would be helpful in reducing the impact of the secular variations of the uncancelled even zonal harmonics dot J_4 and dot J_6 whose impact is difficult to be reliably evaluated.

gr-qc↗
arXiv2004

On the impossibility of using the longitude of the ascending node of GP-B for measuring the Lense-Thirring effect

The possibility of analyzing the node Omega of the GP-B satellite in order to measure also the Lense-Thirring effect on its orbit is examined. This feature is induced by the general relativistic gravitomagnetic component of the Earth gravitational field. The GP-B mission has been launched in April 2004 and is aimed mainly to the measurement of the gravitomagnetic precession of four gyroscopes carried onboard at a claimed accuracy of 1% or better. The aliasing effect of the solid Earth and ocean components of the solar K_1 tidal perturbations would make the measurement of the Lense-Thirring effect on the orbit unfeasible. Indeed, the science period of the GP-B mission amounts to almost one year. During this time span the Lense-Thirring shift on the GP-B node would be 164 milliarcseconds (mas), while the tidal perturbations on its node would have a period of the order of 10^3 years and amplitudes of the order of 10^5 mas.

gr-qc↗
arXiv2004

New ways in testing post-Newtonian gravity in the Solar System scenario from planetary motion analysis

Here we explore the possibility of extending to the Solar System scenario the combined residual approach employed for the deterination of the Lense-Thirring effect in the Earth-LAGEOS satellites system. After calculating the secular gravitoelectric advance of the mean anomaly, we propose several linear combinations of the residuals of the nodes, the perihelia and the mean anomalies of some inner planets in order to measure the gravitoelectric advance, the Lense-Thirring effect and the solar quadrupole mass moment. The obtainable accuracies are comparable to those of new complex and expensive missions involving the launch of one or more spacecrafts. They are 10^-4 for the PPN parameter beta, 10^-5 for gamma, 10^-9 for the solar J2, 20-30% for the Lense-Thirring effect. In the case of the solar gravitomagnetic field, it would be the first attempt to measure its effect on the planetary motions. However, the improvements in the ephemerides of Mercury thanks to the Messenger and BepiColombo missions will map into an increasing accuracy of the proposed tests.

gr-qc↗
arXiv2004

An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity

In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear. No inertial motion steps are considered. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) is seen moving is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We deal with the following questions: I) What is the effect of the finite force acting on (2) on the proper time intervals measured by the two clocks when they reunite? Does a differential aging between the two clocks occur, as it happens when inertial motion and infinite values of the accelerating force is considered? The Special Theory of Relativity is used in order to describe the hyperbolic motion of (2) in the frame I II) Is this effect an absolute one, i.e. does the accelerated observer A comoving with (2) obtain the same results as that in I, both qualitatively and quantitatively, as it is expected? We use the General Theory of Relativity in order to answer this question.

physics.class-ph↗
arXiv2004

On the Clock Paradox in the case of circular motion of the moving clock

In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the proper time interval measured by a given clock is the same both in I and in A. II) From a quantitative point of view, the magnitude of the differential aging between (1) and (2) does depend on the kind of rotational motion performed by A. Indeed, if it is uniform there is no any tangential force in the direction of motion of (2) but only normal to it. In this case, the proper time interval reckoned by (2) does depend only on its constant velocity v=romega. On the contrary, if the rotational motion is uniformly accelerated, i.e. a constant force acts tangentially along the direction of motion, the proper time intervals $do depend$ on the angular acceleration alpha. III) Finally, in regard to the sign of the aging, the moving clock (2) measures always a $shorter$ interval of proper time with respect to (1).

physics.class-ph↗
arXiv2004

Some comments on a recently derived approximated solution of the Einstein equations for a spinning body with negligible mass

Recently, an approximated solution of the Einstein equations for a rotating body whose mass effects are negligible with respect to the rotational ones has been derived by Tartaglia. At first sight, it seems to be interesting because both external and internal metric tensors have been consistently found, together an appropriate source tensor; moreover, it may suggest possible experimental checks since the conditions of validity of the considered metric are well satisfied at Earth laboratory scales. However, it should be pointed out that reasonable doubts exist if it is physically meaningful because it is not clear if the source tensor related to the adopted metric can be realized by any real extended body. Here we derive the geodesic equations of the metric and analyze the allowed motions in order to disclose possible unphysical features which may help in shedding further light on the real nature of such approximated solution of the Einstein equations.

gr-qc↗
arXiv2004

The impact of the new Earth gravity models on the measurement of the Lense-Thirring effect

In this paper we use, in a preliminary way, the recently released EIGEN2 Earth gravity model, which is based on six months of data of CHAMP only, in order to reassess the systematic error due to the mismodelling in the even zonal harmonics of geopotential in the LAGEOS-LAGEOS II Lense-Thirring experiment involving the nodes of both the LAGEOS satellites and the perigee of LAGEOS II. The first results from the GGM01C Earth gravity model including the first GRACE data are very promising.

gr-qc↗
arXiv2004

On the impossibility of measuring a galvano-gravitomagnetic effect with current carrying semiconductors in a space-based experiment

In this paper we investigate the feasibility of a recently proposed space-based experiment aimed to the detection of the effect of the Earth gravitomagnetic field in spaceborne semiconductors carrying radial electric currents and following identical circular equatorial orbits along opposite directions. It turns out that the deviations from this idealized situation due to the unavoidable orbital injection errors would make impossible the measurement of the gravitomagnetic voltage of interest.

gr-qc↗
arXiv2004

The new Earth gravity models and the measurement of the Lense-Thirring effect

We examine how the new forthcoming Earth gravity models from the CHAMP and, especially, GRACE missions could improve the measurement of the general relativistic Lense-Thirring effect according to the various kinds of observables which could be adopted. In a very preliminary way, we use the recently released EIGEN2 CHAMP-only and GRACE01S GRACE-only Earth gravity models in order to assess the impact of the mismodelling in the even zonal harmonic coefficients of geopotential which represents one of the major sources of systematic errors in this kind of measurement.

gr-qc↗