arXiv subjects

Lorenzo Iorio

Publications and source records attributed to Lorenzo Iorio.

At least 37 records · Page 2Linked to original sources

arXiv2023

The Lense-Thirring effect on the Galilean moons of Jupiter

The perspectives of detecting the general relativistic gravitomagnetic Lense-Thirring effect on the orbits of the Galilean moons of Jupiter induced by the angular momentum ${\boldsymbol{S}}$ of the latter are preliminarily investigated. Numerical integrations over one century show that the expected gravitomagnetic signatures of the directly observable right ascension $α$ and declination $δ$ of the satellites are as large as tens of arcseconds for Io, while for Callisto they drop to the $\simeq 0.2\,\mathrm{arcseconds}$ level. Major competing effects due to the mismodeling in the zonal multipoles $J_\ell,\,\ell=2,\,3,\,4,\,\ldots$ of the Jovian non-spherically symmetric gravity field and in the Jupiter's spin axis ${\boldsymbol{\hat{k}}}$ should have a limited impact, especially in view of the future improvements in determining such parameters expected after the completion of the ongoing Juno mission in the next few years. On the other hand, the masses of the satellites, responsible of their mutual $N-$body perturbations, should be known better than now. Such a task should be accomplished with the future JUICE and Clipper missions to the Jovian system. Present-day accuracy in knowing the orbits of the Jovian Galilean satellites is of the order of 10 milliarcseconds, to be likely further improved thanks to the ongoing re-reduction of old photographic plates. This suggests that, in the next future, the Lense-Thirring effect in the main Jovian system of moons might be detectable with dedicated data reductions in which the gravitomagnetic field is explicitly modeled and solved-for.

gr-qc↗

arXiv2023

One EURO for Uranus: the Elliptical Uranian Relativity Orbiter mission

Recent years have seen increasing interest in sending a mission to Uranus, visited so far only by Voyager 2 in 1986. EURO (Elliptical Uranian Relativity Orbiter) is a preliminary mission concept investigating the possibility of dynamically measuring the planet's angular momentum by means of the Lense-Thirring effect affecting a putative Uranian orbiter. It is possible, at least in principle, to separate the relativistic precessions of the orbital inclination to the Celestial Equator and of the longitude of the ascending node of the spacecraft from its classical rates of the pericentre induced by the multipoles of the planet's gravity field by adopting an appropriate orbital configuration. For a wide and elliptical $2\,000\times 100\,000\,\mathrm{km}$ orbit, the gravitomagnetic signatures amount to tens of milliarcseconds per year, while, for a suitable choice of the initial conditions, the peak-to-peak amplitude of the range-rate shift can reach the level of $\simeq 1.5\times 10^{-3}$ millimetre per second in a single pericentre passage of a few hours. By lowering the apocentre height to $10\,000\,\mathrm{km}$, the Lense-Thirring precessions are enhanced to the level of hundreds of milliarcseconds per year. The uncertainties in the orientation of the planetary spin axis and in the inclination are major sources of systematic bias; it turns out that they should be determined with accuracies as good as $\simeq 0.1-1$ and $\simeq 1-10$ milliarcseconds, respectively.

gr-qc↗

arXiv2023

Limitations in Testing the Lense-Thirring Effect with LAGEOS and the Newly Launched Geodetic Satellite LARES 2

