Search

Within the pre-phase A of the Moonlight project proposed and funded by the European Space Agency (ESA), the ATLAS consortium has proposed an architecture to support a Lunar Radio Navigation System (LRNS) capable of providing PNT (Positioning, Navigation, and Timing) services to various lunar users. The Moonlight LRNS will be a powerful tool in support of the lunar exploration endeavors, both human and robotic.The ESA LRNS will consist of a small constellation of 3-4 satellites put in Elliptical Lunar Frozen Orbits (ELFO) with the aposelene above the southern hemisphere to better cover this region, given its interest for future lunar missions. This LRNS will be supported by a ground station network of small dish antennas (~30 cm), which can establish Multiple Spacecraft Per Aperture (MSPA) tracking at K-band. Any Earth station will be capable of sending a single uplink signal to multiple spacecraft thanks to Code Division Multiplexing modulation, while in the downlink multiple carriers can share the same K-band bandwidth by implementing Code Division Multiple Access (CDMA) on the onboard transponders. This allows the implementation of the Same Beam Interferometry (SBI) technique [1], which adds to spread spectrum ranging and Doppler measurements. In the scope of disseminating accurate PNT services to end users, the constellation will also be capable of maintaining a synchronization to the Earth station clocks to the ns level.The performances of the proposed architecture have been validated through numerical simulations performed with the ESA GODOT software, enhanced with additional user-defined features and capabilities. For each satellite of the LRNS constellation, the attainable orbital accuracy is at level of a few meters for most orbit mean anomalies and it has been computed considering a setup which includes a perturbed dynamical model (mainly coming from uncertainties in the accelerations induced by the solar radiation pressure and orbital maneuvers) and a realistic error model for Doppler, ranging and SBI measurements.REFERENCE:Gregnanin, M. et al. (2012). Same beam interferometry as a tool for the investigation of the lunar interior. Planetary and Space Science 74, 194-201

The key scientific objective of the NASA/JPL Discovery-class mission VERITAS (Venus Emissivity, Radio science, INSAR, Topography And Spectroscopy) is understanding the links between the interior, surface, and atmospheric evolution.After a 6-months cruise and a 11-months aerobraking phases, VERITAS is planned to operate during four Venus cycles (4x243 Earth days) in a near circular polar orbit (180x255km in altitude at 85.4 deg. inclination) providing gravity science data thanks to the 2-way X/Ka band Doppler link and VISAR (Venus Interferometric Synthetic Aperture Radar) instrument.The radio science data and VISAR landmark features (tie points) will allow a precise determination of the rotational state of Venus: we show that the precession rate can be measured with an accuracy of 13’’/cy. From this result, the moment of inertia factor (MOIF) C/MR2, can be estimated with a 0.3% accuracy (10x improvement). Moreover, the expected accuracy of the tidal Love number measurement is 0.2%: this will allow to resolve the ambiguity of the core state (solid/liquid) and to distinguish between different interior models (core radius, mantle viscosity) [1].The atmosphere of Venus is subject to a time-dependent mass redistribution due to pressure and temperature variations induced by solar heating. This phenomenon is called “thermal tide" and it moves eastward along the Venus’ surface with a 117d period (i.e. about a Venus solar day).Thermal tides can be detected as a time-variable perturbation to the Venus gravity field due to 1) the moving atmospheric masses (direct effect) and to 2) the planet’s response to the variations of the surface loading (indirect effect, parametrized through the load Love numbers).We show that VERITAS radio science and VISAR data can also be used to measure the load Love numbers up to degree 4 with good accuracy (4% for degree 2). In particular, the degree 2 coefficient can provide independent, and complementary, information on the mantle viscosity and composition.Moreover, a simultaneous measurement of the degree 2 tidal (k2, h2) and loading (k2') Love numbers can be used to provide finer bounds on the mantle viscosity and possibly to constrain the mantle rheology.[1] G. Cascioli, S. Hensley, F. De Marchi, D. Breuer, D. Durante, P. Racioppa, L. Iess, E. Mazarico and S. E. Smrekar (2021) Planet. Sci. J. 2 22

In the framework of the European Space Agency’s Moonlight program, a satellite navigation system is planned for positioning, navigation, timing, and communication on the Moon. The constellation will consist of three or four lunar orbiters in eccentric orbits – with periselene above the northern hemisphere and aposelene above the southern hemisphere; the latter is of special interest in terms of future lunar missions. The eccentric orbits introduce a challenge for precise orbit determination, because large gravity perturbations due to the lunar gravity field occur in the periselene passes, whereas the aposelene passes are associated with the smallest gravity gradients and thus the largest errors in orbit determination.We evaluate the non-gravitational and gravitational perturbing forces acting on lunar orbiters in eccentric orbits. The simulated orbits consider lunar gravity field based on the GRAIL mission, gravity perturbations from the Sun, Earth, and planets considering Earth’s oblateness, tidal deformations, direct solar radiation pressure with lunar and Earth eclipses, albedo, antenna thrust, and relativistic effects. We discuss three methods of proposed representation of the broadcast orbits: based on Keplerian parameters and a set of one-per-revolution corrections (GPS-like or Galileo-like), based on Chebyshev polynomials with a variable number of coefficients and arc-length representation, and based on a series of positions and velocities (GLONASS-like). We discuss the advantages and limitations of all three representations and accuracies provided by different approaches depending on the number of assumed coefficients and arc lengths. Finally, we discuss the impact of inconsistent treatment of the origin, scale, and orientation of the lunar reference frame on the determined positions on the Moon.

