The Galileo satellites Doresa and Milena and their goals in the field of fundamental physics within the Galileo for science (G4S_2.0) project

The G4S_2.0 (Galileo for Science) project is a new proposal funded by the Italian Space Agency (ASI) and aims to perform a set of measurements in the field of Fundamental Physics with the two Galileo satellites DORESA and MILENA. Indeed, the accurate analysis of the orbits of these satellites — characterized by a relatively high eccentricity of about 0.16 — and of their clocks — the most accurate orbiting the Earth — allows to test relativistic gravity by comparing the predictions of Einstein's theory of General Relativity with those of other theories of gravitation. After a general introduction to the project objectives, we will present the preliminary activities of G4S_2.0 which are being developed by IAPS-INAF in Rome. The results of G4S_2.0 will be particularly useful for the applications of the Galileo FOC satellites in the fields of space geodesy and geophysics as some of these activities will concern the improvement of the precise orbit determination of the satellites through an enhancement of the dynamic model of their orbits, analyzing, in particular, the modelling of non-conservative forces

The SaToR-G experiment: testing metric and non-metric theories of gravity in the Earth’s field via laser tracking to geodetic satellites

Satellite Tests of Relativistic Gravity (SaToR-G) is a new experiment in fundamental physics of the National Scientific Committee 2 (CSN2) of the Italian National Institute for Nuclear Physics (INFN). The experiment aims at testing gravitation beyond the predictions of Einstein’s Theory of General Relativity in its weak-field and slow-motion limit, searching for effects foreseen by alternative theories of gravitation and possibly connected with ‘’new physics’’. The predictions of General Relativity on the orbits of geodetic satellites, which play the role of test masses, will be compared with those of alternative theories of gravity both metric and non-metric in their essence. This will allow to test, in addition to other aspects of gravita tion, the field equation of gravity. The natural theoretical framework to test gravitation will be that of the Parameterized Post-Newtonian (PPN) formalism. However, we will also try to apply, as far as possible, the approach suggested by R. H. Dicke more than 50 years ago, usually referred to as the Dicke framework. This is a fairly general framework that allows us to conceive experiments not connected, a priori, with a given physical theory and also provides a way to analyze the results of an experiment under primary hypotheses. The activities of the experiment related to the development of perturbative models to better determine the dynamics of the orbits of the considered satellites will be presented together with preliminary results on possible new constraints to alternative theories of gravitation

The Galileo for science (G4S_2.0) project: fundamental physics experiments with the Galileo satellites Doresa and Milena

G4S_2.0 is a new project funded by the Italian Space Agency which aims to perform measurements in the field of Fundamental Physics with the two satellites DORESA and MILENA of the Galileo-FOC constellation. These satellites are characterized by the high eccentricity of their orbits and the accuracy of their atomic clocks. An accurate orbit determination will allow to carry out a series of measurements in the fields of gravitation and cosmology, and the implementation of an inverse relativistic positioning system. After a general introduction to the main objectives of G4S_2.0, the activities developed at IAPS-INAF in Rome will be presented

First results in testing gravity theories with SatoR-G

The main goal of the SaToR-G (Satellite Test of Relativistic Gravity) experiment is to test and verify gravity beyond the predictions of General Relativity (GR) by focusing on possible effects connected with "new physics" and foreseen by different alternative theories of gravitation. These theories may be both metric and non-metric in their consequences. This objective can be achieved by means of a Precise Orbit Determination of the two LAGEOS and LARES satellites based on an improved dynamical model of their orbits. This implies to consider these passive geodetic satellites as "quasi-ideal" proof masses and measuring the deviation of their trajectory from the pure geodesic motion predicted by GR. A very interesting aspect is represented by the possible existence of a new long-range interaction. This kind of effect in gravitation has some importance since it cannot be interpreted within the standard Parametrized Post-Newtonian formalism currently used in the weak-field and slow-motion limit of GR. Indeed, deviations of the gravitational potential from the Newtonian law would lead to new weak interactions between macroscopic objects that are predicted by several theories of gravity. For these theories, a Yukawa-like parameterization seems general at the lowest order of the interaction and in the non-relativistic limit, independently of the nature of the new field that contributes to mediate the gravitational interaction, that is, of a possible scalar, vector or tensor field. We first introduce the constraint on a Yukawa-like long-range force obtained in the case of LAGEOS II from a precise and accurate analysis of the long-term behavior of its orbit. We then show the possible constraints to alternative theories of gravitation that can be further deduced from this result

