arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

At least 73 records · Page 4Linked to original sources

arXiv2018

Constraining some $r^{-n}$ extra-potentials in modified gravity models with LAGEOS-type laser-ranged geodetic satellites

We focus on several models of modified gravity which share the characteristic of leading to perturbations of the Newtonian potential $\propto K_2~r^{-2}$ and $\propto K_3~r^{-3}$. In particular, by using existing long data records of the LAGEOS satellites, tracked on an almost continuous basis with the Satellite Laser Ranging (SLR) technique, we set preliminary constraints on the free parameters $K_2,~K_3$ in a model-independent, phenomenological way. We obtain $\left|K_2\right|\lesssim 2.1\times 10^6~\textrm{m}^4~\textrm{s}^{-2},~ -2.5\times 10^{12}~\textrm{m}^5~\textrm{s}^{-2}\lesssim K_3 \lesssim 4.1\times 10^{12}~\textrm{m}^5~\textrm{s}^{-2}.$ They are several orders of magnitude tighter than corresponding bounds existing in the literature inferred with different techniques and in other astronomical and astrophysical scenarios. Then, we specialize them to the different parameters characterizing the various models considered. The availability of SLR data records of increasing length and accuracy will allow to further refine and strengthen the present results.

gr-qc↗

arXiv2018

Perspectives on constraining a cosmological constant-type parameter with pulsar timing in the Galactic Center

Independent tests aiming to constrain the value of the cosmological constant $Λ$ are usually difficult because of its extreme smallness $\left(Λ\simeq 1\times 10^{-52}~\textrm{m}^{-2},~\textrm{or}~2.89\times 10^{-122}~\textrm{in Planck units}\right)$. Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the $\simeq 10^{-43}-10^{-44}~\textrm{m}^{-2}~\left(5-1\times 10^{-113}~\textrm{in Planck units}\right)$ level, but they may turn out to be somewhat optimistic since $Λ$ has not yet been explicitly modeled in the planetary data reductions. Accurate $\left(σ_{τ_\textrm{p}}\simeq 1-10~μ\textrm{s}\right)$ timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit $\overline{Δδτ}^Λ_\textrm{p}$, a S2-like orbital configuration with $e=0.8839,~P_\textrm{b}=16~\textrm{yr}$ would allow to obtain preliminarily an upper bound of the order of $\left|Λ\right|\lesssim 9\times 10^{-47}~\textrm{m}^{-2}~\left(\lesssim 2\times 10^{-116}~\textrm{in Planck units}\right)$ if only $σ_{τ_\textrm{p}}$ were to be considered. Our results can be easily extended to modified models of gravity using $Λ-$type parameters.

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arXiv2018

Analytically calculated post-Keplerian range and range-rate perturbations: the solar Lense-Thirring effect and BepiColombo

We analytically calculate the time series for the perturbations $Δρ(t),~Δ\dotρ(t)$ induced by a general disturbing acceleration $\boldsymbol{A}$ on the mutual range $ρ$ and range-rate $\dotρ$ of two test particles $\textrm{A},~\textrm{B}$ orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring effect, due to the primary's spin $\boldsymbol{S}$, and the classical perturbation arising from its quadrupole mass moment $J_2$ for arbitrary orbital geometries and orientation of the source's symmetry axis $\boldsymbol{\hat{S}}$. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the $10~\textrm{m},~10^{-3}~\textrm{cm s}^{-1}$ level, respectively, during the extended phase (2026-2028) of the forthcoming BepiColombo mission to Mercury whose expected tracking accuracy is of the order of $\simeq 0.1~\textrm{m},~2\times 10^{-4}~\textrm{cm s}^{-1}$. The competing signatures due to the solar quadrupole $J_2^\odot$, if modelled at the $σ_{J_2^\odot}\simeq 10^{-9}$ level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects. The position and velocity vectors $\mathbf{r},~\mathbf{v}$ of Mercury and Earth are changed by the solar Lense-Thirring effect by about $10~\textrm{m},~1.5~\textrm{m}$ and $10^{-3}~\textrm{cm s}^{-1},~10^{-5}~\textrm{cm s}^{-1}$, respectively, over 2 yr; neglecting such shifts may have an impact on long-term integrations of the inner solar system dynamics over $\sim\textrm{Gyr}$ timescales.

