arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

285 records · Page 16Linked to original sources

arXiv2002

Recent Improvements in Testing General Relativity with Satellite Laser Ranging

In this work some aspects of the detection of certain general relativistic effects in the weak gravitational field of the Earth via laser-ranged data to some existing or proposed geodetic satellites are examined. The focus is on the Lense-Thirring drag of the orbit of a test body, the gravitomagnetic clock effect and the gravitoelectric perigee shift. The impact of some sources of systematic errors is investigated. An experiment whose goal is the measurement of the PPN parameters beta and gamma in the terrestrial field with LAGEOS satellites at a level of 10^(-3)is presented. A modified version of the proposed LARES mission is examined.

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arXiv2002

Constraints to a Yukawa gravitational potential from laser data to LAGEOS satellites

In this paper we investigate the possibility of constraining the hypothesis of a fifth force at the length scale of two Earth's radii by investigating the effects of a Yukawa gravitational potential on the orbits of the laser--ranged LAGEOS satellites. The existing constraints on the Yukawa coupling $α$, obtained by fitting the LAGEOS orbit, are of the order of | α| < 10^{-5}-10^{-8} for distances of the order of 10^9 cm. Here we show that with a suitable combination of the orbital residuals of the perigee ωof LAGEOS II and the nodes Ωof LAGEOS II and LAGEOS it should be possible to constrain αat a level of 4 X 10^{-12} or less. Various sources of systematic errors are accounted for, as well. Their total impact amounts to 1 X 10^{-11} during an observational time span of 5 years. In the near future, when the new data on the terrestrial gravitational field will be available from the CHAMP and GRACE missions, these limits will be further improved. The use of the proposed LARES laser--ranged satellite would yield an experimental accuracy in constraining αof the order of 1 X 10^{-12}.

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arXiv2002

Is it possible to test directly General Relativity in the gravitational field of the Moon?

In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the post-Newtonian Lense-Thirring gravitomagnetic and the Einstein's gravitoelectric effects on the satellites orbits are calculated and compared to the present-day orbit accuracy of lunar missions. It turns out that for SELENE's Main Orbiter, at present, the gravitoelectric periselenium shift, which is the largest general relativistic effect, is 1 or 2 orders of magnitude smaller than the experimental sensitivity. The systematic error induced by the mismodelled classical periselenium precession due to the first even zonal harmonic J2 of the Moon's non-spherical gravitational potential is 3 orders of magnitude larger than the general relativistic gravitoelectric precession. The estimates of this work could be used for future lunar missions having as their goals relativistic measurements as well.

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arXiv2001

A Gravitomagnetic Effect on the Orbit of a Test Body due to the Earth's Variable Angular Momentum

The well known general relativistic Lense-Thirring drag of the orbit of a test particle in the stationary field of a central slowly rotating body is generated, in the weak-field and slow-motion approximation of General Relativity, by a gravitomagnetic Lorentz-like acceleration in the equations of motion of the test particle. In it the gravitomagnetic field is due to the central body's angular momentum supposed to be constant. In the context of the gravitational analogue of the Larmor theorem, such acceleration looks like a Coriolis inertial term in an accelerated frame. In this paper the effect of the variation in time of the central body's angular momentum on the orbit of a test mass is considered. It can be shown that it is analogue to the inertial acceleration due to the time derivative of the angular velocity vector of an accelerated frame. The possibility of detecting such effect in the gravitational field of the Earth with LAGEOS-like satellites is investigated. It turns out that the orbital effects are far too small to be measured.

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arXiv2001

Testing General Relativity with LAGEOS, LAGEOS II and Ajisai laser-ranged satellites

The accuracy reached in the past few years by Satellite Laser Ranging (SLR) allows for measuring even tiny features of the Earth's gravitational field predicted by Einstein's General Relativity by means of artificial satellites. The gravitomagnetic dragging of the orbit of a test body is currently under measurement by analyzing a suitable combination of the orbital residuals of LAGEOS and LAGEOS II. The lower bound of the error in this experiment amount to 12.92%. It is due to the mismodeling in the even zonal harmonics of the geopotential which are the most important sources of systematic error. A similar approach could be used in order to measure the relativistic gravitoelectric pericenter shift in the field of the Earth with a lower bound of the systematic relative error of 0.6% due to the even zonal harmonics as well. The inclusion of the ranging data to the Japanese passive geodetic satellite Ajisai would improve such limits to 10.78% and 0.08% respectively and would allow to improve the accuracy in the determination of the PPN parameters beta and gamma.