The new geodetic satellite LARES 2, cousin of LAGEOS and sharing with it almost the same orbital parameters apart from the inclination, displaced by 180 deg, was launched last year. Its proponents suggest using the sum of the nodes of LAGEOS and of LARES 2 to measure the sum of the Lense-Thirring node precessions independently of the systematic bias caused by the even zonal harmonics of the geopotential, claiming a final $\simeq 0.2$ percent total accuracy. In fact, the actual orbital configurations of the two satellites do not allow one to attain the sought for mutual cancellation of their classical node precessions due to the Earth's quadrupole mass moment, as their sum is still $\simeq 5000$ times larger than the added general relativistic rates. This has important consequences. One is that the current uncertainties in the eccentricities and the inclinations of both satellites do not presently allow the stated accuracy goal to be met, needing improvements of 3-4 orders of magnitude. Furthermore, the imperfect knowledge of the Earth's angular momentum $S$ impacts the uncancelled sum of the node precessions, from 150 to 4900 percent of the relativistic signal depending on the uncertainty assumed in $S$. It is finally remarked that the real breakthrough in reliably testing the gravitomagnetic field of the Earth would consist in modeling it and simultaneously estimating one or more dedicated parameter(s) along with other ones characterising the geopotential, as is customarily performed for any other dynamical feature.

gr-qc↗

arXiv2023

Might the 2PN perihelion precession of Mercury become measurable in the next future?

The Hermean average perihelion rate $\dotω^\mathrm{2PN}$, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from $-18$ to $-4$ microarcseconds per century $\left(μ\mathrm{as\,cty}^{-1}\right)$, depending on the true anomaly at epoch $f_0$. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun's gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury's perihelion rate $\dotω_\mathrm{exp}$ recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is $σ_{\dotω_\mathrm{exp}}\simeq 8\,μ\mathrm{as\,cty}^{-1}$, corresponding to a relative accuracy of $2\times 10^{-7}$ for the combination $\left(2 + 2γ- β\right)/3$ of the PPN parameters $β$ and $γ$ scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to $\simeq 10-50$ times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recent improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a $\simeq 10^{-7}$ accuracy level in constraining $β$ and $γ$ in an extended mission, despite $\simeq 10^{-6}$ seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not too distant future it will be necessary to include the 2PN acceleration in the Solar System's dynamics as well.

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arXiv2022

Is it possible to measure new general relativistic third-body effects on the orbit of Mercury with BepiColombo?

Recently, Will calculated an additional contribution to the Mercury's precession of the longitude of perihelion $\varpi$ of the order of $\dot\varpi_\textrm{W}\simeq 0.22$ $\textrm{milliarcseconds per century}$ ($\textrm{mas cty}^{-1}$). It is partly a direct consequence of certain 1pN third-body accelerations entering the planetary equations of motion, and partly an indirect, mixed effect due to the simultaneous interplay of the standard 1pN pointlike acceleration of the primary with the Newtonian $N$-body acceleration, to the quadrupole order, in the analytical calculation of the secular perihelion precession with the Gauss equations. We critically discuss the actual measurability of the mixed effects with respect to direct ones. The current uncertainties in either the magnitude of the Sun's angular momentum $S_\odot$ and the orientation of its spin axis ${\boldsymbol{\hat{S}}}_\odot$ impact the precessions $\dot\varpi_{J_2^\odot},~\dot\varpi_\textrm{LT}$ induced by the Sun's quadrupole mass moment and angular momentum via the Lense-Thirring effect to a level which makes almost impossible to measure $\dot\varpi_\textrm{W}$ even in the hypothesis that it comes entirely from the aforementioned 1pN third-body accelerations. On the other hand, from the point of view of the Lense-Thirring effect itself, the mismodeled quadrupolar precession $δ\dot\varpi_{J_2^\odot}$ due to the uncertainties in ${\boldsymbol{\hat{S}}}_\odot$ corresponds to a bias of $\simeq 9\%$ of the relativistic one. The resulting simulated mismodeled range and range-rate times series of BepiColombo are at about the per cent level of the nominal gravitomagnetic ones.