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arXiv2017

Perturbed stellar motions around the rotating black hole in Sgr A* for a generic orientation of its spin axis

Empirically determining the averaged variations of the orbital parameters of the stars orbiting the Supermassive Black Hole (SBH) hosted by the Galactic Centre (GC) in Sgr A* is, in principle, a valuable tool to put on the test the General Theory of Relativity (GTR), in regimes far stronger than those tested so far, and certain key predictions of it like the no-hair theorems. We analytically work out the long-term variations of all the six osculating Keplerian orbital elements of a test particle orbiting a non-spherical, rotating body with quadrupole moment Q_2 and angular momentum S for a generic spatial orientation of its spin axis k. This choice is motivated by the fact that, basically, we do not know the position in the sky of the spin axis of the SBH in Sgr A* with sufficient accuracy. We apply our results to S2, which is the closest star discovered so far having an orbital period P_b = 15.98 yr, and to a hypothetical closer star X with P_b = 0.5 yr. Our calculations are quite general, not being related to any specific parameterization of k, and can be applied also to astrophysical binary systems, stellar planetary systems, and planetary satellite geodesy in which different reference frames, generally not aligned with the primary's rotational axis, are routinely used.

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arXiv2017

Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body

The orbital dynamics of a test particle moving in the non-spherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the Keplerian orbital elements of the test particle arising from the crossing among the first even zonal harmonic $J_2$ of the central body and the post-Newtonian static and stationary components of its gravitational field. We also work out the Newtonian shifts per orbit of order $J_2^2$, and the direct post-Newtonian gravitoelectric effects of order $J_2 c^{-2}$ arising from the equations of motion. In the case of both the indirect and direct gravitoelectric $J_2 c^{-2}$ shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from Earth artificial satellites to stars orbiting supermassive black holes.

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arXiv2017

Is the recently proposed Mars-sized perturber at $65-80~\textrm{AU}$ ruled out by the Cassini ranging data?

Recently, the existence of a pointlike pertuber PX with $1~m_\textrm{Mars}\lesssim m_\textrm{X}\lesssim 2.4~m_\oplus$ supposedly moving at $65-80~\textrm{AU}$ along a moderately inclined orbit has been hypothesized in order to explain certain features of the midplane of the Kuiper Belt Objects (KBOs). We preliminarily selected two possible scenarios for such a PX, and numerically simulated its effect on the Earth-Saturn range $ρ(t)$ by varying some of its orbital parameters over a certain time span; then, we compared our results with some existing actual range residuals. By assuming $m_\textrm{X} = 1~m_\textrm{Mars}$ and a circular orbit, such a putative new member of our Solar System would nominally perturb $ρ(t)$ by a few km over $Δt = 12~\textrm{yr}~(2004-2016)$. However, the Cassini spaceraft accurately measured $ρ(t)$ to the level of $σ_ρ\simeq 100~\textrm{m}$. Nonetheless, such a scenario should not be considered as necessarily ruled out since the Cassini data were reduced so far without explicitly modeling any PX. Indeed, a NASA JPL team recently demonstrated that an extra-signature as large as 4 km affecting the Kronian range would be almost completely absorbed in fitting incomplete dynamical models, i.e. without PX itself, to such simulated data, thus not showing up in the standard post-fit range residuals. Larger anomalous signatures would instead occur for $m_\textrm{X} > 1~m_\textrm{Mars}$. Their nominal} amplitude could be as large as $50-150~\textrm{km}$ for $m_\textrm{X} = 2.4~m_\oplus$, thus making less plausible their existence.

gr-qc↗

arXiv2017

Post-Keplerian effects on radial velocity in binary systems and the possibility of measuring General Relativity with the S2 star in 2018

