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This study provides a continuous ephemeris reconstruction for comet 67P/Churyumov-Gerasimenko by reanalyzing Rosetta radiometric measurements and Earth-based astrometry. Given the comet-to-spacecraft relative trajectory provided by the navigation team, these measurements were used to estimate the comet state and some critical physical parameters, most notably the non-gravitational accelerations induced by the outgassing of surface volatiles, for which different models were tested and compared. The reference reconstructed ephemeris, which uses a stochastic acceleration model, has position uncertainties below 10 km, 30 km, and 80 km in the orbital radial, tangential, and normal directions for the whole duration of the Rosetta proximity phase (from July 2014 to October 2016). Furthermore, the solution can fit ground-based astrometry between March 2010 and July 2018, covering a complete heliocentric orbit of 67P. The estimated comet non-gravitational accelerations are dominated by the orbital radial and normal components, reaching peak values of $(1.28 \pm 0.17) \times 10^{-8} \, \text{m/s}^2$ and $(0.52 \pm 0.20) \times 10^{-8} \, \text{m/s}^2$, respectively 15 days and 24 days after perihelion. Furthermore, the acceleration magnitude is shown to have a steep dependence on the comet heliocentric distance $\text{NGA} \sim r_\odot^{-6}$ and shows asymmetries in the pre- and post-perihelion activities. The estimated acceleration components, agnostic due to the limited physical assumptions, could be used as a constraint for future investigations involving high-fidelity thermophysical models of the comet surface., Comment: Preprint version of conference proceeding for the 2024 AAS/AIAA Astrodynamics Specialist Conference (#AAS24-331)

The CUbesat Solar Polarimeter (CUSP) project is a future CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band, by means of a Compton scattering polarimeter. CUSP will allow us to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. The project is in the framework of the Italian Space Agency Alcor Program, which aims to develop new CubeSat missions. CUSP is approved for a Phase B study that will last for 12 months, starting in mid-2024. We report on the current status of the CUSP mission project as the outcome of the Phase A., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024. arXiv admin note: substantial text overlap with arXiv:2208.06211

The CUbesat Solar Polarimeter (CUSP) project aims to develop a constellation of two CubeSats orbiting the Earth to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter on board of each satellite. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures. CUSP is a project approved for a Phase B study by the Italian Space Agency in the framework of the Alcor program aimed to develop CubeSat technologies and missions. In this paper we describe the a method for a multi-physical simulation analysis while analyzing some possible design optimization of the payload design solutions adopted. In particular, we report the mechanical design for each structural component, the results of static and dynamic finite element analysis, the preliminary thermo-mechanical analysis for two specific thermal cases (hot and cold orbit) and a topological optimization of the interface between the platform and the payload., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

The CUbesat Solar Polarimeter (CUSP) project is a CubeSat mission orbiting the Earth aimed to measure the linear polarization of solar flares in the hard X-ray band by means of a Compton scattering polarimeter. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures of our star. CUSP is a project in the framework of the Alcor Program of the Italian Space Agency aimed to develop new CubeSat missions. It is approved for a Phase B study. In this work, we report on the accurate simulation of the detector's response to evaluate the scientific performance. A GEANT4 Monte Carlo simulation is used to assess the physical interactions of the source photons with the detector and the passive materials. Using this approach, we implemented a detailed CUSP Mass Model. In this work, we report on the evaluation of the detector's effective area as a function of the beam energy., Comment: Proceeding of SPIE Conference "Astronomical Telescopes+ Instrumentation", Yokohama (Japan), 16-21 June 2024

