The renewed interest in lunar exploration and the development of future lunar communication and navigation services highlight the need for a precise, stable, and interoperable geodetic and timing infrastructure on the Moon. NovaMoon, proposed as a scientific and navigation payload for ESA's Argonaut lander, is designed as a lunar-based local differential, geodetic, and timing station supporting both operational needs in the Moon's south polar region and a broad range of scientific investigations. The payload integrates a lunar laser retroreflector, a Very Long Baseline Interferometry transmitter, a receiver for navigation signals compatible with LunaNet standards, high-stability atomic clocks, and direct-to-Earth radio links – making it the first lunar station to co-locate multiple ranging, tracking, and timing techniques. NovaMoon will enable sub-metre to decimetre positioning, provide local differential corrections for lunar users, and ensure an accurate and stable realisation of position and time. Preliminary simulation studies show that this multi-technique dataset improves the lunar reference frame, orientation and ephemerides, and estimates of interior parameters like tidal response and core properties. NovaMoon will also provide the first long-duration physical realisation of a lunar time reference. Beyond its primary goals, it supports improved cartography, precise surface geolocation, and higher-resolution topography, contributing to safer landings and operations. It also enables new tests of fundamental physics, including constraints on relativity and possible deviations from classical gravity.

Violations of Lorentz invariance, a cornerstone of modern physics, are predicted by theories of quantum gravity and by extensions of general relativity involving new vector or tensor fields. In the weak-field limit, such a violation would primarily manifest as a nonzero value for the post-Newtonian parameter α_{1}, which is identically zero in general relativity. We present a new test of local Lorentz invariance by searching for this signature in the orbits of the LAGEOS and LAGEOS II satellites. By applying a phase sensitive detection technique to the mean argument of latitude, derived from about 30 years of satellite laser ranging data, we isolate the periodic signal potentially induced by a preferred reference frame aligned with the cosmic microwave background. Our analysis yields a new constraint |α_{1}|∼2×10^{-5}. This result improves upon the previous best limit from lunar laser ranging and provides the most stringent constraint to date on preferred-frame effects in Earth's gravity.

Strong theoretical arguments suggest that a breakdown of Lorentz Invariance could arise under some very particular conditions. From an experimental point of view, it is important to test the Local Lorentz Invariance with ever greater precision and in all contexts, regardless of the theoretical motivation for the possible violation. In this paper we discuss some aspects of the gravitational sector. Tests of Lorentz Invariance in the context of gravity are difficult and rare in the literature. Possible violations could arise from quantum physics applied to gravity or the presence of vector and tensor fields mediating the gravitational interaction together with the metric tensor of General Relativity. We present our results in the latter case. We analyzed the orbit of the LAGEOS and LAGEOS II satellites over a period of almost three decades. The effects of the possible preferred frame represented by the cosmic microwave background radiation on the mean argument of latitude of the satellites orbit were considered. These effects would manifest themselves mainly through the post-Newtonian parameter α_1, a parameter that has a null value in General Relativity. We constrain this parameterized post-Newtonian parameter down to the level of α_1 ≤ 2×10^-5, improving a previous limit obtained through the Lunar Laser Ranging technique.

High-accuracy measurement systems operating in complex operational environments, such as airborne and seaborne gravimetry, are severely affected by interacting external influences (disturbances) including temperature variations, inertial accelerations, and platform rotations. This work aims to develop and prove a general method for compensating such disturbances beyond the limits of conventional approaches. We present a general framework based on three pillars: a multi-sensor system, supervised machine learning, and a dedicated laboratory -training platform-. This measurement technique was investigated through two experimental case studies relevant to airborne and seaborne gravimetry: (i) temperature and thermal-gradient rejection in a high-sensitivity tri-axial accelerometer, and (ii) pitch and roll rejection for vertical acceleration estimation. The experiments highlighted that, although the general framework provides a useful guideline, its application to airborne and seaborne gravimetry is challenging and not straightforward, requiring the development of dedicated and innovative experimental solutions. This difficulty arises from the specific nature of the measurand-gravity-which cannot be easily varied under controlled conditions. In this work, we present a dedicated approach to addressing these challenges.

