arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

At least 55 records · Page 3Linked to original sources

arXiv2021

On the 2PN pericentre precession in the general theory of relativity and the recently discovered fast orbiting S-stars in Sgr A$^\ast$

Recently, the secular pericentre precession was analytically computed to the second post-Newtonian (2PN) order by the present author with the Gauss equations in terms of the osculating Keplerian orbital elements in order to obtain closer contact with the observations in astronomical and astrophysical scenarios of potential interest. A discrepancy with previous results by other authors was found. Moreover, some of such findings by the same authors were deemed as mutually inconsistent. In this paper, it is demonstrated that, in fact, two calculational errors plagued the most recent calculation by the present author. They are explicitly disclosed and corrected. As a result, all the examined approaches mutually agree yielding the same analytical expression for the total 2PN pericentre precession once the appropriate conversions from the adopted parameterizations are made. It is also shown that, in future, it may become measurable, at least in principle, for some of the recently discovered short-period S-stars in Sgr A$^\ast$ like S62 and S4714.

gr-qc↗

arXiv2020

Is there still something left that Gravity Probe B can measure?

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment $J_2$ of its primary without any restriction on either the gyro's orbital configuration and the orientation in space of the symmetry axis $\boldsymbol{\hat{k}}$ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin's declination $δ$ which may be as large as $\lesssim 30-40\,\mathrm{milliarcseconds\,per\,year\,(\mathrm{mas\,yr}^{-1}})$, depending on the initial orbital phase $f_0$. Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin's declination rate amounts to $σ^\mathrm{GP-B}_{\dotδ}=18.3\,\mathrm{mas\,yr}^{-1}$. We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary's angular momentum $\boldsymbol J$. In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.

gr-qc↗

arXiv2020

Effects of the general relativistic spin precessions on the habitability of rogue planets orbiting supermassive black holes

Recently, the possibility that several starless telluric planets may form around supermassive black holes (SMBHs) and receive an energy input from the hole's accretion disk, which, under certain plausible circumstances, may make them habitable in a terrestrial sense, has gained increasing attention. In particular, an observer on a planet orbiting at distance $r=100$ Schwarzschild radii from a maximally rotating Kerr SMBH with mass $M_\bullet = 1\times 10^8\,M_\odot$ in a plane slightly outside the equator of the latter, would see the gravitationally lensed accretion disk the same size as the Sun as seen from the Earth. Moreover, the accretion rate might be imagined to be set in such a way that the apparent disk's temperature would be identical to that of the solar surface. We demonstrate that the post-Newtonian (pN) de Sitter and Lense--Thirring precessions of the spin axis of such a world would rapidly change, among other things, its tilt, $\varepsilon$, to its orbital plane by tens to hundreds of degrees over a time span of, say, just $Δt =400\,\mathrm{yr}$, strongly depending on the obliquity $η_\bullet$ of the SMBH's spin to the orbital plane. Thus, such relativistic features would have per se a relevant impact on the long-term habitability of the considered planet. Other scenarios are examined as well.

astro-ph.EP↗

arXiv2020

Probing a $r^{-n}$ modification of the Newtonian potential with Exoplanets

The growing availability of increasingly accurate data on transiting exoplanets suggests the possibility of using these systems as possible testbeds for modified models of gravity. In particular, we suggest that the post-Keplerian (pK) dynamical effects from the perturbations of the Newtonian potential falling off as the square or the cube of the distance from the mass of the host star break the degeneracy of the anomalistic, draconitic and sidereal periods. The latter are characteristic temporal intervals in the motion of a binary system, and all coincide in the purely Keplerian case. We work out their analytical expressions in presence of the aforementioned perturbations to yield preliminary insights on the potential of the method proposed for constraining the modified models of gravity considered. A comparison with other results existing in the literature is made.

gr-qc↗

arXiv2020

A comment on "Lense-Thirring frame dragging induced by a fast-rotating white dwarf in a binary pulsar system" by V. Venkatraman Krishnan et al