Solving the null geodesic equations for a ray of light is a difficult task even considering a stationary spacetime. The problem becomes even more difficult if the electromagnetic signal propagates through a flowing optical medium. Indeed, because of the interaction between light and matter, the signal does not follow a null geodesic path of the spacetime metric anymore. However, having a clear description of how the time and frequency transfers are affected in this very situation is of a prime importance in astronomy. As a matter of fact, ranging to satellites and Moon, very long baseline interferometry, global navigation satellite systems, and radio occultation experiments are few examples of techniques involving light propagation in flowing optical media. By applying the time transfer functions formalism to optical spacetime, we show that the time and frequency transfers can be determined iteratively up to any desired order within the quasi-Minkowskian path approximation. We present some applications in the context of radio occultation experiments and discuss possible future applications to the modeling of tropospheric delays., Comment: 11 pages, 5 figures, proceeding des Journ\'ees syst\`emes de r\'ef\'erences spatio-temporels 2023

Hera represents the European Space Agency's inaugural planetary defense space mission and plays a pivotal role in the Asteroid Impact and Deflection Assessment international collaboration with NASA DART mission that performed the first asteroid deflection experiment using the kinetic impactor techniques. With the primary objective of conducting a detailed post-impact survey of the Didymos binary asteroid following the DART impact on its small moon called Dimorphos, Hera aims to comprehensively assess and characterize the feasibility of the kinetic impactor technique in asteroid deflection while conducting an in-depth investigation of the asteroid binary, including its physical and compositional properties as well as the effect of the impact on the surface and shape of Dimorphos. In this work, we describe the Hera radio science experiment, which will allow us to precisely estimate critical parameters, including the mass, which is required to determine the momentum enhancement resulting from the DART impact, mass distribution, rotational states, relative orbits, and dynamics of the asteroids Didymos and Dimorphos. Through a multi-arc covariance analysis, we present the achievable accuracy for these parameters, which consider the full expected asteroid phase and are based on ground radiometric, Hera optical images, and Hera to CubeSats InterSatellite Link radiometric measurements. The expected formal uncertainties for Didymos and Dimorphos GM are better than 0.01% and 0.1%, respectively, while their J2 formal uncertainties are better than 0.1% and 10%, respectively. [...]

The NASA Double Asteroid Redirection Test (DART) mission performed a kinetic impact on asteroid Dimorphos, the satellite of the binary asteroid (65803) Didymos, at 23:14 UTC on September 26, 2022 as a planetary defense test. DART was the first hypervelocity impact experiment on an asteroid at size and velocity scales relevant to planetary defense, intended to validate kinetic impact as a means of asteroid deflection. Here we report the first determination of the momentum transferred to an asteroid by kinetic impact. Based on the change in the binary orbit period, we find an instantaneous reduction in Dimorphos's along-track orbital velocity component of 2.70 +/- 0.10 mm/s, indicating enhanced momentum transfer due to recoil from ejecta streams produced by the impact. For a Dimorphos bulk density range of 1,500 to 3,300 kg/m$^3$, we find that the expected value of the momentum enhancement factor, $\beta$, ranges between 2.2 and 4.9, depending on the mass of Dimorphos. If Dimorphos and Didymos are assumed to have equal densities of 2,400 kg/m$^3$, $\beta$= 3.61 +0.19/-0.25 (1 $\sigma$). These $\beta$ values indicate that significantly more momentum was transferred to Dimorphos from the escaping impact ejecta than was incident with DART. Therefore, the DART kinetic impact was highly effective in deflecting the asteroid Dimorphos., Comment: accepted by Nature

Aims. Understanding the activity is vital for deciphering the structure, formation, and evolution of comets. We investigate models of cometary activity by comparing them to the dynamics of 67P/Churyumov-Gerasimenko. Methods. We matched simple thermal models of water activity to the combined Rosetta datasets by fitting to the total outgassing rate and four components of the outgassing induced non-gravitational force and torque, with a final manual adjustment of the model parameters to additionally match the other two torque components. We parametrised the thermal model in terms of a distribution of relative activity over the surface of the comet, and attempted to link this to different terrain types. We also tested a more advanced thermal model based on a pebble structure. Results. We confirm a hemispherical dichotomy and non-linear water outgassing response to insolation. The southern hemisphere of the comet and consolidated terrain show enhanced activity relative to the northern hemisphere and dust-covered, unconsolidated terrain types, especially at perihelion. We further find that the non-gravitational torque is especially sensitive to the activity distribution, and to fit the pole-axis orientation in particular, activity must be concentrated (in excess of the already high activity in the southern hemisphere and consolidated terrain) around the south pole and on the body and neck of the comet over its head. This is the case for both the simple thermal model and the pebble-based model. Overall, our results show that water activity cannot be matched by a simple model of sublimating surface ice driven by the insolation alone, regardless of the surface distribution, and that both local spatial and temporal variations are needed to fit the data., Comment: Accepted for publication in A&A. 13 pages, 22 figures including appendix