gr-qc↗

arXiv2022

The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A$^\ast$

Recently, some S-stars (S4711, S62, S4714) orbiting the supermassive black hole (SMBH) in Sgr A$^\ast$ with short orbital periods ($7.6\,\mathrm{yr}\leq P_\mathrm{b}\leq 12\,\mathrm{yr}$) were discovered. It was suggested that they may be used to measure the general relativistic Lense-Thirring (LT) precessions of their longitudes of ascending node $\mathitΩ$ induced by the SMBH's angular momentum $\boldsymbol{J}_\bullet$. In fact, the proposed numerical estimates hold only in the particular case of a perfect alignment of $\boldsymbol{J}_\bullet$ with the line of sight, which does not seem to be the case. Moreover, also the inclination $I$ and the argument of perinigricon $ω$ undergo LT precessions for an arbitrary orientation of $\boldsymbol{J}_\bullet$ in space. We explicitly show the analytical expressions of $\dot I^\mathrm{LT},\,\dot{\mathitΩ}^\mathrm{LT},\,ω^\mathrm{LT}$ in terms of the SMBH's spin polar angles $i^\bullet,\,\varepsilon^\bullet$ by finding the range of values for each of them in arcseconds per year ($^{\prime\prime}\,\mathrm{yr}^{-1}$). For each star, the corresponding values of $i^\bullet_\mathrm{max},\,\varepsilon^\bullet_\mathrm{max}$ and $i^\bullet_\mathrm{min},\,\varepsilon^\bullet_\mathrm{min}$ are determined as well, along with those $i_0^\bullet,\,\varepsilon_0^\bullet$ that cancel the LT precessions. The LT perinigricon precessions $\dotω^\mathrm{LT}$ are overwhelmed by the systematic uncertainties in the Schwarzschild ones due to the current errors in the stars' orbital parameters and the mass of Sgr A$^\ast$ itself. [Abridged]

gr-qc↗

arXiv2022

Calculation of the Uncertainties in the Planetary Precessions with the Recent EPM2017 Ephemerides and their Use in Fundamental Physics and Beyond

I tentatively compile the formal uncertainties in the secular rates of change of the orbital elements $a,~e,~I,~Ω$ and $\varpi$ of the planets of the solar system from the recently released formal errors in $a$ and the nonsingular elements $h,~k,~p$ and $q$ estimated for the same bodies with the EPM2017 ephemerides by E.\,V. Pitjeva and N.\,P. Pitjev. The highest accuracies occur for the inner planets and Saturn in view of the extensive use of radiotechnical data collected over the last decades. For the inclination $I$, node $Ω$ and perihelion $\varpi$ of Mercury and Mars, I obtain accuracies $σ_{\dot I},\,σ_{\dotΩ},\,σ_{\dot \varpi}\simeq 1-10\,μ\textrm{as~cty}^{-1}$, while for Saturn they are $σ_{\dot I},\,σ_{\dotΩ},\,σ_{\dot \varpi}\simeq 10\,μ\textrm{as~cty}^{-1}-1\,\textrm{mas~cty}^{-1}$. As far as the semimajor axis $a$ is concerned, its rates for the inner planets are accurate to the $σ_{\dot a}\simeq 1-100\,\textrm{mm~cty}^{-1}$ level, while for Saturn I obtain $σ_{\dot a}\simeq 17\,\textrm{m~cty}^{-1}$. In terms of the parameterized post-Newtonian (PPN) parameters $β$ and $γ$, a formal error as little as $8\,μ\textrm{as~cty}^{-1}$ for the Hermean apsidal rate corresponds to a $\simeq 2\times 10^{-7}$ bias in the combination $\left(2 + 2γ- β\right)/3$ parameterizing the Schwarzschild-type periehlion precession of Mercury. The realistic uncertainties of the planetary precessions may be up to one order of magnitude larger. I discuss their potential multiple uses in fundamental physics, astronomy, and planetology.

gr-qc↗

arXiv2022

Frame-Dragging in Extrasolar Circumbinary Planetary Systems

Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital motion of a relatively distant planet with Lense-Thirring-type precessional effects which, under certain circumstances, may amount to a significant fraction of the static, gravitoelectric ones, analogous to the well known Einstein perihelion precession of Mercury, depending only on the masses of the system's bodies. Instead, when the gravitomagnetic field is due solely to the spin of each of the central star(s), the Lense-Thirring shifts are several orders of magnitude smaller than the gravitoelectric ones. In view of the growing interest in the scientific community about the detection of general relativistic effects in exoplanets, the perspectives of finding new scenarios for testing such a further manifestation of general relativity might be deemed worth of further investigations.