One of the directly measured quantities which are used in monitoring the orbital motions of many of the S stars revolving around the Supermassive Black Hole (SMBH) in the Galactic Center (GC) is their radial velocity (RV) $V$ obtained with near-infrared spectroscopy. Here, we devise a general approach to calculate both the instantaneous variations $ΔV\left(t\right)$ and the net shifts per revolution $\left\langleΔV\right\rangle$ induced on such an observable by some post-Keplerian (pK) accelerations. In particular, we look at the general relativistic Schwarzschild (gravitoelectric) and Lense-Thirring (gravitomagnetic frame-dragging) effects, and the mass quadrupole. It turns out that we may be on the verge of measuring the Schwarzschild-type 1pN static component of the SMBH's field with the S2 star for which RV measurements accurate to about $\simeq 30-50~\textrm{km s}^{-1}$ dating back to $t_0 = 2003.271$ are currently available, and whose orbital period amounts to $P_\textrm{b} = 16$ yr. Indeed, while its expected general relativistic RV net shift per orbit amounts to just $\left\langleΔV^\textrm{GE}\right\rangle = -11.6~\textrm{km s}^{-1}$, it should reach a peak value as large as $ΔV_\textrm{max}^\textrm{GE}\left(t_\textrm{max}\right) = 551~\textrm{km s}^{-1}$ at $t_\textrm{max} = 2018.35$. The periastron shift $Δω^\textrm{GE}$ of S2 over the same time span will not be larger than $0.2$ deg, while the current accuracy in estimating such an orbital element for this star is of the order of $0.6$ deg. The frame-dragging and quadrupole-induced RV shifts are far smaller for S2, amounting to, at most, $0.19~\textrm{km s}^{-1},0.0039~\textrm{km s}^{-1}$, respectively. Further studies should be dedicated to the impact on the RV of possible diffused mass distribution in the GC and of other individual stars inside and outside the orbit of S2.

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arXiv2017

Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the Galactic Center

We develop a general approach to analytically calculate the perturbations $Δδτ_\textrm{p}$ of the orbital component of the change $δτ_\textrm{p}$ of the times of arrival of the pulses emitted by a binary pulsar p induced by the post-Keplerian accelerations due to the mass quadrupole $Q_2$, and the post-Newtonian gravitoelectric (GE) and Lense-Thirring (LT) fields. We apply our results to the so-far still hypothetical scenario involving a pulsar orbiting the Supermassive Black Hole in in the Galactic Center at Sgr A$^\ast$. We also evaluate the gravitomagnetic and quadrupolar Shapiro-like propagation delays $δτ_\textrm{prop}$. By assuming the orbit of the existing S2 main sequence star and a time span as long as its orbital period $P_\textrm{b}$, we obtain $\left|Δδτ_\textrm{p}^\textrm{GE}\right|\lesssim 10^3~\textrm{s},~\left|Δδτ_\textrm{p}^\textrm{LT}\right|\lesssim 0.6~\textrm{s},\left|Δδτ_\textrm{p}^{Q_2}\right|\lesssim 0.04~\textrm{s}$. Faster $\left(P_\textrm{b} = 5~\textrm{yr}\right)$ and more eccentric $\left(e=0.97\right)$ orbits would imply net shifts per revolution as large as $\left|\left\langleΔδτ_\textrm{p}^\textrm{GE}\right\rangle\right|\lesssim 10~\textrm{Ms},~\left|\left\langleΔδτ_\textrm{p}^\textrm{LT}\right\rangle\right|\lesssim 400~\textrm{s},\left|\left\langleΔδτ_\textrm{p}^{Q_2}\right\rangle\right|\lesssim 10^3~\textrm{s}$, depending on the other orbital parameters and the initial epoch. For the propagation delays, we have $\left|δτ_\textrm{prop}^\textrm{LT}\right|\lesssim 0.02~\textrm{s},~\left|δτ_\textrm{prop}^{Q_2}\right|\lesssim 1~μ\textrm{s}$. The expected precision in pulsar timing in Sgr A$^\ast$ is of the order of $100~μ\textrm{s}$, or, perhaps, even $1-10~μ\textrm{s}$.

gr-qc↗

arXiv2017

On the post-Keplerian corrections to the orbital periods of a two-body system and their application to the Galactic Center