NASA's Double Asteroid Redirection Test (DART) is the first full-scale test of an asteroid deflection technology. Results from the hypervelocity kinetic impact and Earth-based observations, coupled with LICIACube and the later Hera mission, will result in measurement of the momentum transfer efficiency accurate to ~10% and characterization of the Didymos binary system. But DART is a single experiment; how could these results be used in a future planetary defense necessity involving a different asteroid? We examine what aspects of Dimorphos's response to kinetic impact will be constrained by DART results; how these constraints will help refine knowledge of the physical properties of asteroidal materials and predictive power of impact simulations; what information about a potential Earth impactor could be acquired before a deflection effort; and how design of a deflection mission should be informed by this understanding. We generalize the momentum enhancement factor $\beta$, showing that a particular direction-specific $\beta$ will be directly determined by the DART results, and that a related direction-specific $\beta$ is a figure of merit for a kinetic impact mission. The DART $\beta$ determination constrains the ejecta momentum vector, which, with hydrodynamic simulations, constrains the physical properties of Dimorphos's near-surface. In a hypothetical planetary defense exigency, extrapolating these constraints to a newly discovered asteroid will require Earth-based observations and benefit from in-situ reconnaissance. We show representative predictions for momentum transfer based on different levels of reconnaissance and discuss strategic targeting to optimize the deflection and reduce the risk of a counterproductive deflection in the wrong direction., Comment: 30 pages, 7 figures. Planetary Science Journal, in press, accepted 2022 September 22

The CUbesat Solar Polarimeter (CUSP) project aims to develop a constellation of two CubeSats orbiting the Earth to measure the linear polarisation of solar flares in the hard X-ray band by means of a Compton scattering polarimeter on board of each satellite. CUSP will allow to study the magnetic reconnection and particle acceleration in the flaring magnetic structures. CUSP is a project approved for a Phase A study by the Italian Space Agency in the framework of the Alcor program aimed to develop CubeSat technologies and missions., Comment: SPIE Astronomical Telescopes + Instrumentation, 17 - 22 July 2022, Montr\'eal, Qu\'ebec, Canada

In this paper, architectures for interplanetary communications that feature the use of a data relay are investigated. In the considered "two-leg" architecture, a spacecraft orbiting the Earth, or in orbit at a Lagrange point, receives data from a deep space probe (leg-1) and relays them towards ground (leg-2). Different wireless technologies for the interplanetary link, namely, radio frequencies above the Ka band and optical frequencies, are considered. Moreover, the cases of transparent and regenerative relaying as well as different different orbital configurations are addressed, offering a thorough analysis of such systems from different viewpoints. Results show that, under certain constraints in terms of pointing accuracy and onboard antenna size, the adoption of a two-leg architecture can achieve the data rates supported by direct space-to-Earth link configurations with remarkably smaller ground station antennas., Comment: 17 pages, 7 figures, 13 tables. To appear in IEEE Transactions on Aerospace and Electronic Systems, 2022

