The lingering anomalous secular increase of the eccentricity of the orbit of the Moon: further attempts of explanation of cosmological origin

A new analysis of extended data records collected with the Lunar Laser Ranging (LLR) technique performed with improved tidal models was not able to resolve the issue of the anomalous rate $\dot e$ of the eccentricity $e$ of the orbit of the Moon, which is still in place with a magnitude of $\dot e=(5\pm 2)\times 10^{-12}$ yr$^{-1}$. Some possible cosmological explanations are offered in terms of the post-Newtonian effects of the cosmological expansion, and of the slow temporal variation of the relative acceleration rate $\ddot{S} S^{-1}$ of the cosmic scale factor $S$. None of them is successful since their predicted secular rates of the lunar eccentricity are too small by several orders of magnitude.Comment: LaTex2e, 4 pages, no figures, no tables. Accepted for publication in Galaxie

Astronomical constraints on some long-range models of modified gravity

In this paper we use the corrections to the usual Newton-Einstein secular precessions of the perihelia of the inner planets of the Solar System, phenomenologically estimated as solve-for parameters by the Russian astronomer E.V. Pitjeva by fitting almost one century of data with the EPM2004 ephemerides, in order to constrain some long-range models of modified gravity recently put forth to address the dark energy and dark matter problems. The models examined here are the four-dimensional ones obtained with the addition of inverse powers and logarithm of some curvature invariants, and the multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP). After working out the analytical expressions of the secular perihelion precessions induced by the corrections to the Newtonian potential of such models, we compare them to the estimated corrections to the rates of perihelia by taking their ratio for different pairs of planets instead of using one perihelion at a time for each planet separately, as done so far in literature. As a result, the curvature invariants-based models are ruled out, even by re-scaling by a factor 10 the errors in the planetary orbital parameters estimated by Pitjeva. Less neat is the situation for the DGP model. Only the general relativistic Lense-Thirring effect, not included, as the other exotic models considered here, by Pitjeva in the dynamical force models used in the estimation process, passes such a test. It would be important to repeat the present analysis by using corrections to the precessions of perihelia independently estimated by other teams of astronomers as well, but, at present, such rates are not yet available.Comment: Latex, 13 pages, no figures, 1 table. Other references added. Minor stylistic changes. To appear in AHEP (Advances in High Energy Physics). Typo corrected in eq. 6: thanks to G.E. Melk

Commentary to "LARES successfully launched in orbit: Satellite and mission description" by A. Paolozzi and I. Ciufolini

We comment on some statements in a recent paper by Paolozzi and Ciufolini concerning certain remarks raised by us on the realistic accuracy obtainable in testing the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the newly launched LARES satellite together with the LAGEOS and LAGEOS II spacecraft in orbit for a long time. The orbital configuration of LARES is different from that of the originally proposed LAGEOS-3. Indeed, while the latter one should have been launched to the same altitude of LAGEOS (i.e. about $h_{\rm L}=5890$ km) in an orbital plane displaced by $180$ deg with respect to that of LAGEOS ($I_{\rm L}=110$ deg, $I_{\rm L3}=70$ deg), LARES currently moves at a much smaller altitude (about $h_{\rm LR}=1440$ km) and at a slightly different inclination ($I_{\rm LR} = 69.5$ deg). As independently pointed out in the literature by different authors, the overall accuracy of a LARES-LAGEOS-LAGEOS II Lense-Thirring test may be unfavorably \textcolor{black}{impacted} by the lower altitude of LARES with respect to the expected $\approx 1$ level claimed by Ciufolini \textit{et al.} because of an enhanced sensitivity to the low-degree even zonal geopotential coefficients inducing orbital precessions competing with the relativistic ones. Concerning the previous tests performed with the combined nodes of only LAGEOS and LAGEOS II, an independent analysis recently appeared in the literature indirectly confirms that the total uncertainty in them is likely far from being as little as $10$.Comment: LaTex2e, 5 pages, no tables, no figures, 10 reference