We use the magnetic and gravity field data jointly to place constraints on the internal structure of Ganymede. The magnetic induction constraint comes mostly from the Galileo data, as the Juno flyby occurred when Ganymede was near the center of the magnetodisk, thus leading to low sensitivity to magnetic induction. The gravity field model of Ganymede jointly derived from the Galileo and Juno data to place constraints on Ganymede’s internal structure. Unlike in the previous works, the hydrostaticity was not imposed on the degree-2 gravity coefficients. Thus, despite including additional data from Juno, the uncertainties on the degree-2 coefficients increased. In addition, we explicitly treat the effect of non-hydrostaticity on the derived moment of inertia and find significantly wider confidence intervals on the moment of inertia. This leads to a larger allowed parameter space for the internal structure model.The new gravity solution confirms the past detection of non-hydrostatic anomalies. In our analysis, localized non-hydrostatic features with amplitudes higher than those found on Titan by the Cassini mission are identified. Titan is a useful comparison case as it shares with Ganymede nearly the same mean radius, mean density, and therefore, surface gravity. Thus, the non-hydrostatic deviations of the same amplitude either in shape or in gravity would correspond to approximately the same level of non-hydrostatic stress. On Titan, the gravity field for degree l > 2 reaches at most 5 mGal (Durante et al., 2019), which is a factor of 5 smaller than the largest anomalies found on Ganymede. One key difference between the two bodies is the lack of atmosphere-based erosion processes on Ganymede. Such erosional processes could have led to faster removal of non-hydrostatic signals at Titan reducing the amplitude of its gravity anomalies. In addition, Titan’s outer shell could be thinner and, therefore, less rigid than that of Ganymede, thus not being able to support as much non-hydrostaticity.Further insights on Ganymede’s interior will be coming from the JUICE mission in the next decade. Currently, the lack of an accurate shape model prevents separating degree-2 hydrostatic and non-hydrostatic contributions. Combined gravity, topography and rotation data acquired by JUICE will be crucial in determining the non-hydrostatic contribution to the degree-2 field to constrain Ganymede’s internal structure.

Recently, the Juno and Cassini spacecraft shed light on the interior of both Jupiter and Saturn, the two gas giants of the Solar System. Juno is currently orbiting Jupiter in a highly elliptical 53.5-day orbit, with a perijove altitude of about 4000 km. After the 33rd passage in April 2021 (labeled PJ33), the mission ended its nominal mission and entered its extended mission. On the contrary, the Cassini spacecraft ended its mission on September 15th, 2017 with a deliberate plunge into Saturn’s atmosphere. In its final phase, the Grand Finale, Cassini provided insights on Saturn’s rings, atmosphere, and interior. Out of the 22 proximal orbits, six pericenter passes have been devoted to the determination of the gravity field of the planet.The gravity science experiments on board Juno and Cassini precisely measured, respectively, Jupiter and Saturn zonal gravitational fields. The measured gravity harmonics have been used to constrain the interior structure and atmospheric zonal flow on both planets.The Cassini data analysis have shown the need to include unknown accelerations to properly fit the data to the expected noise (Iess, 2019). Similar unexplained accelerations have been observed also on Juno gravity data (Durante, 2020). Since Jupiter and Saturn are gas giants, unconventional phenomena can be at play, including normal modes, non-zonal atmospheric dynamics, or flows in the dynamo region.The analysis of the accelerations acting on Cassini provided evidence for p-modes on the planet (Markham, 2020), while the analysis of Juno gravity data revealed p-modes on Jupiter and provided upper bounds on lower frequency f-modes. Here, we show the results for normal modes on both Jupiter and Saturn obtained with the analysis of gravity data of both Juno and Cassini.

A broad class of models that routinely appear in several fields can be expressed as partially or fully discretized Gaussian linear regressions. Besides including classical Gaussian response settings, this class also encompasses probit, multinomial probit and tobit regression, among others, thereby yielding one of the most widely-implemented families of models in routine applications. The relevance of such representations has stimulated decades of research in the Bayesian field, mostly motivated by the fact that, unlike for Gaussian linear regression, the posterior distribution induced by such models does not seem to belong to a known class, under the commonly assumed Gaussian priors for the coefficients. This has motivated several solutions for posterior inference relying either on sampling-based strategies or on deterministic approximations that, however, still experience computational and accuracy issues, especially in high dimensions. The scope of this article is to review, unify and extend recent advances in Bayesian inference and computation for this core class of models. To address such a goal, we prove that the likelihoods induced by these formulations share a common analytical structure implying conjugacy with a broad class of distributions, namely the unified skew-normal (SUN), that generalize Gaussians to include skewness. This result unifies and extends recent conjugacy properties for specific models within the class analyzed, and opens new avenues for improved posterior inference, under a broader class of formulations and priors, via novel closed-form expressions, iid samplers from the exact SUN posteriors, and more accurate and scalable approximations from variational Bayes and expectation-propagation. Such advantages are illustrated in simulations and are expected to facilitate the routine-use of these core Bayesian models, while providing novel frameworks for studying theoretical properties and developing future extensions. Supplementary materials for this article are available online.