We comment on a recent study reporting evidence for the general relativistic Lense-Thirring secular precession of the inclination $I$ of the orbital plane to the plane of the sky of the tight binary system PSR J1141-6545 made of a white dwarf and an emitting radiopulsar of comparable masses. The quadrupole mass moment $Q_2^\mathrm{c}$ and the angular momentum ${\boldsymbol S}^\mathrm{c}$ of the white dwarf cause the detectable effects on $I$ with respect to the present-day accuracy in the pulsar's timing. The history-dependent and model-dependent assumptions to be made on $Q_2^\mathrm{c}$ and ${\boldsymbol S}^\mathrm{c}$, required even just to calculate the analytical expressions for the resulting post-Keplerian precessions, may be deemed as too wide in order to claim a successful test of the Einsteinian gravitomagnetic effect. Moreover, depending on how $Q_2^\mathrm{c}$ is calculated, the competing quadrupole-induced rate of change, which is a major source of systematic uncertainty, may be up to $\lesssim 30-50\%$ of the Lense-Thirring effect for most of the allowed values in the 3D parameter space spanned by the white dwarf's spin period $P_\mathrm{s}$, and the polar angles $i_\mathrm{c},\,ζ_\mathrm{c}$ of its spin axis. The possible use of the longitude of periastron $\dot\varpi$ is investigated as well. It turns out that a measurement of its secular precession, caused, among other things, also by $Q_2^\mathrm{c},\,{\boldsymbol{S}}^\mathrm{c}$, could help in further restricting the permitted regions in the white dwarf's parameter space.

gr-qc↗

arXiv2020

Revisiting the 2PN pericentre precession in view of possible future measurements of it

At the second post-Newtonian (2PN) order, the secular pericentre precession $\dotω^\mathrm{2PN}$ of either a full two-body system made of well detached non-rotating monopole masses of comparable size and a restricted two-body system composed of a point particle orbiting a fixed central mass have been analytically computed so far with a variety of approaches. We offer our contribution by analytically computing $\dotω^\mathrm{2PN}$ in a perturbative way with the method of variation of elliptical elements by explicitly calculating both the direct contribution due to the 2PN acceleration ${\boldsymbol A}^\mathrm{2PN}$, and also an indirect part arising from the self-interaction of the 1PN acceleration ${\boldsymbol A}^\mathrm{1PN}$ in the orbital average accounting for the instantaneous shifts induced by ${\boldsymbol A}^\mathrm{1PN}$ itself. Explicit formulas are straightforwardly obtained for both the point particle and full two-body cases without recurring to simplifying assumptions on the eccentricity $e$. Two different numerical integrations of the equations of motion confirm our analytical results for both the direct and indirect precessions. The values of the resulting effects for Mercury and some binary pulsars are confronted with the present-day level of experimental accuracies in measuring/constraining their pericentre precessions. The supermassive binary black hole in the BL Lac object OJ 287 is considered as well. A comparison with some of the results appeared in the literature is made.

gr-qc↗

arXiv2020

New general relativistic contributions to Mercury's orbital elements and their measurability

We numerically and analytically work out the first-order post-Newtonian (1pN) orbital effects induced on the semimajor axis $a$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $Ω$, the longitude of perihelion $\varpi$, and the mean longitude at epoch $ε$ of a test particle orbiting its primary, assumed static and spherically symmetric, by a distant massive third body X. For Mercury, the rates of change of the linear trends found are $\dot I_\mathrm{1pN}^\mathrm{X} = -4.3\,\mathrm{microarcseconds\,per\,century}\,\left(μ\mathrm{as\,cty}^{-1}\right)$, $\dotΩ_\mathrm{1pN}^\mathrm{X} = 18.2\,μ\mathrm{as\,cty}^{-1}$, $\dot\varpi_\mathrm{1pN}^\mathrm{X} = 30.4\,μ\mathrm{as\,cty}^{-1}$, $\dotε_\mathrm{1pN}^\mathrm{X} = 271.4\,μ\mathrm{as\,cty}^{-1}$, respectively. Such values, which are due to the added actions of the other planets from Venus to Saturn, are essentially at the same level of, or larger by one order of magnitude than, the latest formal errors in the Hermean orbital precessions calculated with the EPM2017 ephemerides. The perihelion precession $\dot\varpi_\mathrm{1pN}^\mathrm{X}$ turns out to be smaller than some values recently appeared in the literature in view of a possible measurement with the ongoing BepiColombo mission. Linear combinations of the supplementary advances of the Keplerian orbital elements for several planets, if determined experimentally by the astronomers, could be set up in order to disentangle the 1pN $N$-body effects of interest from the competing larger precessions like those due to the Sun's quadrupole moment $J_2$ and angular momentum $\boldsymbol{S}$.

gr-qc↗

arXiv2020

What Would Happen If We Were About 1 pc Away from a Supermassive Black Hole?