gr-qc↗

arXiv2022

Effect of some modified models of gravity on the radial velocity of binary systems

For many classes of astronomical and astrophysical binary systems, long observational records of their radial velocity $V$, which is their directly observable quantity, are available. For exoplanets close to their parent stars, they cover several full orbital revolutions, while for wide binaries like, e.g., the Proxima/$α$ Centauri AB system, only relatively short orbital arcs are sampled by existing radial velocity measurements. Here, the changes $ΔV$ induced on a binary's radial velocity by some long-range modified models of gravity are analytically calculated. In particular, extra-potentials proportional to $r^{-N},\,N=2,\,3$ and $r^2$ are considered; the Cosmological Constant $Λ$ belongs to the latter group. Both the net shift per orbit and the instantaneous one are explicitly calculated for each model. The Cosmological Constant induces a shift in the radial velocity of the Proxima/$α$ Centauri AB binary as little as $\left|ΔV\right|\lesssim 10^{-7}\,\mathrm{m\,s}^{-1}$, while the present-day accuracy in measuring its radial velocity is $σ_V\simeq 30\,\mathrm{m\,s}^{-1}$. The calculational scheme presented here is quite general, and can be straightforwardly extended to any other modified gravity.

gr-qc↗

arXiv2022

Post-Newtonian effects on some characteristic timescales of transiting exoplanets

Some measurable characteristic timescales $\left\{t_\mathrm{trn}\right\}$ of transiting exoplanets are investigated in order to check preliminarily if their cumulative shifts over the years induced by the post-Newtonian (pN) gravitoelectric (Schwarzschild) and gravitomagnetic (Lense-Thirring) components of the stellar gravitational field are, at least in principle, measurable. Both the primary (planet in front of the star) and the secondary (planet behind the star) transits are considered along with their associated characteristic time intervals: the total transit duration $t_D$, the ingress/egress transit duration $τ$, the full width at half maximum primary transit duration $t_H$, and also the time of conjunction $t_\mathrm{cj}$. For each of them, the net changes per orbit $\langleΔt_D\rangle,\,\langleΔτ\rangle,\,\langleΔt_H\rangle,\,\langleΔt_\mathrm{cj}\rangle$ induced by the aforementioned pN accelerations are analytically obtained; also the Newtonian effect of the star's quadrupole mass moment $J_2^\star$ is worked out. They are calculated for a fictitious Sun-Jupiter system in an edge-on elliptical orbit, and the results are compared with the present-day experimental accuracies for the HD 286123 b exoplanet. Its pN gravitoelectric shift $\left\langleΔt_\mathrm{cj}^\mathrm{1pN}\right\rangle$ may become measurable, at least in principle, at a $\simeq 8\times 10^{-5}$ level of (formal) relative accuracy after about 30 years of continuous monitoring corresponding to about 1000 transits. Systematics like, e.g., confusing time standards, neglecting star spots, neglecting clouds, would likely deteriorate the actual accuracy. The method presented is general enough to be applied also to modified models of gravity.

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arXiv2022

Impact of Lorentz violation models on exoplanets dynamics

Many exoplanets were detected thanks to the radial velocity method, according to which the motion of a binary system around its center of mass can produce a periodical variation of the Doppler effect of the light emitted by the host star. These variations are influenced by both Newtonian and non-Newtonian perturbations to the dominant inverse-square acceleration; accordingly, exoplanetary systems lend themselves to test theories of gravity alternative to General Relativity. In this paper, we consider the impact of Standard Model Extension (a model that can be used to test all possible Lorentz violations) on the perturbation of radial velocity, and suggest that suitable exoplanets configurations and improvements in detection techniques may contribute to obtain new constraints on the model parameters.

astro-ph.EP↗

arXiv2022

Why the mean anomaly at epoch is not used in tests of non-Newtonian gravity?