On the long-term behavior of LAGEOS II semi-major axis and thermal thrust perturbations

We analyzed the orbit residuals of the two LAGEOS (LAser GEOdynamic Satellite) satellites and of LARES (LAser RElativity Satellite) after modeling the main gravitational and non-gravitational perturbations acting on their orbits. The purpose of this activity is to study the residuals in the different Keplerian elements and then comparing them with the predictions of the non-conservative force models -- not included in the a priori models used for the Precise Orbit Determination -- which we are developing with the aim of improving the global dynamic model of the orbits of these satellites. Among these non-conservative forces there are those related to the thermal thrust produced by the pressure of solar and terrestrial (albedo and infrared) radiations. Due to the thermal inertia of the different elements that make up the surface of these passive satellites, as for that linked to their cube corner retroreflectors, a non-uniform distribution of temperature on their surface originates, which causes an anisotropic emission of radiation with significant long-term effects on different orbital elements. The different weight of these forces, strictly influenced by the rotational state of the satellites -- both in orientation and in rate -- seems to be the main cause of the inversion observed in the decay of the semi-major axis of the LAGEOS II starting from mid-March 2012, approximately 19 years after the launch of the satellite. This behavior, apparently unexpected and far from its previous interpretation, will be described and discussed in the light of the thermal thrust and spin models of the satellite that we have developed. This study and research activity is part of a broader activity in the field of fundamental physics that aims to use these geodetic satellites as proof masses to test and compare the predictions of General Relativity with those of other alternative theories of gravitation in the context of the SaToR-G (Satellite Test of Relativistic Gravity) experiment

Thermal thrust perturbations, spin evolution and the long-term behavior of LAGEOS II semi-major axis

Understanding the effects of Non-Gravitational Perturbations (NGPs) has characterized the study of the dynamic model of LAGEOS satellites since their launch. These passive geodetic satellites, tracked by the Satellite Laser Ranging technique, are the most extensively studied so far in the literature for the development of ad-hoc perturbative models. Besides their significant applications in geodesy and geophysics, this is related to the numerous measurements and investigations that have characterized these satellites in the field of gravitational physics and the verification of the predictions of General Relativity. Among the numerous NGPs, thermal thrust forces arise as a consequence of a non uniform distribution of temperature across the surface of the satellite. This temperature distribution is responsible for an anisotropic emission of radiation with also significant long-term effects on the orbital elements. These effects are produced by the pressure of solar and terrestrial radiations (albedo and infrared). The different importance of these forces, strictly influenced by the rotational state of the satellites ⎯ both in orientation and in rate ⎯ seems to be the main cause of the inversion observed in the decay of the semi-major axis of LAGEOS-II starting from mid-March 2012, approximately 19 years after its launch. This behavior, apparently unexpected and far from its previous interpretation, will be described and discussed in light of the thermal thrust and spin models of the satellite that we have developed and compared with Precise Orbit Determination results. This research is part of a broader activity in the field of fundamental physics, aiming to use geodetic satellites as proof masses to test and compare the predictions of General Relativity with those of other alternative theories of gravitation, in the context of the project SaToR-G (Satellite Test of Relativistic Gravity)

Fundamental physics results in testing gravitation with laser-ranged satellites: the LARASE and SaToR-G experiments

Launched into orbit in 1976 and 1992 respectively, the two satellites LAGEOS (NASA) and LAGEOS II (ASI/NASA) have up to now constituted two very precious sources of scientific results thanks to the precise laser tracking of their orbits. Space geodesy, geophysics and gravitational physics have been extensively studied with their tracking and modeling of their orbits, but also space-to-ground quantum communication has been successfully verified. Several research teams and institutions have exploited the orbits of these satellites ⎯ and more recently with the inclusion of the LARES satellite (ASI-2012) ⎯ for tests of General Relativity and other theories of gravitation. We will present the results obtained in this field of fundamental physics from two Italian projects called LARASE (2013-2019) and SaToR-G (2020-2024), funded by the National Scientific Commission II of the National Institute for Nuclear Physics (INFN)

The Galileo for science (G4S_2.0) project: a new concept of accelerometer for future Galileo satellites