Recent years have seen increasing interest in sending a mission to Uranus, visited so far only by Voyager 2 in 1986. EURO (Elliptical Uranian Relativity Orbiter) is a preliminary mission concept investigating the possibility of dynamically measuring the planet's angular momentum by means of the Lense-Thirring effect affecting a putative Uranian orbiter. It is possible, at least in principle, to separate the relativistic precessions of the orbital inclination to the Celestial Equator and of the longitude of the ascending node of the spacecraft from its classical rates of the pericentre induced by the multipoles of the planet's gravity field by adopting an appropriate orbital configuration. For a wide and elliptical $2\,000\times 100\,000\,\mathrm{km}$ orbit, the gravitomagnetic signatures amount to tens of milliarcseconds per year, while, for a suitable choice of the initial conditions, the peak-to-peak amplitude of the range-rate shift can reach the level of $\simeq 1.5\times 10^{-3}$ millimetre per second in a single pericentre passage of a few hours. By lowering the apocentre height to $10\,000\,\mathrm{km}$, the Lense-Thirring precessions are enhanced to the level of hundreds of milliarcseconds per year. The uncertainties in the orientation of the planetary spin axis and in the inclination are major sources of systematic bias; it turns out that they should be determined with accuracies as good as $\simeq 0.1-1$ and $\simeq 1-10$ milliarcseconds, respectively., Comment: LaTex2e, 40 pages, 7 figures, no tables. Minor revisions. Accepted in Monthly Notices of the Royal Astronomical Society

Since the first gravity measurements of Juno at Jupiter, the odd gravity harmonics J3 to J9 have been used to determine the depth of the zonal wind observed at the cloud level. Later on, combining solutions from internal models, the gravity harmonics J6, J8 and J10 were added to the analysis, which reinforced the conclusion that the observed zonal flows extend to a depth of around 3,000 km. The harmonics higher than J10 were not used in the analysis since their individual uncertainty was too large. In this study, we revisit the wind-gravity analysis, using new gravity data from Juno and a new analysis method, showing results for higher harmonic gravity measurements. This gives more detail about the structure of the deep zonal flows and allows better explaining the structure of the gravity spectrum. This confirms that indeed the observed flows are the ones which imprint the gravity spectrum. Moreover, this analysis allows to better determine which part of the wind field most contributes to the gravity signal, implying on the depth of individual jet streams. We also show how the new gravity measurement analysis allows to refine the surface gravity field, particularly in the latitudinal range of the closest approach of the spacecraft.

The JUpiter Icy Moons Explorer is an ESA mission set for launch in 2023 April and arrival in the Jovian system in 2031 July to investigate Jupiter and its icy satellites with a suite of 10 instruments. The mission will execute several flybys of the icy moons Europa, Callisto, and Ganymede before ending the mission with a 9-month orbit around Ganymede. The 3GM experiment on board the spacecraft will exploit accurate range and Doppler (range-rate) measurements to determine the moons’ orbit, gravity field, and tidal deformation. The focus of this paper is on the retrieval of Europa’s and Callisto’s gravity field, without delving into the modeling of their interior structures. By means of a covariance analysis of the data acquired during flybys, we assess the expected results from the 3GM gravity experiment. We find that the two Europa flybys will provide a determination of the J 2 and C 22 quadrupole gravity field coefficients with an accuracy of 3.8 × 10−6 and 5.1 × 10−7, respectively. The 21 Callisto flybys will provide a determination of the global gravity field to approximately degree and order 7, the moon ephemerides, and the time-variable component of the gravitational tide raised by Jupiter on the moon. The k 2 Love number, describing the Callisto tidal response at its orbital period, can be determined with an uncertainty σ k2 ∼ 0.06, allowing us to distinguish with good confidence between a moon with or without an internal ocean. The constraints derived by 3GM gravity measurements can then be used to develop interior models of the moon.

Predictive models for binary data are fundamental in various fields, and the growing complexity of modern applications has motivated several flexible specifications for modeling the relationship between the observed predictors and the binary responses. A widely-implemented solution is to express the probability parameter via a probit mapping of a Gaussian process indexed by predictors. However, unlike for continuous settings, there is a lack of closed-form results for predictive distributions in binary models with Gaussian process priors. Markov chain Monte Carlo methods and approximation strategies provide common solutions to this problem, but state-of-the-art algorithms are either computationally intractable or inaccurate in moderate-to-high dimensions. In this article, we aim to cover this gap by deriving closed-form expressions for the predictive probabilities in probit Gaussian processes that rely either on cumulative distribution functions of multivariate Gaussians or on functionals of multivariate truncated normals. To evaluate these quantities we develop novel scalable solutions based on tile-low-rank Monte Carlo methods for computing multivariate Gaussian probabilities, and on mean-field variational approximations of multivariate truncated normals. Closed-form expressions for the marginal likelihood and for the posterior distribution of the Gaussian process are also discussed. As shown in simulated and real-world empirical studies, the proposed methods scale to dimensions where state-of-the-art solutions are impractical., Comment: 14 pages, 4 figures