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arXiv2001

An alternative derivation of the Lense-Thirring drag on the orbit of a test body

A new strategy in deriving the Lense-Thirring effect, in the weak field and slow motion approximation of general relativity, on the orbital elements of a test body in the field of different central rotating sources exhibiting axial symmetry is presented. The approach adopted in the present work, in the case of a perfectly spherical source, leads for all the Keplerian orbital elements of the freely falling particle to the well known Lense-Thirring equations. The case of a central nonspherical body is also worked out.

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arXiv2001

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}.

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arXiv2001

On the gravitomagnetic clock effect

General relativity predicts that two freely counter-revolving test particles in the exterior field of a central rotating mass take different periods of time to complete the same full orbit; this time difference leads to the gravitomagnetic clock effect. The effect has been derived for circular equatorial orbits; moreover, it has been extended via azimuthal closure to spherical orbits around a slowly rotating mass. In this work, a general formula is derived for the main gravitomagnetic clock effect in the case of slow motion along an arbitrary {\it elliptical} orbit in the exterior field of a slowly rotating mass. Some of the implications of this result are briefly discussed.

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arXiv2001

Testing the gravitomagnetic clock effect on the Earth with neutron interferometry

The general relativistic gravitomagnetic clock effect consists in the fact that two point particles orbiting a central spinning object along identical, circular equatorial geodesic paths, but in opposite directions, exhibit a time difference in describing a full revolution. It turns out that the particle rotating in the same sense of the central body is slower than the particle rotating in the opposite sense. In this paper it is proposed to measure such effect in an Earth laboratory experiment involving interferometry of slow neutrons. With a sphere of 2.5 cm radius and spinning at 4.3 x 10^4 rad/s as central source, and using neutrons with wavelength of 1 Angstrom it should be possible to obtain, for a given sense of rotation of the central source, a phase shift of 0.18 rad, well within the experimental sensitivity. By reversing the sense of rotation of the central body it should be possible to obtain a 0.06 fringe shift.

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arXiv2001

Satellite gravitational orbital perturbations and the gravitomagnetic clock effect

In order to detect the gravitomagnetic clock effect by means of two counter-orbiting satellites placed on identical equatorial and circular orbits around the Earth with radius 7000 km their radial and azimuthal positions must be known with an accuracy of delta r =10^{-1} mm and delta phi =10^{-2} mas per revolution. In this work we investigate if the radial and azimuthal perturbations induced by the dynamical and static parts of the Earth' s gravitational field meet this requirements. While the radial direction is affected only by harmonic perturbations with periods up to some tens of days, the azimuthal location is perturbed by a secular drift and very long period effects.It results that the present level of accuracy in the knowledge both of the Earth solid and ocean tides, and of the static part of the geopotential does not allow an easy detection of the gravitomagnetic clock effect, at least by using short arcs only.

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arXiv2001

Satellite non-gravitational orbital perturbations and the detection of the gravitomagnetic clock effect

The general relativistic gravitomagnetic clock effect consists in the fact that two massive test bodies orbiting a central spinning mass in its equatorial plane along two identical circular trajectories, but in opposite directions, take different times in describing a full revolution with respect to an asymptotically inertial observer. In the field of the Earth such time shift amounts to 10^{-7} s. Detecting it by means of a space based mission with artificial satellites is a very demanding task because there are severe constraints on the precision with which the radial and azimuthal positions of a satellite must be known: delta r= 10^{-2} cm and delta phi= 10^{-2} milliarcseconds per revolution. In this paper we assess if the systematic errors induced by various non-gravitational perturbations allow to meet such stringent requirements. A couple of identical, passive laser-ranged satellites of LAGEOS type with their spins aligned with the Earth's one is considered. It turns out that all the non vanishing non-gravitational perturbations induce systematic errors in r and phi within the required constraints for a reasonable assumption of the mismodeling in some satellite's and Earth's parameters and/or by using dense satellites with small area-to-mass ratio. However, the error in the Earth's GM is by far the largest source of uncertainty in the azimuthal location which is affected at a level of 1.2 milliarcseconds per revolution.