The G4S_2.0 project, funded by the Italian Space Agency (ASI), aims to test fundamental physics in the field of the Earth by using the satellites of the Galileo FOC Constellation. Three Italian research centers are involved in the project: ASI-CGS in Matera, Politecnico di Torino and IAPS-INAF in Rome which is the project lead institution. We will present one of the ongoing activities at IAPS-INAF, regarding the development of a new accelerometer for a next generation of Galileo satellites. As well known in the literature of the Global Navigation Satellite Systems (GNSS), the precise modeling of the Non-Gravitational Perturbations (NGPs) represents today the most important challenge for a further and significant improvement of the Precise Orbit Determination (POD) of all navigation satellites and, consequently, of all products that can be obtained from the analysis of the orbits and clocks of the satellites of the GNSS. Indeed, the suboptimal modeling of the direct Solar Radiation Pressure (SRP) ⎯ the largest NGPs on the orbit of Galileo FOC satellites and in general of all navigation satellites ⎯ is currently the main source of error in determining their orbit. The complex shape of these satellites (bus and wings) combined with their particular attitude law ⎯ which requires the face of the satellite that collects the different antennas continuously pointsto the nadir while the face near the atomic clocks points to the deep space and at the same time the array of solar panels must continuously point towards the Sun for energy reasons ⎯ make the modeling of this perturbation and its optimal insertion into the POD process a non-trivial issue. Consequently, the capability to perform direct measurement, by means of an onboard accelerometer, of the accelerations produced by the complex and subtle non-gravitational forces acting on the satellite's surfaces is considered an extremely important and significant system improvement for the direct impact it would have on the accuracy of the POD of satellites and on the products that the GNSS community derives from it in the fields of positioning, timing, geophysics and fundamental physics. We will present the main characteristics of the accelerometer concept under development, giving an overview of its working principle and expected measurement performance. Furthermore, we will introduce a methodology to remove the thermal disturbances on the accelerometer readings at low frequencies

Measurement in the field of gravitation of the Galileo for science project

The Galileo for Science (G4S 2.0) project, funded by the Italian Space Agency (ASI), aims to perform a set of gravitational measurements with the two Galileo satellites GSAT-0201 (Doresa) and GSAT-0202 (Milena) exploiting the relatively high eccentricity of their orbits with respect to that of the other satellites of the Full Operational Capability (FOC) constellation. These two satellites have been already used in 2018 by both ZARM and SYRTE for a new measurement of the gravitational redshift (GRS) that has improved the 1976 measurement of Gravity Probe A by a factor between 4 and 6 respectively. In fact, from an accurate analysis of the orbits and clocks of these two Galileo satellites, a set of relativistic tests can be performed with the objectives of comparing the predictions of Einstein’s theory of General Relativity with those of other gravitational theories concerning, mainly, the motion of a test particle along a geodesic of space-time and the time dilation of the on-board clocks. Three Italian research institutes are involved in G4S 2.0: Center for Space Geodesy (ASI-CGS) in Matera, Istituto di Astrofisica e Planetologia Spaziali (IAPS-INAF) in Roma and Politecnico (POLITO) in Torino. We will present some of the ongoing activities at IAPS-INAF in the field of tests and measurements of gravitational interaction. Among these, the possibility of measuring the relativistic precessions of the orbits of the satellites, the constraints on a possible long-range force at a scale comparable to the semi-major axis of the satellite orbit and, consequently, on the validity of the Newtonian inverse square law and, finally, on the validity of the Local Position Invariance (i.e., a measurement of the GRS), that is one of the three ingredients that constitute, in its modern conception, Einstein’s Principle of Equivalence. A key aspect, to perform such measurements in the field of fundamental physics, is to improve the dynamic model for the non-conservative forces acting on the Galileo FOC satellites, starting from that of the solar radiation pressure, the largest non-gravitational perturbation on navigation satellite

The Galileo for science (G4S 2.0) project: precise orbit determination for fundamental physics experiments with the Galileo satellites Doresa and Milena.

G4S 2.0 is a new project funded by the Italian Space Agency which aims to perform measurements in the field of Fundamental Physics with the two satellites DORESA (E18) and MILENA (E14) of the Galileo-FOC constellation. These satellites, as the others of the constellation, have onboard accurate atomic clocks, but are characterized by an orbit with high eccentricity. After a general introduction to the main objectives of the G4S 2.0 project, the preliminary activities developed at IAPS-INAF in Rome regarding the Precise Orbit Determination (POD) of the satellites will be presented. The PODs will be performed with two different codes, GEODYN II (NASA/GSFC) and BERNESE (AIUB), with the main aimof performing measurements of the relativistic precession of the orbits and a new accurate measurement of the gravitational redshift. In particular, an accurate measurement of the overall precession of the pericenter of the orbit allows to verify the validity of the inverse square law of the distance for the gravitational interaction on a characteristic scale of about 14000 km