Summary Regression models for dichotomous data are ubiquitous in statistics. Besides being useful for inference on binary responses, these methods serve as building blocks in more complex formulations, such as density regression, nonparametric classification and graphical models. Within the Bayesian framework, inference proceeds by updating the priors for the coefficients, typically taken to be Gaussians, with the likelihood induced by probit or logit regressions for the responses. In this updating, the apparent absence of a tractable posterior has motivated a variety of computational methods, including Markov chain Monte Carlo routines and algorithms that approximate the posterior. Despite being implemented routinely, Markov chain Monte Carlo strategies have mixing or time-inefficiency issues in large-$p$ and small-$n$ studies, whereas approximate routines fail to capture the skewness typically observed in the posterior. In this article it is proved that the posterior distribution for the probit coefficients has a unified skew-normal kernel under Gaussian priors. This result allows efficient Bayesian inference for a wide class of applications, especially in large-$p$ and small-to-moderate-$n$ settings where state-of-the-art computational methods face notable challenges. These advances are illustrated in a genetic study, and further motivate the development of a wider class of conjugate priors for probit models, along with methods for obtaining independent and identically distributed samples from the unified skew-normal posterior.

International audience

Uranus and Neptune are the archetypes of "ice giants", a class of planets that may be among the most common in the Galaxy. They hold the keys to understand the atmospheric dynamics and structure of planets with hydrogen atmospheres inside and outside the solar system; however, they are also the last unexplored planets of the Solar System. Their atmospheres are active and storms are believed to be fueled by methane condensation which is both extremely abundant and occurs at low optical depth. This means that mapping temperature and methane abundance as a function of position and depth will inform us on how convection organizes in an atmosphere with no surface and condensates that are heavier than the surrounding air, a general feature of giant planets. Owing to the spatial and temporal variability of these atmospheres, an orbiter is required. A probe would provide a reference atmospheric profile to lift ambiguities inherent to remote observations. It would also measure the abundances of noble gases which can be used to reconstruct the history of planet formation in the Solar System. Finally, mapping the planets' gravity and magnetic fields will be essential to constrain their global composition, atmospheric dynamics, structure and evolution. An exploration of Uranus or Neptune will be essential to understand these planets and will also be key to constrain and analyze data obtained at Jupiter, Saturn, and for numerous exoplanets with hydrogen atmospheres., arXiv admin note: substantial text overlap with arXiv:1908.02092

As of April 2021, Juno is close to complete its nominal mission, awaiting to enter its extended mission. Thanks to the extremely accurate Doppler data (having an accuracy as low as 10 micron/s at an integration time of 60 s) acquired during close perijove passes in the last 4 years, Juno provided an unprecedented view of Jupiter’s gravity field, which is crucial to determine its interior structure. In order to recover the gravity field of the planet, the orbits of Juno have to be reconstructed to a very high accuracy. The latest gravity field reconstruction showed hints to a non-static and/or non-axially symmetric field, possibly related to several different phenomena, such as normal modes, localized atmospheric or deeply-rooted dynamics. These tiny phenomena produces a residual signal at a level of few tens of micron/s in Juno Doppler data. To confidently study these tiny unconventional phenomena, the dynamical model of Juno’s spacecraft have been accurately characterized and possible error sources investigated and ruled out.The focus of this study is Jupiter’s normal modes. Our main goal is to assess whether the residuals signatures can be explained by the gravitational disturbances induced by normal modes inside the planet, assuming reasonable physical constraints. Ground-based observations of Jupiter’ normal modes can be used as a guide.

The ESA/JAXA mission BepiColombo, launched on 20 October 2018 is in cruise towards Mercury and will arrive at Mercury in 2025 to investigate its surface, interior structure and magnetosphere. The Mercury Orbiter Radio-science Experiment (MORE) onboard the Mercury Planetary Orbiter (MPO) aims at determining the gravity field, the rotational state and librations of the planet, using precise tracking of the spacecraft during its orbital phase around Mercury. Range and range-rate measurements collected during the cruise phase will be used to test the theory of general relativity starting in March 2021. The MORE experiment exploits two-way multifrequency microwave links from ESA and NASA: two downlinks in X- and Ka-band coherent with the X-band uplink and one Ka-band downlink coherent with the Ka-band uplink. The range-rate and range measurements accurately BepiColombo’s line-of-sight velocity and the round-trip light-time of the signal, respectively. The calibration of the dispersive plasma noise component through the combination of the X/X, X/Ka and Ka/Ka links and the use of water vapor radiometers to correct for the path delay due to Earth’s troposphere will result in an accuracy of ~3 µm/sec (at 1000-s integration time) on the Doppler and centimeter-level range accuracies. We report on the analysis of dedicated tests executed on range and Doppler data collected by ESA and NASA stations at X and Ka-band. The comparison of the observed noise with the predictions shows results exceeding the expectations. In particular, the 24 Mcps pseudo-noise modulation of the Ka-band carrier, enabled by MORE’s KaT transponder built by Thales Alenia Space Italia, provided two-way range measurements accurate to ~3 cm with just 4 s integration time, at a distance of 0.7 AU, September 2021, and 1.3 AU, November 2021. Under favorable weather conditions, the range rate has shown an accuracy of 25 µm/s at 10 s integration time, in line with the expected end-to-end performance. Under unfavorable weather conditions the performance was slightly over the requirements. We must remark that calibrations from water vapor radiometers were not available during these tests and only GNSS calibration were applied.