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band – a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in highly eccentric Earth orbits (e ≳ 0.7, period P ≳ 33 h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the μHz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of GM_⊕ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

The Italian Spring Accelerometer (ISA) is a three axis mass-spring accelerometer, one of the payloads of the BepiColombo joint space mission between the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA). At launch in October 2018, BepiColombo started its seven-year cruise as a stack of three different modules, overall named Mercury Composite Spacecraft (MCS). The spacecraft will provide BepiColombo the necessary Delta V to reach Mercury with its electric thrusters and along with one, two and six gravity assists, respectively with Earth, Venus and Mercury. The accelerometer is accommodated on the Mercury Planetary Orbiter (MPO) module and, jointly with the Ka-band Transponder (KaT) tracking data, will primarily serve the BepiColombo Radio Science Experiment (BC-RSE). During the second Venus swing-by, strong tidal effect and external perturbations was expected to act on the spacecraft and to become detectable by ISA. The swing-by had a closest approach of about 550 km and the gravity gradient expected on the IDA sensing elements was perfectly measured. Hence, in this paper, the first direct Gravity Gradient effect detection generated by an extraterrestrial body is shown. Nevertheless, around the closest approach, the measurements evidenced a spurious acceleration event lasting for several minutes. This work, exploiting information on the Attitude and Orbit Control System (AOCS) commanded torques, focuses and analyses this ISA acceleration signal, ascribing it to a net force really acting on the MCS spacecraft. Furthermore, using an estimation method, the application point of the force is confined to an area close to the MPO radiator.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and has several goals in the field of Fundamental Physics to be achieved by exploiting the satellites of the Galileo-FOC Constellation. In this regard, a key point is to obtain a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD). To this purpose modeling in a reliable way the complex effects of the Non-Conservative Forces, i.e. of Non-Gravitational Perturbations (NGPs), is essential. The activities undertaken in the construction of a Box-Wing model and of a Finite Element Model of the satellite will be presented with the preliminary results obtained by including these models into the POD of the Galileo satellites. In particular, using the orbital element residuals obtained from a POD we can test our new models and the improvements in POD quality.

The Galileo for Science Project (G4S_2.0) is funded by the Italian Space Agency and hasseveral goals in the field of Fundamental Physics to be achieved by exploiting the satellitesof the Galileo-FOC Constellation and the accuracy of their onboard atomic clocks. Inparticular, the clock-bias, estimated in the data reduction of the tracking observationsallows to place constraints on the possible presence of Dark Matter in our galaxy in theform of Domain Walls (DW) eventually produced in the very early Universe by ultralightscalar field(s). The impact of the DW on an atomic clock would provide a delta-liketransient shift on the pseudo-derivative of the clock-bias. Such signal depends both on thenature of the clock and the characteristics of the ultralight scalar comprising the DW.Ongoing work on the clock-bias will be introduced as regards to data pre-processing andsimulations on false alarm and detection efficiency.

The Galileo for Science Project (G4S_2.0) is an ongoing project funded by the Italian Space Agency that has several goals in the field of Fundamental Physics by exploiting the Galileo-FOC Constellation and, in particular, GSAT0201 (E18) and GSAT0202 (E14), the two satellite in elliptical orbit. By exploiting the accuracy of the atomic clocks on board the satellites, in particular of the clock-bias estimated in the process of data reduction of the tracking observations during a Precise Orbit Determination (POD), it allows on the one hand to measure the gravitational redshift, constraining the Local Position Invariance (LPI) and, on the other hand, to place constraints on the possible presence of dark matter in our galaxy in the form of Domain Walls. A fundamental point is obtaining a suitable satellite orbit solution by performing an accurate POD. In this context, the activities carried out with the Bernese code will be presented.

BepiColombo, the joint ESA/JAXA mission to Mercury, was launched in October 2018 and is scheduled to arrive at Mercury in November 2026 after an 8-year cruise. Like other planetary missions, its scientific objectives focus mostly on the nominal, orbiting phase of the mission. However, due to the long duration of the cruise phase covering distances between 1.2 and 0.3 AU, the BepiColombo mission has been able to outstandingly contribute to characterise the solar wind and transient events encountered by the spacecraft, as well as planetary environments during the flybys of Earth, Venus, and Mercury, and contribute to the characterisation of the space radiation environment in the inner Solar System and its evolution with solar activity. In this paper, we provide an overview of the cruise observations of BepiColombo, highlighting the most relevant science cases, with the aim of demonstrating the importance of planetary missions to perform cruise observations, to contribute to a broader understanding of Space Weather in the Solar System, and in turn, increase the scientific return of the mission.