The mean anomaly at epoch $η$ is one of the standard six Keplerian orbital elements in terms of which the motion of the two-body problem is parameterized. Along with the argument of pericenter $ω$, $η$ experiences long-term rates of change induced, among other things, by general relativity and several modified models of gravity. Thus, in principle, it may be fruitfully adopted together with $ω$ in several tests of post-Newtonian gravity performed with astronomical and astrophysical binary systems. This would allow to enhance the gravitational signature one is interested in and to disentangle some competing disturbing effects acting as sources of systematic bias. Nonetheless, for some reasons unknown to the present author, $η$ has never been used so far by astronomers in actual data reductions. This note aims to raise interest in the community about the possible practical use of such an orbital element or, at least, to induce experts in astronomical data processing to explicitly make clear if it is not possible to use $η$ for testing gravitational models and, in this case, why.

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arXiv2021

The impact of the spin-orbit misalignment and of the spin of B on the Lense-Thrirring orbital precessions of the Double Pulsar PSR J0737-3039A/B

In the Double Pulsar, the Lense-Thirring periastron precession $\dotω^\mathrm{LT}$ should be measured by the end of this decade. The analyses recently appeared in the literature rely upon a formula for $\dotω^\mathrm{LT,\,A}$ induced by the spin angular momentum ${\boldsymbol{S}}^\mathrm{A}$ of A valid if the orbital angular momentum $\boldsymbol{L}$ and ${\boldsymbol{S}}^\mathrm{A}$ are aligned, and neglecting $\dotω^\mathrm{LT,\,B}$ because of the smallness of ${\boldsymbol{S}}^\mathrm{B}$. The impact on $\dotω^\mathrm{LT,\,A}$ of the departures of the ${\boldsymbol{S}}^\mathrm{A}$-$\boldsymbol{L}$ geometry from the ideal alignment is calculated. With the current upper bound on the misalignment angle $δ_\mathrm{A}$ between them, the angles $λ_\mathrm{A},\,η_\mathrm{A}$ of ${\boldsymbol{S}}^\mathrm{A}$ are constrained within $85^\circ \lesssim λ_\mathrm{A}\lesssim 92^\circ,\, 266^\circ \lesssim η_\mathrm{A} \lesssim 274^\circ$. In units of $\dotω^\mathrm{GR}=16.89^\circ\,\mathrm{yr}^{-1}$, a range variation as little as $Δ\dotω^\mathrm{LT,\,A}\doteq\dotω^\mathrm{LT,\,A}_\mathrm{max} - \dotω^\mathrm{LT,\,A}_\mathrm{min} = 8\times 10^{-8}\,ω^\mathrm{GR}$ is implied. The experimental uncertainty $σ_{\dotω_\mathrm{obs}}$ in measuring the periastron rate with the SKA 1-mid telescope should become smaller by 2028-2030. Then, the spatial orientation of ${\boldsymbol{S}}^\mathrm{B}$ is constrained from the existing bounds on the misalignment angle $δ_\mathrm{B}$, and $\dotω^\mathrm{LT,\,B}\simeq 2\times 10^{-7}\,\dotω^\mathrm{GR}$ is correspondingly calculated. The error $σ_{\dotω_\mathrm{obs}}$ should become smaller at the transition from MeerKAT+ facility to SKA 1-mid around 2025. (Abridged)