Non-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian state-space models — where filtering, predictive and smoothing distributions are available in closed form — binary state-space models require approximations or sequential Monte Carlo strategies for inference and prediction. This is due to the apparent absence of conjugacy between the Gaussian states and the likelihood induced by the observation equation for the binary data. In this article we prove that the filtering, predictive and smoothing distributions in dynamic probit models with Gaussian state variables are, in fact, available and belong to a class of unified skew-normals (sun) whose parameters can be updated recursively in time via analytical expressions. Also the key functionals of these distributions are, in principle, available, but their calculation requires the evaluation of multivariate Gaussian cumulative distribution functions. Leveraging sun properties, we address this issue via novel Monte Carlo methods based on independent samples from the smoothing distribution, that can easily be adapted to the filtering and predictive case, thus improving state-of-the-art approximate and sequential Monte Carlo inference in small-to-moderate dimensional studies. Novel sequential Monte Carlo procedures that exploit the sun properties are also developed to deal with online inference in high dimensions. Performance gains over competitors are outlined in a financial application.

There is a growing interest in learning how the distribution of a response variable changes with a set of observed predictors. Bayesian nonparametric dependent mixture models provide a flexible approach to address this goal. However, several formulations require computationally demanding algorithms for posterior inference. Motivated by this issue, we study a class of predictor-dependent infinite mixture models, which relies on a simple representation of the stick-breaking prior via sequential logistic regressions. This formulation maintains the same desirable properties of popular predictor-dependent stick-breaking priors, and leverages a recent Polya-gamma data augmentation to facilitate the implementation of several computational methods for posterior inference. These routines include Markov chain Monte Carlo via Gibbs sampling, expectation–maximization algorithms, and mean-field variational Bayes for scalable inference, thereby stimulating a wider implementation of Bayesian density regression by practitioners. The algorithms associated with these methods are presented in detail and tested in a toxicology study.

Measuring the depth of Jupiter’s storms The atmosphere of Jupiter consists of bands of winds rotating at different rates, punctuated by giant storms. The largest storm is the Great Red Spot (GRS), which has persisted for more than a century. It has been unclear whether the storms are confined to a thin layer near the top of the atmosphere or if they extend deep into the planet. Bolton et al . used microwave observations from the Juno spacecraft to observe several storms and vortices. They found that the storms extended below the depths at which water and ammonia are expected to condense, implying a connection with the deep atmosphere. Parisi et al . analyzed gravity measurements taken while Juno flew over the GRS. They detected a perturbation in the planet’s gravitational field caused by the storm, finding that it was no more than 500 kilometers deep. In combination, these results constrain how Jupiter’s meteorology links to its deep interior. —KTS

The jovian moon Io disperses about 1ton/s of material in the planetary magnetosphere, mainly by sublimation of SO2 from the surface and by its intense volcanic activity. The ejected material supplies the plasma cloud surrounding Jupiter known as Io Plasma Torus (IPT). The radio communication between Juno and the Earth DSN station crosses the IPT near the closest approach. Being a dispersive medium, the IPT introduces a path delay in the signal, which can be analyzed to retrieve the density distribution of electrons. We used radio tracking data from the first 25 orbits to investigate the morphology of the IPT and its variability. We adopted a static and axisymmetric model for the electron density and we updated it including temporal and longitudinal variability. We found that our best fit model must include both variabilities, even though on average the morphology of the IPT agrees with previous analyses. Our results suggest that the density of the outer region of the IPT fluctuates over 50% the average value over a typical time scale of about 420days.