We consider a hypothetical planet with the same mass $m$, radius $R$, angular momentum $\boldsymbol{S}$, oblateness $J_2$, semimajor axis $a$, eccentricity $e$, inclination $I$, and obliquity $\varepsilon$ of the Earth orbiting a main-sequence star with the same mass $M_\star$ and radius $R_\star$ of the Sun at a distance $r_\bullet \simeq 1\,\mathrm{parsec}\,\left(\mathrm{pc}\right)$ from a supermassive black hole in the center of the hosting galaxy with the same mass $M_\bullet$ of, say, $\mathrm{M87}^\ast$. We preliminarily investigate some dynamical consequences of its presence in the neighborhood of such a stellar system on the planet's possibility of sustaining complex life over time. In particular, we obtain general analytic expressions for the long-term rates of change, doubly averaged over both the planetary and the galactocentric orbital periods $P_\mathrm{b}$ and $P_\bullet$, of $e,\,I,\,\varepsilon$, which are the main quantities directly linked to the stellar insolation. We find that, for certain orbital configurations, the planet's perihelion distance $q=a\left(1-e\right)$ may greatly shrink and lead to, in some cases, an impact with the star. $I$ may also notably change, with variations even of the order of tens of degrees. On the other hand, $\varepsilon$ does not seem to be particularly affected, being shifted, at most, by $\simeq 0^\circ.02$ over 1 Myr. Our results strongly depend on the eccentricity $e_\bullet$ of the galactocentric motion.

astro-ph.EP↗

arXiv2019

Are the planetary orbital effects of the Solar dark matter wake detectable?

Recently, a discussion about the effects of the anisotropy in the spatial density of Dark Matter in the Solar neighbourhood due to the motion of the Sun through the Galactic halo on the orbital motion of the solar system's planets and their ability to be effectively constrained by the radiotechnical observations collected by the Cassini spacecraft appeared in the literature. We show that the semilatus rectum $p$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $Ω$, the longitude of perihelion $\varpi$, and the mean anomaly at epoch $η$ of a test particle of a restricted two-body system affected by the gravity of a Dark Matter wake undergo secular rates of change. In the case of Saturn, they are completely negligible, being at the $\simeq 0.1$ millimeter per century and $\simeq 0.05-2$ nanoarcseconds per century level; the current (formal) accuracy level in constraining any anomalous orbital precessions is of the order of $\simeq 0.002-2$ milliarcseconds per century for Saturn. We also numerically simulate the Earth-Saturn range signature $Δρ(t)$ due to the Dark Matter wake over the same time span (2004-2017) covered by the Cassini data record. We find that it is as little as $\simeq 0.1-0.2\,\mathrm{m}$, while the existing range residuals, computed by the astronomers without modeling any Dark Matter wake effect, are at the $\simeq 30\,\mathrm{m}$ level. The local Dark Matter density $\varrho_\mathrm{DM}$ should be larger than the currently accepted value of $\varrho_\mathrm{DM}=0.018\,\mathrm{M}_\odot\,\mathrm{pc}^{-3}$ by a factor of $2.5\times 10^6$ in order to induce a geocentric Kronian range signature so large as to make it discernible in the present-day residuals.

gr-qc↗

arXiv2019

On the mean anomaly and the mean longitude in tests of post-Newtonian gravity

The distinction between the mean anomaly $\mathcal{M}(t)$ and the mean anomaly at epoch $η$, and the mean longitude $l(t)$ and the mean longitude at epoch $ε$ is clarified in the context of a possible use of such orbital elements in post-Keplerian tests of gravity, both Newtonian and post-Newtonian. In particular, the perturbations induced on $\mathcal{M}(t),\,η,\,l(t),\,ε$ by the post-Newtonian Schwarzschild and Lense-Thirring fields, and the classical accelerations due to the atmospheric drag and the oblateness $J_2$ of the central body are calculated for an arbitrary orbital configuration of the test particle and a general orientation of the primary's spin axis $\boldsymbol{\hat{S}}$. They provide us with further observables which could be fruitfully used, e.g., in better characterizing astrophysical binary systems and in more accurate satellite-based tests around major bodies of the Solar System. Some erroneous and misleading claims by Ciufolini and Pavlis appeared in the literature are confuted. In particular, it is shown that there are no net perturbations of the Lense-Thirring acceleration on either the semimajor axis $a$ and the mean motion $n_\mathrm{b}$. Furthermore, the quadratic signatures on $\mathcal{M}(t)$ and $l(t)$ due to certain disturbing non-gravitational accelerations like the atmospheric drag can be effectively disentangled from the post-Newtonian linear trends of interest provided that a sufficiently extended temporal interval for the data analysis is assumed. A possible use of $η$ along with the longitudes of the ascending node $Ω$ in tests of general relativity with the existing LAGEOS and LAGEOS II satellites is suggested.