gr-qc↗

arXiv2021

On the 2PN periastron precession of the Double Pulsar PSR J0737-3039A/B

One of the post-Keplerian (PK) parameters determined in timing analyses of several binary pulsars is the fractional periastron advance per orbit $k^\mathrm{PK}$. Along with other PK parameters, it is used in testing general relativity once it is translated into the periastron precession $\dotω^\mathrm{PK}$. It was recently remarked that the periastron $ω$ of PSR J0737--3039A/B may be used to measure/constrain the moment of inertia of A through the extraction of the general relativistic Lense-Thirring precession $\dotω^\mathrm{LT,\,A}\simeq -0.00060^\circ\,\mathrm{yr}^{-1}$ from the experimentally determined periastron rate $\dotω_\mathrm{obs}$ provided that the other post--Newtonian (PN) contributions to $\dotω_\mathrm{exp}$ can be accurately modeled. Among them, the 2PN one seems to be of the same order of magnitude of $\dotω^\mathrm{LT,\,A}$. An analytical expression of the total 2PN periastron precession $\dotω^\mathrm{2PN}$ in terms of the osculating Keplerian orbital elements, valid not only for binary pulsars, is provided elucidating the subtleties implied in correctly calculating it from $k^\mathrm{1PN}+k^\mathrm{2PN}$ and correcting some past errors by the present author. The formula for $\dotω^\mathrm{2PN}$ is demonstrated to be equivalent to that obtainable from $k^\mathrm{1PN}+k^\mathrm{2PN}$ by Damour and Schäfer expressed in the Damour-Deruelle (DD) parameterization. $\dotω^\mathrm{2PN}$ actually depends on the initial orbital phase, hidden in the DD picture, so that $-0.00080^\circ\,\mathrm{yr}^{-1} \leq\dotω^\mathrm{2PN}\leq -0.00045^\circ\,\mathrm{\,yr}^{-1}$. A recently released prediction of $\dotω^\mathrm{2PN}$ for \psrab\, is discussed.

gr-qc↗

arXiv2021

Perturbations of the orbital elements due to the magnetic-like part of the field of a plane gravitational wave

We focus on the secular changes of the orbital elements of a planet in the solar system, determined by the magnetic-like part of a gravitational wave field. Using Fermi coordinates we show that the total force acting on a test particle is made of two contributions: a gravito-electric one and a gravito-magnetic one. While the electric-like force has been thoroughly discussed in the past, the effect of the gravito-magnetic force, which depends on the velocity of the test particle, has not been considered yet. We obtain approximated results to some orders in the orbital eccentricity and show that these effects are much smaller than the corresponding gravito-electric ones.

gr-qc↗

arXiv2021

The impact of classical and General Relativistic obliquity precessions on the habitability of circumstellar neutron stars' planets

Recently, it has been shown that rocky planets orbiting neutron stars can be habitable under non unrealistic circumstances. If a distant, pointlike source of visible light such as a Sun-like main sequence star or the gravitationally lensed accretion disk of a supermassive black hole is present as well, possible temporal variations $Δ\varepsilon_\mathrm{p}(t)$ of the planet's axial tilt $\varepsilon_\mathrm{p}$ to the ecliptic plane should be included in the overall habitability budget since the obliquity determines the insolation at a given latitude on a body' s surface. I point out that, for rather generic initial spin-orbit initial configurations, general relativistic and classical spin variations induced by the post-Newtonian de Sitter and Lense-Thirring components of the field of the host neutron star and by its pull to the planetary oblateness $J_2^\mathrm{p}$ may induce huge and very fast variations of $\varepsilon_\mathrm{p}$ which would likely have an impact on the habitability of such worlds. In particular, for a planet's distance of, say, $0.005\,\mathrm{au}$ from a $1.4\,M_\odot$ neutron star corresponding to an orbital period $P_\mathrm{b}=0.109\,\mathrm{d}$, obliquity shifts $Δ\varepsilon_\mathrm{p}$ as large as $\varepsilon^\mathrm{max}_\mathrm{p}-\varepsilon_\mathrm{p}^\mathrm{min}\simeq 50^\circ-100^\circ$ over characteristic timescales as short as $10\,\mathrm{d}$ ($J_2^\mathrm{p}$) to $3\,\mathrm{Myr}$ (Lense-Thirring) may occur for arbitrary orientations of the orbital and spin angular momenta $\boldsymbol{L},\,{\boldsymbol{S}}_\mathrm{ns},\,{\boldsymbol{S}}_\mathrm{p}$ of the planet-neutron star system. In view of this feature of their spins, I dub such hypothetical planets as ``nethotrons".