The accuracy achieved by modern deep space radio tracking systems has dramatically increased the precision of planetary ephemerides in the last decade. This improvement is particularly beneficial to the study of the trans-Neptunian solar system, still a relatively unknown region (Prialnik et al. 2020). The Kuiper belt has a pivotal role in our understanding of the outer solar system, and a better constrain of its mass inferred by its gravity perturbations on the planets can help to explain the observed clustering of Kuiper belt objects (KBO), and the potential presence of a ninth planet beyond the orbit of Neptune, P9 (Batygin et al. 2019). We thus provide a new estimate of the cumulative mass of KBOs located in the 2:1 and 3:2 mean motion resonances with Neptune deduced from INPOP19a. INPOP19a is the last version of INPOP planetary ephemeris, which, among the numerous updates (Fienga et al. 2019), benefits from the addition of the new normal points obtained with the gravity experiment of the Juno mission and the new normal points deduced from Cassini radio tracking data. The latter, in particular, play a decisive role for constraining the mass of the Kuiper belt, thanks to the enhanced accuracy registered in the analysis of navigation and gravity data (Di Ruscio et al. 2020; Durante et al. 2019) and the extended time-frame covered with the inclusion of the Grand Finale measurements (Iess et al. 2019). We modeled the Kuiper belt by including in INPOP dynamical model three circular, not inclined rings located at 39.4, 44.0, and 47.5 AU, to which we attributed one-sixth, two-thirds, and one-sixth of the total mass, respectively, using the same approach adopted by Pitjeva & Pitjev (2018). In addition, we included the orbits of nine KBOs, beside Pluto, whose masses are independently constrained by observations of their satellites dynamics. Solving for the mass of the Kuiper belt together with the orbits of the eight planets of the solar system, Pluto, and the Moon, plus the mass of 343 asteroids of the main belt, we fitted the entire INPOP dataset (Fienga et al. 2019) and estimated a total mass for the rings of KBOs of (0.061 ± 0.001)M⊕. We also provide new constraints on the location of P9 by analyzing the potential gravity perturbation on planetary ephemerides, specifically on the orbit of Saturn. We used two statistical criteria to identify the possible regions compatible with INPOP19a: i) based on the propagated covariance matrix, and ii) on the χ2 likelihood of P9-perturbed postfit residuals (Fienga et al. 2020). We show that, according to INPOP19a, there is no clear evidence for the existence of P9, but we identified two zones for which its existence is compatible with the accuracy of INPOP planetary ephemerides (see Fig. 1). Fig. 1. The plots show the two compatible zones we identified for the potential location of P9 with a mass of 5 M⊕ at a distance of 600 AU. The x and y axes report the angular position in Right Ascension (RA) and Declination (Dec) of the planet in the International Celestial Reference Frame. The colorbar indicates the χ2 Likelihood computed for each P9-perturbed solution. References: Batygin, K., Adams, F. C., Brown, M. E., and Becker, J. C. 2019, “The Planet Nine Hypothesis”, Physics Reports, 805 Di Ruscio, A., Fienga, A., Durante, D., Iess, L., Laskar, J., and Gastineau, M. 2020, “Analysis of Cassini radio tracking data for the construction of INPOP19a: A new estimate of the Kuiper belt mass”, A&A, Forthcoming article Durante, D., Hemingway, D. J., Racioppa, P., Iess, L., and Stevenson, D. J. 2019, “Titan's gravity field and interior structure after Cassini”, Icarus, 326, 123 Fienga, A., Deram, P., Viswanathan, V., Di Ruscio, A., Bernus, L., Durante, D., Gastineau, M., and Laskar, J. 2019, “INPOP19a planetary ephemerides”, NSTIM, 109 Fienga, A., Di Ruscio, A., Bernus, L. Deram, P., Durante, D., Laskar, J., and Iess, L. 2020, “New constraints on the location of P9 obtained with the INPOP19a planetary ephemeris”, A&A, Forthcoming article Iess, L., Militzer, B., Kaspi, Y., et al. 2019, “Measurement and implications of Saturn’s gravity field and ring mass”, Science, 364 Pitjeva, E. V. & Pitjev, N. P. 2018, “Mass of the Kuiper belt”, Celest. Mech. Dyn. Astron, 130, 57 Prialnik, D., Barucci, M., and Young, L. 2020, “The Trans-Neptunian Solar System”, Elsevier

Context.We used the new released INPOP19a planetary ephemerides benefiting from Jupiter-updated positions by theJunomission and reanalyzedCassiniobservations.Aims.We test possible locations of the unknown planet P9. To do this, we used the perturbations it produces on the orbits of the outer planets, more specifically, on the orbit of Saturn.Methods.Two statistical criteria were used to identify possible acceptable locations of P9 according to (i) the difference in planetary positions when P9 is included compared with the propagated covariance matrix, and (ii) theχ2likelihood of postfit residuals for ephemerides when P9 is included.Results.No significant improvement of the residuals was found for any of the simulated locations, but we provide zones that induce a significant degradation of the ephemerides.Conclusions.Based on the INPOP19a planetary ephemerides, we demonstrate that if P9 exists, it cannot be closer than 500 AU with a 5M⊕and no closer than 650 AU with a 10M⊕. We also show that there is no clear zone that would indicate the positive existence of planet P9, but there are zones for which the existence of P9 is compatible with the 3σaccuracy of the INPOP planetary ephemerides.

The Juno spacecraft arrived at Jupiter’s system on July 4th, 2016 and reached the mid-point of its nominal mission in December 2018, after completing 17 perijove passes. Juno is currently orbiting Jupiter in a highly eccentric orbit, with a perijove altitude of about 4000 km that provides great sensitivity to the gravitational field of the planet. The radioscience instrumentation on board Juno enables very accurate radial velocity (Doppler) measurements, with noise as low as 10 micron/s at an integration time of 60 s. The gravity field of the planet is recovered though detailed reconstruction of Juno’s motion and observation model, performed with JPL’s and University of Pisa’s latest precise orbit determination codes, MONTE and ORBIT14 respectively.We provide an update on Jupiter’s gravity field, its tidal response and spin axis motion over the first half of Juno’s mission. Although the Doppler data collected during the first two gravity-dedicated perijove passes have been reduced to the noise level by assuming a purely axially symmetric field for the gas giant, the current dataset, which includes ten passes, hints to a non-static and/or non-axially symmetric field, possibly related to several different mechanisms, such as normal modes, localized atmospheric or deeply-rooted dynamics.