Detailed numerical analyses of the orbital motion of a test particle around a spinning primary are performed. They aim to investigate the possibility of using the post-Keplerian (pK) corrections to the orbiter's periods (draconitic, anomalistic and sidereal) as a further opportunity to perform new tests of post-Newtonian (pN) gravity. As a specific scenario, the S-stars orbiting the Massive Black Hole (MBH) supposedly lurking in Sgr A$^\ast$ at the center of the Galaxy is adopted. We, first, study the effects of the pK Schwarzchild, Lense-Thirring and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. It turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the size of all the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH's spin axis orientation are considered as well. The pK accelerations considered lead to corrections of the orbital periods of the order of 1-100d (Schwarzschild), 0.1-10h (Lense-Thirring) and 1-10^3s (quadrupole) for a target star with a=300-800~AU and e ~ 0.8, which could be possibly measurable by the future facilities.

astro-ph.GA↗

arXiv2017

Are we close to put the anomalous perihelion precessions from Verlinde's emergent gravity to the test?

In the framework of the emergent gravity scenario by Verlinde, it was recently observed by Liu and Prokopec that, among other things, an anomalous pericenter precession would affect the orbital motion of a test particle orbiting an isolated central body. Here, it is shown that, if it were real, its expected magnitude for the inner planets of the Solar System would be at the same level of the present-day accuracy in constraining any possible deviations from their standard perihelion precessions as inferred from long data records spanning about the last century. The most favorable situation for testing the Verlinde-type precession seems to occur for Mars. Indeed, according to recent versions of the EPM and INPOP planetary ephemerides, non-standard perihelion precessions, of whatsoever physical origin, which are larger than some $\approx 0.02-0.11$ milliarcseconds per century are not admissible, while the putative precession predicted by Liu and Prokopec amounts to $0.09$ milliarcseconds per century. Other potentially interesting astronomical and astrophysical scenarios like, e.g., the Earth's LAGEOS II artificial satellite, the double pulsar system PSR J0737-3039A/B and the S-stars orbiting the Supermassive Black Hole in Sgr A$^\ast$ are, instead, not viable because of the excessive smallness of the predicted effects for them.

gr-qc↗

arXiv2017

A comment on "A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model", by I. Ciufolini et al

Recently, Ciufolini et al. reported on a test of the general relativistic gravitomagnetic Lense-Thirring effect by analyzing about 3.5 years of laser ranging data to the LAGEOS, LAGEOS II, LARES geodetic satellites orbiting the Earth. By using the GRACE-based GGM05S Earth's global gravity model and a linear combination of the nodes $Ω$ of the three satellites designed to remove the impact of errors in the first two even zonal harmonic coefficients $J_2,~J_4$ of the multipolar expansion of the Newtonian part of the Earth's gravitational potential, they claimed an overall accuracy of $5\%$ for the Lense-Thirring caused node motion. We show that the scatter in the nominal values of the uncancelled even zonals of degree $\ell = 6,~8,~10$ from some of the most recent global gravity models does not yet allow to reach unambiguously and univocally the expected $\approx 1\%$ level, being large up to $\lesssim 15\%~(\ell=6),~6\%~(\ell=8),~36\%~(\ell=10)$ for some pairs of models.

gr-qc↗

arXiv2016

Preliminary constraints on the location of the recently hypothesized new planet of the Solar System from planetary orbital dynamics

(Abridged) The trajectory of Saturn is nowadays known at essentially the same accuracy level of the inner planets due to the telemetry of the Cassini spacecraft. Thus, the expected perturbations $\dot\varpi,~\dotΩ$ due to PX, for which we suggest the name Telisto in view of its remarkable distance, on the Kronian apsidal and draconitic orbital motions are theoretically investigated to tentatively constrain the configuration space of Telisto/Planet Nine itself. To this aim, we compare our predictions $\dot\varpi_\textrm{theo},~\dotΩ_\textrm{theo}$ to the currently available experimental intervals of values $Δ\dotΩ_\textrm{obs},~Δ\dot\varpi_\textrm{obs}$ determined by astronomers in the recent past without explicitly modeling and solving for PX itself. As such, our results, despite being plausible and in agreement to a large extent with other constraints released in the literature, should be regarded as proof-of-principle investigations aimed to encourage more accurate analyses in future. It turns out that the admissible region in its configuration space is moderately narrow as far as its position along its orbit, reckoned by the true anomaly $f_\textrm{X}$, is concerned, being concentrated around approximately $130~\textrm{deg}\lesssim f_\textrm{X}\lesssim 240~\textrm{deg}$. Telisto/Planet Nine is certainly far from its perihelion ($f_\textrm{X}=0~\textrm{deg}$), in agreement with other recent studies. The future analysis of the data from the ongoing New Horizons mission might be helpful in further constraining the scenario considered here for Telisto/Planet Nine. Its impact on the spaceraft's range over a multi-year span is investigated with a preliminary sensitivity analysis.

