Accurate Measurement in the Field of the Earth of the General-Relativistic Precession of the LAGEOS II Pericenter and New Constraints on Non-Newtonian Gravity

Abstract

The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the Newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein's theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α| 1 · 10 −11 , a huge improvement at a range of about 1 Earth radius.PACS numbers: 04.80. Cc, 91.10.Sp, 95.10.Eg, 95.40.+s Tests for Newtonian gravity and for a possible violation of the weak equivalence principle are strongly related and represent a powerful approach in order to validate Einstein's theory of general relativity (GR) with respect to alternative theories of gravity and to tune, from the experimental point of view, gravity itself into the realm of quantum physics. Moreover, new long range interactions (NLRIs) may be thought of as the residual of a cosmological primordial scalar field related with the inflationary stage (dilaton scenario) [1]. Twenty-four years ago, the possibility of a fifth force of nature prompted new experimental investigation of possible deviations from the gravitational inverse-square law [2]. In fact, the deviations from the usual 1/r law for the gravitational potential would lead to new weak interactions between macroscopic objects.Interestingly, these supplementary interactions may be either consistent with Einstein's equivalence principle or not. In this second case, nonmetric phenomena will be produced with tiny, but significant, consequences in the gravitational experiments [3]. The feature of such interactions, which are predicted by several theories, is to produce deviations for separations of masses ranging through several orders of magnitude, starting from the submillimeter level up to the astronomical scale. Among the various techniques useful for the search of this additional physics to the various scales, the accurate measurement of the pericenter shift of binary systems may be used to test for a NLRI with a characteristic range comparable with the system semimajor axis [4].These very weak NLRI are usually described by means of a Yukawa-like potential with strength α and range λ and transmitted by a field of very small mass µ = /λc. If G ∞ represents the gravitational constant, M ⊕ and m s the mass of the primary body and of the satellite, r their separation, c the speed of light and the reduced Planck constant, we can write:where the strength α depends both on the mass-energy content of the sources and on their coupling strengths, K ⊕ and K s , respectively.In...

Constraints from orbital motions around the Earth of the environmental fifth-force hypothesis for the OPERA superluminal neutrino phenomenology

“…It can be noted that there is an improvement of 2 − 5 orders of magnitude with respect to Figure 1 of [55], Figure 1 of [35], and Figure 4 of [39]; see also Figure 1 of [57]. Lucchesi and Peron [72], using the approximate analytical results by [40] and a data record 13 yr long for LAGEOS II, claim |α| ≤ 9.9× 10 −12 at λ = 1 R e . However, such a figure should be considered just as a preliminary result coming from the statistical errors of the linear fitting of the post-fit numerically integrated residuals of the perigee since, as pointed out by Lucchesi and Peron themselves [72], it does not include an analysis of the systematic errors due to the uncertainties in the zonals' geopotential.…”

“…However, such a figure should be considered just as a preliminary result coming from the statistical errors of the linear fitting of the post-fit numerically integrated residuals of the perigee since, as pointed out by Lucchesi and Peron themselves [72], it does not include an analysis of the systematic errors due to the uncertainties in the zonals' geopotential. Lucchesi and Peron [72] used the GRACE-only model EIGEN-GRACE02S [73], which released a calibrated σ C 2,0 = 5.304 × 10 −11 . Moreover, Lucchesi and Peron [72] did not explicitly include a Yukawa-like fifth force in the dynamical models fitted to the data of LAGEOS II, by assuming that it would entirely be accounted for by their numerically integrated residuals of the perigee.…”

“…Lucchesi and Peron [72], using the approximate analytical results by [40] and a data record 13 yr long for LAGEOS II, claim |α| ≤ 9.9× 10 −12 at λ = 1 R e . However, such a figure should be considered just as a preliminary result coming from the statistical errors of the linear fitting of the post-fit numerically integrated residuals of the perigee since, as pointed out by Lucchesi and Peron themselves [72], it does not include an analysis of the systematic errors due to the uncertainties in the zonals' geopotential. Lucchesi and Peron [72] used the GRACE-only model EIGEN-GRACE02S [73], which released a calibrated σ C 2,0 = 5.304 × 10 −11 .…”

“…Lucchesi and Peron [72] used the GRACE-only model EIGEN-GRACE02S [73], which released a calibrated σ C 2,0 = 5.304 × 10 −11 . Moreover, Lucchesi and Peron [72] did not explicitly include a Yukawa-like fifth force in the dynamical models fitted to the data of LAGEOS II, by assuming that it would entirely be accounted for by their numerically integrated residuals of the perigee. A similar approach with the LAGEOS satellite was followed by March et al [74] in constraining other non-Newtonian putative effects.…”

Effects of non-Newtonian gravity on the properties of strange stars

“…In order to have a better understanding of nonNewtonian gravity, many investigations have been dedicated to study its possible existence and properties (Eckhardt et al 1988;Kamyshkov et al 2008;Gudkov et al 2011;Boynton et al 2014) and constrain its strength parameter from experimental researches (Geraci et al 2008;Lucchesi & Peron 2010;Biedermann et al 2015). In addition, this issue has attracted a great deal of attention in a nuclear physics context, for instance, it has strong effects on finite nuclei (Xu et al 2013), dark matter (Schmidt 1990), nuclear matter (Wen et al 2009;Zhang et al 2011), and neutron star processes (Sulaksono et al 2011;Wen & Zhou 2013).…”