Fertility rates show dynamically–varying shapes when modeled as a function of the age at delivery. We incorporate this behavior under a novel Bayesian approach for dynamic modeling of proportionate age–specific fertility rates via skewed processes. The model assumes a skew–normal distribution for the age at the moment of childbirth, while allowing the location and the skewness parameters to evolve in time via Gaussian processes priors. Posterior inference is performed via Monte Carlo methods, leveraging results on unified skew–normal distributions. The proposed approach is illustrated on Italian age–specific fertility rates from 1991 to 2014, providing forecasts until 2030.

We propose the system design of a small orbiter of the Jovian moon Europa (Europa Tomography Probe, ETP in short) aimed at unveiling its interior structure. ETP is conceived as a piggyback probe of a larger spacecraft to the Jovian system (such as Europa Clipper). Its payload comprises only a magnetometer and transponder. The former will be used to measure the time-varying, induction magnetic field of the moon at different orbital and rotational frequencies, a measurement inaccessible to a flyby spacecraft. An Inter-Satellite Link (ISL) between ETP and the main spacecraft, enabled by the on-board transponder, will be used to accurately determine Europa's gravity field, rotational state and tidal deformation. By combining magnetic and gravity field measurements, ETP could characterize the interior structure of Europa with an accuracy only attainable by a low-altitude orbiter, thus constraining the thickness and conductivity of the subsurface ocean. Following the announcement that a 250-300-kg mass allowance was available on the upcoming NASA Europa Clipper spacecraft, we propose ETP's mission and spacecraft design assuming Clipper's nominal trajectory as a baseline. The concept can be adapted to a class of missions to the Jovian and Saturnian systems based upon a mother-daughter spacecraft system. The spacecraft design has been pursued under the philosophy of determining the minimum required total mass and volume that allows to meet the scientific requirements, rather than finding out what science return could be obtained with pre-assigned system constraints. Since ETP shall autonomously reach its final orbit, the propulsion system has been one of the primary focuses. The radiation analysis has also been essential because the shielding structure affects both the mission duration and the mass budget. We show that the ETP concept could be, indeed, technically feasible with an overall system mass budget just above 250 kg, thus providing a valuable yet affordable augmentation to a larger flyby mission to Europa.

We analyze the range-rate residual data from Cassini’s gravity experiment that cannot be explained with a static, zonally symmetric gravity field. We reproduce the data using a simple forward model of gravity perturbations from normal modes. To do this, we stack data from multiple flybys to improve sensitivity. We find a partially degenerate set of normal-mode energy spectra that successfully reproduce the unknown gravity signal from Cassini’s flybys. Although there is no unique solution, we find that the models most likely to fit the data are dominated by gravitational contributions from p-modes between 500 and 700 μHz. Because f-modes at lower frequencies have stronger gravity signals for a given amplitude, this result would suggest strong frequency dependence in normal-mode excitation on Saturn. We predict peak amplitudes for p-modes on the order of several kilometers, at least an order of magnitude larger than the peak amplitudes inferred by Earth-based observations of Jupiter. The large p-mode amplitudes we predict on Saturn, if they are indeed present and steady state, would imply weak damping with a lower bound of Q > 107 for these modes, consistent with theoretical predictions.

The Juno spacecraft reached the mid‐point of its nominal mission in December 2018, after completing 17 perijove passes. Ten of these were dedicated to the determination of the gravity field of the planet, with the aim of constraining its interior structure. We provide an update on Jupiter's gravity field, its tidal response and spin axis motion over time. The analysis of the Doppler data collected during the perijove passes hints to a non‐static and/or non‐axially symmetric field, possibly related to several different physical mechanisms, such as normal modes or localized atmospheric or deeply‐rooted dynamics.

BepiColombo's Mercury orbiter radio science experiment (MORE) was conceived to enable extremely accurate radio tracking measurements of the Mercury Planetary Orbiter to precisely determine the gravity field and the rotational state of Mercury, and to test theories of gravitation (e.g., Einstein's theory of general relativity). The design accuracy of the radio tracking data was 0.004 mm/s (at 1000 s integration time) for the range-rate measurements and 20 cm for the range (at a few seconds of the integration time). These accuracies are attained due to a combination of simultaneous two-way microwave links at X (7.2–8.4 GHz) and Ka-band (32–34 GHz) to calibrate the dispersive plasma noise component. In this letter, we present the first analysis of the range and range-rate data collected by ESA's deep-space antenna (DSA) during the initial cruise phase of BepiColombo. The novel 24 Mcps pseudonoise (PN) modulation of the Ka-band carrier, enabled by MORE's Ka-band transponder, built by Thales Alenia Space Italy, Rome, Italy, provided two-way range measurements to the centimeter-level accuracy, with an integration time of 4.2 s at 0.29 astronomical units. In tracking passes with favorable weather conditions, the range-rate measurements attained an average accuracy of 0.01 mm/s at 60 s integration time. Data from May 20–24, 2019 were combined in a multi-pass analysis to test the link stability on a longer timescale. The results confirm the noise level observed with the single-pass analysis and provide a preliminary indication that the MORE PN ranging system at 24 Mcps is compatible with the realization of an absolute measurement, where the need to introduce the range biases in the orbital fit is much more limited than in the past. We show that in the initial cruise test the BepiColombo radio link provided the range measurements of unprecedented accuracy for a planetary mission, and that, in general, all target accuracies for radio-metric measurements were exceeded.