The BepiColombo ESA-JAXA mission, launched on October 20, 2018, is scheduled to reach Mercury in November 2026. The Mercury Composite Spacecraft comprises three modules: the Mercury Planetary Orbiter, the Mercury Magnetospheric Orbiter, and the Mercury Transfer Module. Currently, BepiColombo is in its seven-year cruise phase, having completed one Earth flyby, two Venus flybys, and three Mercury flybys. The spacecraft is equipped with the high-accuracy Italian Spring Accelerometer, capable of measuring non- gravitational acceleration variations at frequencies between [3x 10 -5 , 10-1] Hz. Interpreting accelerometer data can be challenging due to overlapping dynamic effects. During the second Venus flyby, the accelerometer data revealed significant signatures of the gravity gradient signal induced by the planet on the proof masses. Notably, a large, unexpected acceleration spike was detected near the closest approach, lasting a few minutes. Further analysis determined that this spike was most likely caused by outgassing from the Mercury Planetary Orbiter radiator. This paper analyzes the Italian Spring Accelerometer data from the second Venus flyby, focusing on the unexpected acceleration spike. By combining the torque data from the reaction wheel with accelerometer data, the team was able to estimate the outgassing location, confirming it as the spacecraft radiator. Additionally, data from the Mass Spectrum Analyzer sensor, part of the Mercury Plasma Particle Experiment, suggest that H2O outgassing occurred. The estimated mass of sublimated water is approximately 2 grams.

The ESA/JAXA BepiColombo mission is currently on its way to Mercury, aiming to unveil the secrets held by the innermost planet of the Solar System. The radio tracking measurements, in combination with the data acquired by the onboard accelerometer, will enable a precise navigation of the spacecraft addressing the scientific objectives of the mission. A series of planetary flybys are required during the interplanetary transfer orbit to save propellant for the orbital insertion around Mercury. We present here a joint analysis of the radio tracking and accelerometer measurements collected during the second Venus flyby and the first two Mercury flybys. A precise orbit determination process is carried out to yield a combined adjustment of the spacecraft trajectory and parameters associated with dynamical and observational modeling. The accelerometer data enabled the detection of unmodeled dynamical perturbations including outgassing and thermal recoil. Our analysis of Mercury flybys allowed us for the first time to combine BepiColombo and MESSENGER radiometric measurements, leading to significant improvements in the modeling of the gravitational forces.

The Mercury Orbiter Radio Science Experiment onboard the European Space Agency/Japan Aerospace Exploration Agency (JAXA) BepiColombo mission aims at determining the gravity field and the rotational state of the planet to provide insight into its internal structure and at performing tests of general relativity. The experiment will rely on accurate radiometric data provided by the onboard Ka-band transponder and on measurements of the nonconservative perturbations acting on the spacecraft, provided by the Italian Spring Accelerometer. This paper presents a software implementation of a pseudo-drag-free system which includes the accelerometer measurements in the orbit determination process. Numerical simulations focus on the identification of a suitable calibration strategy to fulfill the experiment goals pertaining to geodesy and geophysics. The achievement of the expected scientific results will depend meaningfully on the quality of the accelerometer data. Perturbative analysis aided in the identification of a calibration strategy for the accelerometer data processing that allows obtaining an unbiased solution and compensating for accelerometer errors.

This paper concerns the development of a first simplified model to take into account the perturbations produced by the nongravitational forces acting on the satellites of the Galileo FOC constellation and the corresponding first orbital determinations within the G4S_2.0 project. G4S_2.0 has a series of objectives in verifying the gravitational interaction in the weak field limit of the theory of general relativity, exploiting in particular the eccentricity of the orbits of some Galileo FOC satellites and the precise measurements that can be derived from the atomic clocks on board these satellites. The study focused on the model for the acceleration produced by direct solar radiation pressure on the satellites. This is the largest of all nongravitational perturbations. It is therefore necessary to build a sufficiently accurate model for it before being able to seriously consider smaller perturbation effects, such as those related to terrestrial radiation and thermal thrust effects. The work presents new aspects in the literature of navigation satellites. One of these is the determination of the effects in the Keplerian elements produced by the direct solar acceleration obtained from a box -wing model of the satellite. A second aspect is the comparison of these predictions in the orbital elements with the corresponding orbital residuals achieved from an orbit determination of the satellite. The study therefore highlights even more the importance of being able to improve the model of the perturbation originating from solar radiation in the field of global navigation satellite systems. This is very important if one wants to extract gravitational measurements from the orbit and clock -bias measurements of these satellites to verify the predictions of general relativity and compare them with those of alternative theories of gravitation.