gr-qc↗

arXiv2019

Classical and general relativistic post-Keplerian effects in binary pulsars hosting fast rotating main sequence stars

We consider a binary system composed of a pulsar and a massive, fast rotating, highly distorted main sequence star as a potential scenario to dynamically put to the test certain post-Keplerian effects of both Newtonian and post-Newtonian nature. We numerically produce time series of the perturbations $Δ\left(δτ\right)$ of the Rømer-like, orbital component of the pulsar's time delay $δτ$ induced over 10 years by the pN gravitoelectric mass monopole, quadrupole, gravitomagnetic spin dipole and octupole accelerations along with the Newtonian quadrupolar one. We do not deal with the various propagation time delays due to the travelling electromagnetic waves. It turns out that, for a Be-type star with $M = 15\ \textrm{M}_\odot$, $R_\textrm{e} = 5.96\ \textrm{R}_\odot$, $ν= 0.203$, $S = 3.41\times 10^{45}\ \textrm{J}\ \textrm{s}$, $J_2 = 1.92\times 10^{-3}$ orbited by a pulsar with an orbital period $P_\textrm{b}\simeq 40-70\ \textrm{d}$, the classical oblateness-driven effects are at the $\lesssim 4-150\ \textrm{s}$ level, while the pN shifts are of the order of $\lesssim 1.5-20\ \textrm{s}\ \left(GMc^{-2}\right)$, $\lesssim 10-40\ \textrm{ms}\ \left(GMR^2_\textrm{e} J_2 c^{-2}\right)$, $\lesssim 0.5 - 6\ \textrm{ms}\ \left(GSc^{-2}\right)$, $\lesssim 5 - 20\ μ\textrm{s}\ \left(GSR^2_\textrm{e} \varepsilon^2 c^{-2}\right)$, depending on their orbital configuration. The root-mean-square (rms) timing residuals $σ_τ$ of almost all the existing non-recycled, non-millisecond pulsars orbiting massive, fast rotating main sequence stars are $\lesssim\textrm{ms}$. Thus, such kind of binaries have the potential to become interesting laboratories to measure, or, at least, constrain, some Newtonian and post-Newtonian key features of the distorted gravitational fields of the fast rotating stars hosted by them [Abridged].

gr-qc↗

arXiv2019

A comment on "Can observations inside the Solar System reveal the gravitational properties of the quantum vacuum?" by D.S. Hajdukovic

The modified gravitational theory by Hajdukovic [arXiv:1210.7421], based on the idea that quantum vacuum contains virtual gravitational dipoles, predicts, among other things, anomalous secular precessions of the planets of the Solar System as large as $\simeq 700-6,000$ milliarceconds per century. We demonstrate that they are ruled out by several orders of magnitude by the existing bounds on any anomalous orbital secular rates obtained with the EPM and INPOP ephemerides.

physics.gen-ph↗

arXiv2019

The post-Newtonian gravitomagnetic spin-octupole moment of an oblate rotating body and its effects on an orbiting test particle; are they measurable in the Solar System?