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arXiv2001

Earth tides and Lense-Thirring effect

The general relativistic Lense-Thirring effect can be measured by inspecting a suitable combination of the orbital residuals of the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II. The solid and ocean Earth tides affect the recovery of the parameter by means of which the gravitomagnetic force is accounted for in the combined residuals. Thus an extensive analysis of the perturbations induced on these orbital elements by the solid and ocean Earth tides is carried out. It involves the l=2 terms for the solid tides and the l=2,3,4 terms for the ocean tides. The perigee of LAGEOS II turns out to be very sensitive to the l=3 part of the ocean tidal spectrum, contrary to the nodes of LAGEOS and LAGEOS II. The uncertainty in the solid tidal perturbations, mainly due to the Love number k2, ranges from 0.4% to 1.5%, while the ocean tides are uncertain at 5%-15% level. The obtained results are used in order to check in a preliminary way which tidal constituents the Lense-Thirring shift is sensitive to. In particular it is tested if the semisecular 18.6-year zonal tide really does not affect the combined residuals. It turns out that, if modeled at the level of accuracy worked out in the paper, the l=2,4 m=0 and also, to a lesser extent, the l=3 m=0 tidal perturbations cancel out.

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arXiv2001

The impact of tidal errors on the determination of the Lense-Thirring effect from satellite laser ranging

The general relativistic Lense-Thirring effect can be detected by means of a suitable combination of orbital residuals of the laser-ranged LAGEOS and LAGEOS II satellites. While this observable is not affected by the orbital perturbation induced by the zonal Earth solid and ocean tides, it is sensitive to those generated by the tesseral and sectorial tides. The assessment of their influence on the measurement of the parameter mu, with which the gravitomagnetic effect is accounted for, is the goal of this paper. After simulating the combined residual curve by calculating accurately the mismodeling of the more effective tidal perturbations, it has been found that, while the solid tides affect the recovery of mu at a level always well below 1%, for the ocean tides and the other long-period signals Delta mu depends strongly on the observational period and the noise level: Delta mu(tides) amounts to almost 2% after 7 years. The aliasing effect of K1 l=3 p=1 tide and SRP(4241) solar radiation pressure harmonic, with periods longer than 4 years, on the perigee of LAGEOS II yield to a maximum systematic uncertainty on $\m_{LT}$ of less than 4% over different observational periods. The zonal 18.6-year tide does not affect the combined residuals.

gr-qc↗

arXiv2001

Tidal satellite perturbations and the Lense-Thirring effect

The tiny general relativistic Lense-Thirring effect can be measured by means of a suitable combination of the orbital residuals of the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II. This observable is affected, among other factors, by the Earth' s solid and ocean tides. They induce long-period orbital perturbations that, over observational periods of few years, may alias the detection of the gravitomagnetic secular trend of interest. In this paper we calculate explicitly the most relevant tidal perturbations acting upon LAGEOSs and assess their influence on the detection of the Lense-Thirring effect. The present day level of knowledge of the solid and ocean tides allow us to conclude that their influence on it ranges from almost 4% over 4 years to less than 2% over 7 years.

gr-qc↗

arXiv2000

Solid and ocean tides and the detection of some gravitomagnetic effects

The detection of some tiny gravitomagnetic effects in the field of the Earth by means of artificial satellites is a very demanding task because of the various other perturbing forces of gravitational and non-gravitational origin acting upon them. Among the gravitational perturbations a relevant role is played by the Earth solid and ocean tides. In this communication I outline their effects on the detection of the Lense-Thirring drag of the orbits of LAGEOS and LAGEOS II, currently analyzed, and the proposed GP-C experiment devoted to the measurement of the clock effect.

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