Pose estimation of an uncooperative space resident object is a key asset towards autonomy in close proximity operations. In this context monocular cameras are a valuable solution because of their low system requirements. However, the associated image processing algorithms are either too computationally expensive for real time on-board implementation, or not enough accurate. In this paper we propose a pose estimation software exploiting neural network architectures which can be scaled to different accuracy-latency trade-offs. We designed our pipeline to be compatible with Edge Tensor Processing Units to show how low power machine learning accelerators could enable Artificial Intelligence exploitation in space. The neural networks were tested both on the benchmark Spacecraft Pose Estimation Dataset, and on the purposely developed Cosmo Photorealistic Dataset, which depicts a COSMO-SkyMed satellite in a variety of random poses and steerable solar panels orientations. The lightest version of our architecture achieves state-of-the-art accuracy on both datasets but at a fraction of networks complexity, running at 7.7 frames per second on a Coral Dev Board Mini consuming just 2.2W., Comment: Improved literature review; added Figure 2; revised tables for better readibility; corrected typos

Radio occultations are commonly used to assess remotely the thermodynamic properties of planets or satellites' atmospheres within the solar system. The data processing usually involves the so-called Abel inversion method or the numerical ray-tracing technique. Both these approaches are now well established, however, they do not allow to easily determine the uncertainty profiles in the atmospheric properties, and this makes the results difficult to interpret statistically. Recently, a purely analytical approach based on the time transfer functions formalism was proposed for modeling radio occultation data. Using this formulation, we derive uncertainty relationships between the frequency shift and the thermodynamic properties of the neutral atmosphere such as the temperature, pressure, and neutral number density. These expressions are important for interpreting previous results from past radio occultation experiments. They are especially relevant for deriving the system requirements for future missions in a rigorous manner and consistently with the scientific requirements about the atmospheric properties retrieval., Comment: 18 pages, 5 figures, 1 table

The Venus Express Radio Science Experiment (VeRa) was part of the scientific payload of the Venus Express (VEX) spacecraft and was targeted at the investigation of Venus' atmosphere, surface, and gravity field as well as the interplanetary medium. This paper describes the methods and the required calibrations applied to VEX-VeRa raw radio occultation data used to retrieve vertical profiles of Venus' ionosphere and neutral atmosphere. In this work we perform an independent analysis of a set of 25 VEX, single-frequency (X-band), occultations carried out in 2014, recorded in open-loop at the NASA Deep Space Network. Our temperature, pressure and electron density vertical profiles are in agreement with previous studies available in the literature. Furthermore, our analysis shows that Venus' ionosphere is more influenced by the day/night condition than the latitude variations, while the neutral atmosphere experiences the opposite. Our scientific interpretation of these results is based on two major responsible effects: Venus' high thermal inertia and the zonal winds. Their presence within Venus' neutral atmosphere determine why in these regions a latitude dependence is predominant on the day/night condition. On the contrary, at higher altitudes the two aforementioned effects are less important or null, and Venus' ionosphere shows higher electron density peaks in the probed day-time occultations, regardless of the latitude.

Tidal effects in planetary systems are the main driver in the orbital migration of natural satellites. They result from physical processes occurring deep inside celestial bodies, whose effects are rarely observable from surface imaging. For giant planet systems, the tidal migration rate is determined by poorly understood dissipative processes in the planet, and standard theories suggest an orbital expansion rate inversely proportional to the power 11/2 in distance, implying little migration for outer moons such as Saturn's largest moon, Titan. Here, we use two independent measurements obtained with the Cassini spacecraft to measure Titan's orbital expansion rate. We find Titan migrates away from Saturn at 11.3 $\pm$ 2.0 cm/year, corresponding to a tidal quality factor of Saturn of Q $\simeq$ 100, and a migration timescale of roughly 10 Gyr. This rapid orbital expansion suggests Titan formed significantly closer to Saturn and has migrated outward to its current position. Our results for Titan and five other moons agree with the predictions of a resonance locking tidal theory, sustained by excitation of inertial waves inside the planet. The associated tidal expansion is only weakly sensitive to orbital distance, motivating a revision of the evolutionary history of Saturn's moon system. The resonance locking mechanism could operate in other systems such as stellar binaries and exoplanet systems, and it may allow for tidal dissipation to occur at larger orbital separations than previously believed., Comment: Published in Nature Astronomy, SharedIt link: https://rdcu.be/b4I3Q