Constraining the Preferred-Frame α1\alpha_1, α2\alpha_2 parameters from Solar System planetary precessions

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the PPN parameters $\alpha_1$, $\alpha_2$. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a-priori bias of unmodelled/mismodelled standard effects such as the general relativistic Lense-Thirring precessions and the classical rates due to the Sun's oblateness $J_2$, allows to infer $|\alpha_1| \leq 6\times 10^{-6}, |\alpha_2| \leq 3.5\times 10^{-5}$. Such bounds should be improved in the near future after processing the data that are being collected by the MESSENGER spacecraft, currently orbiting Mercury. Further improvements may come in the mid-future from the approved BepiColombo mission to Mercury. The constraint $|\alpha_2|\leq 10^{-7}$ existing in the literature is critically discussed (Abridged).Comment: LaTex2e, 39 pages, 2 figures, 2 tables, 97 references. Matching the version at press in International Journal of Modern Physics D (IJMPD

A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation, or Sun/Earth Mass Losses?

Given a solar luminosity L_Ar = 0.75 L_0 at the beginning of the Archean 3.8 Gyr ago, where L_0 is the present-day one, if the heliocentric distance r of the Earth was r_Ar = 0.956 r_0, the solar irradiance would have been as large as I_Ar = 0.82 I_0. It would allowed for a liquid ocean on the terrestrial surface which, otherwise, would have been frozen, contrary to the empirical evidence. By further assuming that some physical mechanism subsequently displaced the Earth towards its current distance in such a way that the irradiance stayed substantially constant over the entire Archean from 3.8 Gyr to 2.5 Gyr ago, a relative recession rate as large as \dot r/r \simeq 3.4 x 10^-11 yr^-1 would have been required. Although such a figure is roughly of the same order of magnitude of the value of the Hubble parameter 3.8 Gyr ago H_Ar = 1.192 H_0 = 8.2 x 10^-11 yr^-1, standard general relativity rules out cosmological explanations for the hypothesized Earth' s recession rate. Instead, a class of modified theories of gravitation with nonminimal coupling between the matter and the metric naturally predicts a secular variation of the relative distance of a localized two-body system, thus yielding a potentially viable candidate to explain the putative recession of the Earth' s orbit. Another competing mechanism of classical origin which could, in principle, allow for the desired effect is the mass loss which either the Sun or the Earth itself may have experienced during the Archean. On the one hand, this implies that our planet should have lost 2% of its present mass in the form of eroded/evaporated hydrosphere which, thus, should have been two orders of magnitude larger than now. On the other hand, it is widely believed that the Sun could have lost mass at an enhanced rate due to a stronger solar wind in the past for not more than \sim 0.2-0.3 Gyr.Comment: LaTex2e, 18 pages, no tables, 1 figure, 79 references. Accepted for publication in Galaxie

Orbital effects of Lorentz-violating Standard Model Extension gravitomagnetism around a static body: a sensitivity analysis

We analytically work out the long-term rates of change of the six osculating Keplerian orbital elements of a test particle acted upon by the Lorentz-violating gravitomagnetic acceleration due to a static body, as predicted by the Standard Model Extension (SME). We neither restrict to any specific spatial orientation for the symmetry-violating vector s nor make a priori simplifying assumptions concerning the orbital configuration of the perturbed test particle. Thus, our results are quite general, and can be applied for sensitivity analyses to a variety of specific astronomical and astrophysical scenarios. We find that, apart from the semimajor axis a, all the other orbital elements undergo non-vanishing secular variations. By comparing our results to the latest determinations of the supplementary advances of the perihelia of some planets of the solar system we preliminarily obtain s_x = (0.9 +/- 1.5) 10^-8, s_y = (-4 +/- 6) 10^-9, s_z = (0.3 +/- 1) 10^-9. Bounds from the terrestrial LAGEOS and LAGEOS II satellites are of the order of s\sim 10^-3-10^-4.Comment: LaTex2e, 9 pages, no figures, 3 tables, 25 references. Typos fixe