gr-qc↗

arXiv2021

The effect of post-Newtonian spin precessions on the evolution of exomoons' obliquity

Putative natural massive satellites (exomoons) has gained increasing attention, where they orbit Jupiter-like planets within the habitable zone of their host main sequence star. An exomoon is expected to move within the equatorial plane of its host planet, with its spin ${\boldsymbol S}_\mathrm{s}$ aligned with its orbital angular momentum $\boldsymbol L$ which, in turn, is parallel to the planetary spin ${\boldsymbol S}_\mathrm{p}$. If, in particular, the common tilt of such angular momenta to the satellite-planet ecliptic plane, assumed fixed, has certain values, the latitudinal irradiation experienced on the exomoon from the star may allow it to sustain life as we know it, at least for certain orbital configurations. An Earth--analog (similar in mass, \textcolor{black}{radius, oblateness} and obliquity) is considered, which orbits within $5-10$ planetary radii $R_\mathrm{p}$ from its Jupiter-like host planet. The de Sitter and Lense--Thirring spin precessions due to the general relativistic post-Newtonian (pN) field of the host planet have an impact on an exomoon's habitability for a variety of different initial spin-orbit configurations. Here, I show it by identifying long--term variations in the satellite's obliquity $\varepsilon_\mathrm{s}$, where variations can be $\lesssim 10^\circ-100^\circ$, depending on the initial spin-orbit configuration, with a timescale of $\simeq 0.1-1$ million years. Also the satellite's quadrupole mass moment $J_2^\mathrm{s}$ induces obliquity variations which are faster than the pN ones, but do not cancel them.

astro-ph.EP↗

arXiv2021

Post-Keplerian obliquity variations and the habitability of rocky planets orbiting fast spinning, oblate late M dwarfs

A couple of dozen Earth-like planets orbiting M dwarfs have been discovered so far. Some of them have attracted interest because of their potential long-term habitability; such a possibility is currently vigorously debated in the literature. I show that post-Keplerian (pK) orbit precessions may impact the habitability of a fictitious telluric planet orbiting an oblate late-type M dwarf of spectral class M9V with $M_\star=0.08\,M_\odot$ at $a=0.02\,\mathrm{au}$, corresponding to an orbital period $P_\mathrm{b}\simeq 4\,\mathrm{d}$, inducing long-term variations of the planetary obliquity $\varepsilon$ which, under certain circumstances, may not be deemed as negligible from the point of view of life's sustainability. I resume the analytical orbit-averaged equations of the pK precessions, both classical and general relativistic, of the unit vectors $\boldsymbol{\hat{S}},\,\boldsymbol{\hat{h}}$ of both the planet's spin and orbital angular momenta $\boldsymbol S,\,\boldsymbol{L}$ entering $\varepsilon$, and numerically integrate them by producing time series of the pK changes $Δ\varepsilon(t)$ of the obliquity. For rapidly rotating M dwarfs with rotational periods of the order of $P_\star \simeq 0.1-1\,\mathrm{d}$, the planet's obliquity $\varepsilon$ can undergo classical pK large variations $Δ\varepsilon(t)$ up to tens of degrees over timescales $Δt \simeq 20-200\,\mathrm{kyr}$, depending on the mutual orientations of the star's spin ${\boldsymbol J}_\star$, of $\boldsymbol S$, and of $\boldsymbol L$. Instead, $Δ\varepsilon(t)$ are $\lesssim 1-1.5^\circ$ for the planet b of the Teegarden's Star. In certain circumstances, the M dwarf's oblateness $J_2^\star$ should be considered as one of the key dynamical features to be taken into account in compiling budgets of the long-term habitability of rocky planets around fast spinning late M dwarfs. (Abridged)

gr-qc↗