The core of every orbit determination process is the comparison between the measured observables and their predicted values, computed using the adopted mathematical models, and the minimization, in a least square sense, of their differences, known as residuals. In interplanetary orbit determination, Doppler observables, obtained by measuring the average frequency shift of the received carrier signal over a certain count time, are compared against their predicted values, usually computed by differencing two round-trip light-times. This formulation is known to be sensitive to round-off errors, caused by the use of finite arithmetic in the computation, giving rise to an additional noise in the residuals, called numerical noise, that degrades the accuracy of the orbit determination solution. This paper presents a mathematical model for the expected numerical errors in two-way and three-way Doppler observables, computed using the differenced light-time formulation. The model was validated by comparing its prediction to the actual noise in the computed observables, obtained by NASA/Jet Propulsion Laboratory's Orbit Determination Program. The model proved to be accurate within $3 \times 10^{-3} \,\text{mm/s}$ at $60 \,\text{s}$ integration time. Then it was applied to the case studies of Cassini's and Juno's nominal trajectories, proving that numerical errors can assume values up to $6 \times 10^{-2} \,\text{mm/s}$ at $60 \,\text{s}$ integration time, and consequently that they are an important noise source in the Doppler-based orbit determination processes. Three alternative strategies are proposed and discussed in the paper to mitigate the effects of numerical noise.

During its mission in the Saturn system, Cassini performed five close flybys of Dione. During three of them, radio tracking data were collected during the closest approach, allowing estimation of the full degree-2 gravity field by precise spacecraft orbit determination. The gravity field of Dione is dominated by $J_{2}$ and $C_{22}$, for which our best estimates are $J_{2} \times 10^6 = 1496 \pm 11$ and $C_{22} \times 10^6 = 364.8 \pm 1.8$ (unnormalized coefficients, 1-$\sigma$ uncertainty). Their ratio is $J_{2}/C_{22} = 4.102 \pm 0.044$, showing a significative departure (about 17-$\sigma$) from the theoretical value of $10/3$, predicted for a relaxed body in slow, synchronous rotation around a planet. Therefore, it is not possible to retrieve the moment of inertia directly from the measured gravitational field. The interior structure of Dione is investigated by a combined analysis of its gravity and topography, which exhibits an even larger deviation from hydrostatic equilibrium, suggesting some degree of compensation. The gravity of Dione is far from the expectation for an undifferentiated hydrostatic body, so we built a series of three-layer models, and considered both Airy and Pratt compensation mechanisms. The interpretation is non-unique, but Dione's excess topography may suggest some degree of Airy-type isostasy, meaning that the outer ice shell is underlain by a higher density, lower viscosity layer, such as a subsurface liquid water ocean. The data permit a broad range of possibilities, but the best fitting models tend towards large shell thicknesses and small ocean thicknesses.

Uranus and Neptune, and their diverse satellite and ring systems, represent the least explored environments of our Solar System, and yet may provide the archetype for the most common outcome of planetary formation throughout our galaxy. Ice Giants will be the last remaining class of Solar System planet to have a dedicated orbital explorer, and international efforts are under way to realise such an ambitious mission in the coming decades. In 2019, the European Space Agency released a call for scientific themes for its strategic science planning process for the 2030s and 2040s, known as Voyage 2050. We used this opportunity to review our present-day knowledge of the Uranus and Neptune systems, producing a revised and updated set of scientific questions and motivations for their exploration. This review article describes how such a mission could explore their origins, ice-rich interiors, dynamic atmospheres, unique magnetospheres, and myriad icy satellites, to address questions at the heart of modern planetary science. These two worlds are superb examples of how planets with shared origins can exhibit remarkably different evolutionary paths: Neptune as the archetype for Ice Giants, whereas Uranus may be atypical. Exploring Uranus' natural satellites and Neptune's captured moon Triton could reveal how Ocean Worlds form and remain active, redefining the extent of the habitable zone in our Solar System. For these reasons and more, we advocate that an Ice Giant System explorer should become a strategic cornerstone mission within ESA's Voyage 2050 programme, in partnership with international collaborators, and targeting launch opportunities in the early 2030s., Comment: 34 pages, 9 figures, accepted to Planetary and Space Science