This paper introduces the main problems related to the modeling of the effects of nongravitational perturbations on satellites of the Galileo FOC constellation. The problem is addressed from the point of view of the scientific objectives of the Galileo for Science (G4S_2.0) project. These objectives are reflected in a set of fundamental physics measurements that will exploit the orbits and atomic clocks aboard the Galileo satellites, in particular the GSAT-0201 and GSAT-0202 satellites characterized by elliptical orbits, and not by almost circular orbits such as in the case of the remaining satellites of the constellation. The main focus is on the modeling of the direct solar radiation pressure, the largest nongravitational perturbation on GNSS satellites. After an in-depth presentation of the main nongravitational perturbations of interest, and of the models currently in use in the literature for their consideration, the work focuses on the amplitudes of the different effects and, with particular attention, on their intrinsic knowledge. Finally, two different models are introduced for the structure of the Galileo satellite specially developed for the objectives of G4S_2.0. The first is a simple model of the box-wing type, developed on the basis of the information currently available on the characteristics of the satellite. The second is a 3D model of the Galileo spacecraft, somewhat sophisticated due to the richness of the details on the structure and the various elements that make up the surfaces of the satellite. The activities carried out and in progress with these models and those planned with their subsequent updated versions are described.

ISA (Italian Spring Accelerometer) is a high sensitivity, relative, mass-spring accelerometer. It flies as scientific payload on-board the Mercury Planetary Orbiter (MPO), module of BepiColombo ESA mission to Mercury. The accelerometer is sensitive to any acceleration, greater than 2*10-8 ms-2Hz-1/2, that changes the spacecraft motion from a pure free fall: the, so called, Non Gravitational Perturbations (NGP). ISA data will be added, at Mercury, to the orbit determination estimation in order to help reconstructing the orbit and to make the MPO an a-posteriori free-fall satellite. After the first commissioning phase, performed in between November 2018 - August 2019, and that allowed to verify the functionality of the instrument itself, the first direct verification of the correct behaviour of the system was carried out during the BepiColombo Earth Flyby. Indeed, the spacecraft crossed the planet Earth shadow during the flyby and the direct Solar Radiation Pressure (SRP), the main contribution of NGP accelerations, dropped suddenly, marking a clear leap (gap) in the gathered data. The scientific team compared, on the base of the satellite surface exposition and radiative characteristics, the observed “drop” in the acceleration, once removed the on-board disturbances and inertial accelerations due to spacecraft rotations. In the talk, other ISA data recorded during the Earth Flyby are reported and expected signals for the upcoming Venus#2 Flyby and Mercury #1 Flyby are presented.

Temperature is a major source of inaccuracy in high-sensitivity accelerometers and gravimeters. Active thermal control systems require power and may not be ideal in some contexts such as airborne or spaceborne applications. We propose a solution that relies on multiple thermometers placed within the accelerometer to measure temperature and thermal gradient variations. Machine Learning algorithms are used to relate the temperatures to their effect on the accelerometer readings. However, obtaining labeled data for training these algorithms can be difficult. Therefore, we also developed a training platform capable of replicating temperature variations in a laboratory setting. Our experiments revealed that thermal gradients had a significant effect on accelerometer readings, emphasizing the importance of multiple thermometers. The proposed method was experimentally tested and revealed a great potential to be extended to other sources of inaccuracy, such as rotations, as well as to other types of measuring systems, such as magnetometers or gyroscopes.

<p>The Galileo for Science Project (G4S_2.0) is an ongoing project funded by the Italian Space Agency that has several goals in the field of Fundamental Physics by exploiting the Galileo-FOC Constellation and, in particular, GSAT-0201 and GSAT-0202, the two FOC in elliptical orbit. The high eccentricity of their orbits and the accuracy of their atomic clocks allow to measure gravitational redshift and relativistic precessions of the orbits. These results will place new constraints on possible alternative theories of gravitation, both metric and non-metric in their structure. Furthermore, constraints on the presence of Dark Matter in our Galaxy can be placed by analysing data of the satellites’ atomic clocks.</p><p>In this framework a fundamental point is obtaining a suitable satellite orbit solution by performing an accurate Precise Orbit Determination (POD). To this purpose modeling, as better as possible, the complex effects of the Non-Gravitational Perturbations (NGPs) is essential. In particular, the direct Solar Radiation Pressure (SRP) represents the main source of error in determining the orbit of any GNSS spacecraft, as it is the largest NGPs perturbation.</p><p>Our final goal is to build a refined Finite Element Model (FEM) of the Galileo FOC spacecraft to compute the perturbing accelerations that will be used in the POD procedure.</p><p>As an intermediate step a Box-Wing (BW) model, as well as a 3D-CAD of the spacecraft, have been developed. We will present the results for the perturbing accelerations produced by SRP, Earth’s infrared radiation and Earth’s albedo in the case of a BW model built using the ESA Galileo metadata.</p><p>Moreover, accounting for multiple reflections and mutual shadowing effects is crucial to improve the POD and the scientific results. To this purpose we apply the so-called Ray Tracing technique to the spacecraft FEM. We will present our ongoing work on this technique by using the software COMSOL and Matlab on the current development we obtained for the FEM.</p><p>Finally, by using the residuals in the orbital elements obtained from a POD, we can test our new models and the improvements in the quality of the POD. In order to prove the reliability and robustness of the scientific results that will be obtained within G4S_2.0, we aim to exploit both GEODYN II and the Bernese software for the POD.</p>