Context. Recent discoveries of new trans-Neptunian objects have greatly increased the attention by the scientific community to this relatively unknown region of the solar system. The current level of precision achieved in the description of planet orbits has transformed modern ephemerides in the most updated tools for studying the gravitational interactions between solar system bodies. In this context, the orbit of Saturn plays a primary role, especially thanks to Cassini tracking data collected during its 13-year mission around the ringed planet. Planetary ephemerides are currently mainly built using radio data, in particular with normal points derived from range and Doppler observables exchanged between ground stations and interplanetary probes. Aims. We present an analysis of Cassini navigation data aimed at producing new normal points based on the most updated knowledge of the Saturnian system developed throughout the whole mission. We provide additional points from radio science dedicated passes of Grand Finale orbits and Titan flybys. An updated version of the INPOP planetary ephemerides based upon these normal points is presented, along with a new estimate of the mass of trans-Neptunian object rings located in the 2:1 and 3:2 mean motion resonances with Neptune. Methods. We describe in detail the orbit determination process performed to construct the normal points and their associated uncertainties and how we process those points to produce a new planetary ephemeris. Results. From the analysis, we obtained 623 new normal points for Saturn with metre-level accuracy. The ephemeris INPOP19a, including this new dataset, provides an estimated mass for the trans-Neptunian object rings of (0.061 ± 0.001)M⊕.

The innermost galileian moon Io hosts an intense volcanic activity, which ejects about 103 kg/s of gas into Jupiter's magnetosphere. Here these neutrals are ionized by interaction with the background plasma and they are accelerated from keplerian velocity to corotation velocity thanks to Alfvén's theorem. This plasma cloud around the planet (the so-called Io Plasma Torus or IPT) slowly diffuses across Jupiter's magnetic field, but high electron densities (>1000-2000 cm-3) are found between 5-8 RJ.Juno is travelling along highly eccentric, polar orbits around the planet and flies very close to Jupiter's surface during each perijove. Thus, the radio links used for ground communication and radio science cross the IPT both in the uplink and the downlink leg. Being a dispersive medium, the torus introduces a different path delay on the X/X and Ka/Ka links established between the Ground Station and the spacecraft. Thus, the path delay can be extracted through a linear combination of the two links, and then quantitatively analyzed and fitted to different parametric models of the IPT.In this work we have used almost all the available Juno radio occultations of the IPT in order to improve an already existing model by introducing both longitudinal and temporal variations of the electron density. To this end, we looked for the 2D Fourier expansion in longitude and time of the parameters of this model with the goal of minimizing the residuals of the fit and pointing out periodicities in the morphology of the torus.

There is a wide variety of models in which the dimension of the parameter space is unknown. For example, in factor analysis the number of latent factors is typically not known and has to be inferred from the observed data. Although classical shrinkage priors are useful in these contexts, increasing shrinkage priors can provide a more effective option, which progressively penalizes expansions with growing complexity. In this article we propose a novel increasing shrinkage prior, named the cumulative shrinkage process, for the parameters controlling the dimension in over-complete formulations. Our construction has broad applicability, simple interpretation, and is based on a sequence of spike and slab distributions which assign increasing mass to the spike as model complexity grows. Using factor analysis as an illustrative example, we show that this formulation has theoretical and practical advantages over current competitors, including an improved ability to recover the model dimension. An adaptive Markov chain Monte Carlo algorithm is proposed, and the methods are evaluated in simulation studies and applied to personality traits data., Comment: 8 pages, 2 tables and 1 figure; v2: more theory, algorithms (adaptive Gibbs sampler added) and empirical studies (simulations, sensitivity analyses, real-data application); v3: small typos fixed and GitHub link added to the abstract

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.

There is wide interest in studying how the distribution of a continuous response changes with a predictor. We are motivated by environmental applications in which the predictor is the dose of an exposure and the response is a health outcome. A main focus in these studies is inference on dose levels associated with a given increase in risk relative to a baseline. In addressing this goal, popular methods either dichotomize the continuous response or focus on modeling changes with the dose in the expectation of the outcome. Such choices may lead to information loss and provide inaccurate inference on dose–response relationships. We instead propose a Bayesian convex mixture regression model that allows the entire distribution of the health outcome to be unknown and changing with the dose. To balance flexibility and parsimony, we rely on a mixture model for the density at the extreme doses, and express the conditional density at each intermediate dose via a convex combination of these extremal densities. This representation generalizes classical dose–response models for quantitative outcomes, and provides a more parsimonious, but still powerful, formulation compared to nonparametric methods, thereby improving interpretability and efficiency in inference on risk functions. A Markov chain Monte Carlo algorithm for posterior inference is developed, and the benefits of our methods are outlined in simulations, along with a study on the impact of dde exposure on gestational age.

International audience; Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown1,2, limiting our ability to probe the structure and composition of the planet3,4. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric5 and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops6. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno5 and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation7. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.