Ground-based astro-geodetic observations and atmospheric occultations, are two examples of observational techniques requiring a scrutiny analysis of atmospheric refraction. In both cases, the measured changes in observables are geometrically related to changes in the photon path and the light time of the received electromagnetic signal. In the context of geometrical optics, the change in the physical properties of the signal are related to the refractive profile of the crossed medium. Therefore, having a clear knowledge of how the refractivity governs the photon path and the light time evolution is of prime importance to clearly understand observational features. Analytical studies usually focused on spherically symmetric atmospheres and only few aimed at exploring the effect of the non-spherical symmetry on the observables. In this paper, we analytically perform the integration of the photon path and the light time of rays traveling across a planetary atmosphere. We do not restrict our attention to spherically symmetric atmospheres and introduce a comprehensive mathematical framework which allows to handle any kind of analytical studies in the context of geometrical optics. To highlight the capabilities of this new formalism, we carry out five realistic applications for which we derive analytical solutions. The accuracy of the method of integration is assessed by comparing our results to a numerical integration of the equations of geometrical optics in the presence of a quadrupolar moment $J_2$. This shows that the analytical solution leads to the determination of the light time and the refractive bending with relative errors at the level of one part in $10^8$ and one part in $10^5$, for typical values of the refractivity and the $J_2$ parameter at levels of $10^{-4}$ and $10^{-2}$, respectively.

The present work describes the investigation of the navigation anomaly of Pioneer 10 and 11 probes which became known as the Pioneer Anomaly. It appeared as a linear drift in the Doppler data received by the spacecraft, which has been ascribed to an approximately constant sunward acceleration of about $8.5 \times 10^{-13} km/s^2$. Since then, the existence of the anomaly has been confirmed independently by several groups and a large effort was devoted to find its origin. The present study consists of two main parts: thermal modeling of the spacecraft throughout its trajectory, and orbit determination analysis. Based on existing documentation and published telemetry data we built a thermal finite element model of the spacecraft, whose complexity has been constrained to a degree allowing for sensitivity analysis, leading to the computation of its formal uncertainty. The trajectory analysis and orbit determination was carried out using NASA/JPL's ODP (Orbit Determination Program) and our results show that orbital solutions may be achieved that do not require the addition of any "unknown" acceleration other than the one of thermal origin., Comment: 34 pages, 10 figures

Radio remote sensing of the heliosphere using spacecraft radio signals has been used to study the near-sun plasma in and out of the ecliptic, close to the sun, and on spatial and temporal scales not accessible with other techniques. Studies of space-time variations in the inner solar wind are particularly timely because of the desire to understand and predict space weather, which can disturb satellites and systems at 1AU and affect human space exploration. Here we demonstrate proof-of-concept of a new radio science application for spacecraft radio science links. The differing transfer functions of plasma irregularities to spacecraft radio up- and downlinks can be exploited to localize plasma scattering along the line of sight. We demonstrate the utility of this idea using Cassini radio data taken in 2001-2002. Under favorable circumstances we demonstrate how this technique, unlike other remote sensing methods, can determine center-of-scattering position to within a few thousandths of an AU and thickness of scattering region to less than about 0.02 AU. This method, applied to large data sets and used in conjunction with other solar remote sensing data such as white light data, has space weather application in studies of inhomogeneity and nonstationarity in the near-sun solar wind., Comment: 28 Pages including 14 Figures (7 unique figures in both inline format and full-page format).