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arXiv2016

On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center

The S-stars discovered in the Galactic center (GC) are expected to provide unique dynamical tests of the Kerr metric of the massive black hole (MBH) orbited by them. In order to obtain unbiased measurements of its spin and the related relativistic effects, a comprehensive understanding of the gravitational perturbations of the stars and stellar remnants around the MBH is quite essential. Here, we study the perturbations on the observables of a typical target star, i.e., the apparent orbital motion and the redshift, due to both the spin-induced relativistic effects and the Newtonian attractions of a single or a cluster of disturbing object(s). We find that, in most cases, the Newtonian perturbations on the observables are mainly attributed to the perturbed orbital period of the target star, rather than the Newtonian orbital precessions. The Newtonian perturbations have their unique features when they peak around the pericenter passage in each revolution, which is quite different from those of the spin-induced effects. Looking at the currently detected star S2/S0-2, we find that its spin-induced effects on both the image position and redshift are very likely obscured by the gravitational perturbations from the star S0-102 alone. We also investigate and discuss the Newtonian perturbations on a hypothetical S-star located inside the orbits of the currently detected ones. By considering a number of possible stellar distributions near the central MBH, we find that the spin-induced effects on the apparent position and the redshift dominate over the stellar perturbations for target stars with orbital semimajor axis smaller than $100-400$AU if the MBH is maximally spinning. Our results suggest that, in principle, the stellar perturbations can be removed as they have distinctive morphologies comparing to those of the relativistic Kerr-type signatures.

astro-ph.GA↗

arXiv2016

Post-Keplerian corrections to the orbital periods of a two-body system and their measurability

The orbital motion of a binary system is characterized by various characteristic temporal intervals which, by definition, are different from each other: the draconitic, anomalistic and sidereal periods. They all coincide in the Keplerian case. Such a degeneracy is removed, in general, when a post-Keplerian acceleration is present. We analytically work out the corrections to such otherwise Keplerian periods which are induced by general relativity (Schwarzschild and Lense-Thirring) and, at the Newtonian level, by the quadrupole of the primary. In many astronomical and astrophysical systems, like exoplanets, one of the most accurately determined quantities is just the time span characterizing the orbital revolution, which is often measured independently with different techniques like the transit photometry and the radial velocities. Thus, our results could be useful, in principle, to either constrain the physical properties of the central body and/or perform new tests of general relativity, especially when no other standard observables like, e.g., the orbital precessions are accessible to observations. The difference of two independently measured periods would cancel out the common Keplerian term leaving just a post-Keplerian correction. Furthermore, by comparing the theoretically predicted post-Keplerian expressions $T^{(\textrm{pK})}$ with the experimental accuracy $σ_{T_\textrm{exp}}$ in measuring the orbital period(s) it is possible to identify those systems whose observations should be re-processed with genuine post-Keplerian models if $T^{(\textrm{pK})}>σ_{T_\textrm{exp}}$. It seems just the case for WASP-33 b since $σ_{T_\textrm{exp}}=0.04$ s, while $3$ s$\leq T_\textrm{dra}^{(J_2)}\leq 9.5$ s, $T_\textrm{dra}^{(\textrm{GE)}}=0.36$ s.