We analytically work out the orbital effects induced by the gravitomagnetic spin-octupole moment of an extended spheroidal rotating body endowed with angular momentum $\boldsymbol{S}$ and quadrupole mass moment $J_2$. Our results, proportional to $S J_2 c^{-2}$, hold for an arbitrary orientation of the body's symmetry axis $\boldsymbol{\hat{S}}$ and a generic orbital configuration of the test particle. Such effects may be measurable, in principle, with a dedicated spacecraft-based mission to Jupiter. For a moderately eccentric and fast path, the gravitomagnetic precessions of the node and the pericenter of a dedicated orbiter could be as large as $400~\textrm{milliarcseconds~per~year}$ or even $1,600-4,000~\textrm{milliarcseconds~per~year}$ depending on the orientation of its orbital plane in space. Numerical simulations of the Earth-probe range-rate signal confirm such expectations since its magnitude reaches the $\simeq 0.03-0.3~\textrm{millimeter~per~second}$ level after just 1 day. The precision of the current two-way Ka-band Doppler measurements of the spacecraft Juno, presently orbiting Jupiter, amounts to $\simeq 0.003~\textrm{millimeter~per~second}$ after $1,000$ seconds. Also other general relativistic effects could be measurable, including also those proportional to $GMJ_2c^{-2}$, never put to the test so far. Most of the competing Newtonian signals due to the classical multipoles of the planet's gravity field have quite different temporal signatures with respect to the post-Newtonian ones, making, thus, potentially easier disentangling them.

gr-qc↗

arXiv2019

A HERO for general relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios: a fast, 4-hr orbit with high perigee height of $1,047\,\mathrm{km}$, and a slow, 21-hr path with a low perigee height of $642\,\mathrm{km}$. HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment $J_2$ of the Earth which affects the semimajor axis $a$ via a secular trend of $\simeq 4-12\,\mathrm{cm\,yr}^{-1}$, depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as $0.7\,\mathrm{cm\,yr}^{-1}$. Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations. Moreover, the large eccentricity of the orbit would allow to constrain several long-range modified models of gravity and to accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the $GJ_2/c^2$ signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles $J_\ell$ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors $σ_{J_\ell}$ of a recent global Earth's gravity field model are better than $1\%$ for all the post-Newtonian effects considered, with a peak of $\simeq 10^{-7}$ for the Schwarzschild-like shifts. [Abridged]

gr-qc↗

arXiv2019

A post-Newtonian gravitomagnetic effect on the orbital motion of a test particle around its primary induced by the spin of a distant third body

We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum ${\boldsymbol S}_\textrm{X}$ of a rotating mass $M_\textrm{X}$ orbited at distance $r_\textrm{X}$ by a local gravitationally bound restricted two-body system $\mathcal{S}$ of size $r\ll r_\textrm{X}$ consisting of a test particle revolving around a massive body $M$. At the lowest post-Newtonian order, we analytically work out the doubly averaged rates of change of the Keplerian orbital elements of the test particle by finding non-vanishing long-term effects for the inclination $I$, the node $Ω$ and the pericenter $ω$. Such theoretical results are confirmed by a numerical integration of the equations of motion for a fictitious 3-body system. We numerically calculate the magnitudes of the post-Newtonian gravitomagnetic 3-body precessions for some astronomical scenarios in our solar system. For putative man-made orbiters of the natural moons Enceladus and Europa in the external fields of Saturn and Jupiter, the relativistic precessions due to the angular momenta of the gaseous giant planets can be as large as $\simeq 10-50~\textrm{milliarcseconds~per~year}~\left(\textrm{mas~yr}^{-1}\right)$. A preliminary numerical simulation shows that, for certain orbital configurations of a hypothetical Europa orbiter, its range-rate signal $Δ\dotρ$ can become larger than the current Doppler accuracy of the existing spacecraft Juno at Jupiter, i.e. $σ_{\dotρ}=0.015~\textrm{mm~s}^{-1}$, after 1 d. The effects induced by the Sun's angular momentum on artificial probes of Mercury and the Earth are at the level of $\simeq 1-0.1~\textrm{microarcseconds~per~year}~\left(μ\textrm{as~yr}^{-1}\right)$.

gr-qc↗

arXiv2019

Measuring the De Sitter precession with a new Earth's satellite to the $\mathbf{\simeq 10^{-5}}$ level: a proposal