<p>Within the G4S_2.0 (Galileo for Science) project, funded by the Italian Space Agency (ASI), two activities in the field of Fundamental Physics are under investigation and development: a new measure of the Gravitational Red Shift (GRS) and a search for possible Dark Matter (DM) candidates in the form of domain walls. Both researches are based on data from high-accuracy clocks aboard the satellites.</p><p>The GRS measurement exploits the two Galileo satellites DORESA and MILENA injected in 2014 into a wrong orbit characterized by a too high eccentricity. The corrected orbit, still has a relatively high eccentricity (about 0.16) suitable for gravitational measurements. Consequently, the clocks frequency of these two satellites is modulated with the changes of the Earth’s gravitational potential at the height of the satellite.</p><p>The search for DM matter is done by looking for the expected rapid perturbations in on-board clocks when a structure like a domain wall crosses Earth’s orbit and the Galileo constellation.  If this occurs, on-board clocks would have to change their frequency relative to a reference clock on Earth.</p><p>For both targets, a careful knowledge of the satellite’s position is required, to be obtained with a Precise Orbit Determination (POD) in which the main non gravitational perturbations, such as direct solar radiation pressure, are adequately modeled and accounted for. Furthermore, the clock data needs to be cleaned up by removing long-term drift and fast time jumps unrelated to the effects we want to measure.</p><p>We will present the preliminary results obtained within these activities.</p>

G4S_2.0 is a project funded by the Italian Space Agency aiming to perform a set of Fundamental Physics measurements using the two Galileo FOC satellites GSAT0201 (Doresa) and GSAT0202 (Milena). Indeed, the orbits of these satellites are characterized by a relatively high eccentricity, about 0.16, which represents a good prerequisite for a series of tests and measurements concerning the predictions of different theories of gravitation, as compared with the General Relativity (GR) ones. The main objectives include a new measurement of the gravitational redshift effect of the on-board atomic clocks --- thanks to its modulation with the orbital period due to the high eccentricity of the orbits --- and the measurement of the main precessions of relativistic origin, primarily the Schwarzschild one. To achieve these significant results, and possibly improve the current constraints of several theories of gravitation with respect to GR, it is of fundamental importance to take a step forward --- compared to the state of the art --- in the reliability of the dynamic model used for the orbits of the satellites and, as a direct consequence of this, in their precise orbit determination (POD). In this context, non-gravitational perturbations (NGPs) are the most subtle and difficult to model because of the complex shape of the Galileo satellites and their attitude law. In this regard, the main challenge is represented by a more refined and reliable model for the direct solar radiation pressure (SRP), the largest NGP on Galileo satellites, as well as on every satellite of every GNSS constellation. Our final goal is to build a finite element model (FEM) of the Galileo FOC spacecraft, as refined as possible, and apply a dedicated raytracing technique to it to compute the perturbing accelerations due to radiation pressure. In view of this, we have already developed a 3D-CAD model of the spacecraft. As an intermediate step, we have built a Box-Wing (BW) model based on the relatively poor information presently available on the geometrical and physical properties of the spacecraft. This BW model has been used to compute the perturbing accelerations due to the direct SRP and to the Earth's albedo and infrared radiation. The results obtained for the accelerations, to be included in the POD process, will be presented in various cases. Then, by computing the residuals in the orbital elements, it will be possible to verify the goodness of the POD results and observe the expected progressive improvement starting from the BW model towards the FEM one. The present analyses were made using the nominal attitude law of the Galileo FOC spacecraft; the application of this law will be discussed in the case of satellites in elliptical orbit. We finally highlight that the results of G4S_2.0 in terms of POD improvements are particularly useful for all applications of the Galileo FOC satellites in the fields of space Geodesy and Geophysics.