gr-qc↗

arXiv2016

Constraining the Schwarzschild-de Sitter Solution in Models of Modified Gravity

The Schwarzschild-de Sitter (SdS) solution exists in the large majority of modified gravity theories, as expected, and in particular the effective cosmological constant is determined by the specific parameters of the given theory. We explore the possibility to use future extended radio-tracking data from the currently ongoing New Horizons mission in the outskirts peripheries of the Solar System, at about 40 au, in order to constrain this effective cosmological constant, and thus to impose constrain on each scenario's parameters. We investigate some of the recently most studied modified gravities, namely $f(R)$ and $f(T)$ theories, dRGT massive gravity, and Hořava-Lifshitz gravity, and we show that New Horizons mission may bring an improvement of one-two orders of magnitude with respect to the present bounds from planetary orbital dynamics.

gr-qc↗

arXiv2016

Perspectives on effectively constraining the location of a massive trans-Plutonian object with the New Horizons spacecraft: a sensitivity analysis

The radio tracking apparatus of the New Horizons spacecraft, currently traveling to the Pluto system where its arrival is scheduled for July 2015, should be able to reach an accuracy of 10 m (range) and 0.1 mm s^-1 (range-rate) over distances up to 50 au. This should allow to effectively constrain the location of a putative trans-Plutonian massive object, dubbed Planet X (PX) hereafter, whose existence has recently been postulated for a variety of reasons connected with, e.g., the architecture of the Kuiper belt and the cometary flux from the Oort cloud. Traditional scenarios involve a rock-ice planetoid with mX = 0.7mE at some 100 - 200 au, or a Jovian body with mX = 5mJ at about 10,000 - 20,000 au; as a result of our preliminary sensitivity analysis, they should be detectable by New Horizons since they would impact its range at a km level or so over a time span six years long. Conversely, range residuals statistically compatible with zero having an amplitude of 10 m would imply that PX, if it exists, could not be located at less than about 4,500 au (mX = 0.7mE) or 60,000 au (mX = 5mJ), thus making a direct detection quite demanding with the present-day technologies. As a consequence, it would be appropriate to rename such a remote body as Telisto. Also fundamental physics would benefit from this analysis since certain subtle effects predicted by MOND for the deep Newtonian regions of our Solar System are just equivalent to those of a distant pointlike mass.

astro-ph.EP↗

arXiv2016

The Solar Lense-Thirring effect: perspectives for a future measurement

The predicted Lense-Thirring perihelion precession of Mercury induced by the Sun's angular momentum through its general relativistic gravitomagnetic field amounts to 2 milliarcseconds per century. It turned out to be compatible with the latest experimental determinations of the supplementary perihelion precession of Mercury with the INPOP15a ephemerides, whose accuracy level has nowadays reached the magnitude of the predicted relativistic effect itself thanks to the analysis of some years of tracking data of the MESSENGER spacecraft, which orbited Mercury from 2011 to 2015. A dedicated analysis of three years of MESSENGER data with the DE ephemerides allowed for a $25\%$ determination of the Sun's angular momentum by means of the Lense-Thirring effect, which turned out to be highly correlated with the signature due to the Solar quadrupole mass moment $J_2^{\odot}$.

gr-qc↗

arXiv2015

Does the Newton's gravitational constant vary sinusoidally with time? Orbital motions say no

A sinusoidally time-varying pattern of the values of the Newton's constant of gravitation $G$ measured in Earth-based laboratories over the latest decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain $G$ itself in a direct and independent way. We numerically integrated the ad-hoc modified equations of motion of the major bodies of the Solar System by finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension $α$, declination $δ$ and range $ρ$ would be affected up to $10^4-10^5$ milliarcseconds and $10^5$ km, respectively; the present-day residuals of such observables are as little as about $4$ milliarcseconds and $10^{-1}$ km, respectively. \textcolor{black}{We analytically calculated the long-term orbital effects induced by the putative harmonic variation of $G$ at hand finding non-zero rates of change for the semimajor axis $a$, the eccentricity $e$ and the argument of pericenter $ω$ of a test particle. For the LAGEOS satellite, an orbital increase as large as $3.9$ m yr$^{-1}$ is predicted, in contrast with the observed decay of $-0.203\pm 0.035$ m yr$^{-1}$. An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it down to the $10^{-4}$ arcseconds per century level. The rejection level provided by Mercury is of the same order of magnitude.

gr-qc↗