The inclination $I$ of an Earth's satellite in polar orbit undergoes a secular De Sitter precession of $-7.6$ milliarcseconds per year for a suitable choice of the initial value of its non-circulating node $Ω$. The competing long-periodic harmonic rates of change of $I$ due to the even and odd zonal harmonics of the geopotential vanish for either a circular or polar orbit, while no secular rates occur at all. This may open up, in principle, the possibility of measuring the geodesic precession in the weak-field limit with an accurately tracked satellite by improving the current bound of $9\times 10^{-4}$ from Lunar Laser Ranging, which, on the other hand, may be even rather optimistic, by one order of magnitude, or, perhaps, even better. The most insidious competing effects are due to the solid and ocean components of the $K_1$ tide since their perturbations have nominal huge amplitudes and the same temporal pattern of the De Sitter signature. They vanish for polar orbits. Departures of $\simeq 10^{-5}-10^{-3}~\textrm{deg}$ from the ideal polar geometry allow to keep the $K_1$ tidal perturbations to a sufficiently small level. Most of the other gravitational and non-gravitational perturbations vanish for the proposed orbital configuration, while the non-vanishing ones either have different temporal signatures with respect to the De Sitter effect or can be modeled with sufficient accuracy. In order to meet the proposed goal, the measurement accuracy of $I$ should be better than $\simeq 35~\textrm{microarcseconds}=0.034~\textrm{milliarcseconds}$ over, say, 5 yr.

gr-qc↗

arXiv2019

Measuring general relativistic dragging effects in the Earth's gravitational field with ELXIS: a proposal

In a geocentric kinematically rotating ecliptical coordinate system in geodesic motion through the deformed spacetime of the Sun, both the longitude of the ascending node $Ω$ and the inclination $I$ of an artificial satellite of the spinning Earth are affected by the post-Newtonian gravitoelectric De Sitter and gravitomagnetic Lense-Thirring effects. By choosing a circular orbit with $I = Ω= 90°$ for a potential new spacecraft, which we propose to name ELXIS, it would be possible to measure each of the gravitomagnetic precessions separately at a percent level, or, perhaps, even better depending on the level of accuracy of the current and future global ocean tide models since the competing classical long-term perturbations on $I,~Ω$ due to the even and odd zonal harmonics $J_\ell,~\ell=2,~3,~4,\ldots$ of the geopotential vanish. Moreover, a suitable linear combination of $I,~Ω$ would be able to cancel out the solid and ocean tidal perturbations induced by the $K_1$ tide and, at the same time, enforce the geodetic precessions yielding a secular trend of $-8.3~\textrm{milliarcseconds~per~year}$, thus strengthening the goal of a $\simeq 10^{-5}$ test of the De Sitter effect recently proposed in the literature in the case of an equatorial coordinate system. Relatively mild departures $ΔI = ΔΩ\simeq 0.01-0.1°$ from the ideal orbital configuration with $I = Ω= 90°$ are allowed. [Abridged]

gr-qc↗

arXiv2018

On testing frame-dragging with LAGEOS and a recently announced geodetic satellite

Recently, Ciufolini and coworkers announced the forthcoming launch of a new cannonball geodetic satellite in 2019. It should be injected in an essentially circular path with the same semimajor axis $a$ of LAGEOS, in orbit since 1976, and an inclination $I$ of its orbital plane supplementary with respect to that of its existing cousin. According to their proponents, the sum of the satellites' precessions of the longitudes of the ascending nodes $Ω$ should allow one to test the general relativistic Lense-Thirring effect to a $\simeq 0.2\%$ accuracy level, with a contribution of the mismodeling in the even zonal harmonics $J_\ell,~\ell=2,4,6,\ldots$ of the geopotential to the total error budget as little as $0.1\%$. Actually, such an ambitious goal seems to be hardly attainable because of the direct and indirect impact of, at least, the first even zonal $J_2$. On the one hand, the lingering scatter of the estimated values of such a key geophysical parameter from different recent GRACE/GOCE-based global gravity field solutions is representative of an uncertainty which may directly impact the summed Lense-Thirring node precessions at a $\simeq 70-80\%$ in the worst scenarios, and to a $\simeq 3-10\%$ level in other, more favorable cases. On the other hand, the phenomenologically measured secular decay $\dot a$ of the semimajor axis of LAGEOS (and, presumably, of the other satellite as well), currently known at a $σ_{\dot a}\simeq 0.03~\textrm{m~yr}^{-1}$ level after more than 30 yr, will couple with the sum of the $J_2$-induced node precessions yielding an overall bias as large as $\simeq 20-40\%$ after $5-10$ yr. A further systematic error of the order of $\simeq 2-14\%$ may arise from an analogous interplay of the secular decay of the inclination $\dot I$ with the oblateness-driven node precessions.

gr-qc↗