D. Dirkx
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To overcome these limitations, we present geoMCMC, an open-source Python library developed to provide a unified, consistent, and modular computational framework for planetary interior analysis. By standardizing the inversion workflow, this library aims to enhance model sharing, cross-disciplinary collaboration, and methodological reproducibility across the planetary science community. Originally conceptualized to investigate the subsurface oceans of icy satellites [5], geoMCMC has evolved into a generalized, high-performance computational framework designed for the Bayesian inversion of both rocky and icy planetary bodies.
At its core, the software relies on a plugin-based architecture orchestrated by a central inference problem pattern. As illustrated in Fig. 1, this architecture explicitly decouples statistical inference from physical modeling through a five-pillar design: the Body (managing planetary layer states and geometry), the Parameter Set (linking statistical priors to interior attributes), the Observation Set (handling geophysical forward models), the Constraint Set (enforcing physical assumptions), and the Sampler (the Bayesian inference engine). This modularity ensures that state definitions, geometry, model constraints, and sampling algorithms function as independent, interchangeable components. For instance, users can seamlessly swap constraint modules, i.e. the functional blocks responsible for enforcing fundamental a priori physical assumptions, such as mass balance, hydrostatic equilibrium, or advanced thermodynamic models. In fact, these modules automatically resolve interdependent properties to guarantee physical consistency before any forward model is evaluated. Furthermore, the architecture is designed for high-performance parallel processing, allowing computationally intensive physical models to be offloaded to a high-efficiency compiled C++ kernel. ...
To overcome these limitations, we present geoMCMC, an open-source Python library developed to provide a unified, consistent, and modular computational framework for planetary interior analysis. By standardizing the inversion workflow, this library aims to enhance model sharing, cross-disciplinary collaboration, and methodological reproducibility across the planetary science community. Originally conceptualized to investigate the subsurface oceans of icy satellites [5], geoMCMC has evolved into a generalized, high-performance computational framework designed for the Bayesian inversion of both rocky and icy planetary bodies.
At its core, the software relies on a plugin-based architecture orchestrated by a central inference problem pattern. As illustrated in Fig. 1, this architecture explicitly decouples statistical inference from physical modeling through a five-pillar design: the Body (managing planetary layer states and geometry), the Parameter Set (linking statistical priors to interior attributes), the Observation Set (handling geophysical forward models), the Constraint Set (enforcing physical assumptions), and the Sampler (the Bayesian inference engine). This modularity ensures that state definitions, geometry, model constraints, and sampling algorithms function as independent, interchangeable components. For instance, users can seamlessly swap constraint modules, i.e. the functional blocks responsible for enforcing fundamental a priori physical assumptions, such as mass balance, hydrostatic equilibrium, or advanced thermodynamic models. In fact, these modules automatically resolve interdependent properties to guarantee physical consistency before any forward model is evaluated. Furthermore, the architecture is designed for high-performance parallel processing, allowing computationally intensive physical models to be offloaded to a high-efficiency compiled C++ kernel.
The recent discovery of strong tidal dissipation in Saturn’s interior has radically changed our view of the Saturnian system. While some questions are naturally answered by the new paradigm, others are emerging and require further measurement. This article presents the next key questions to be addressed by future space missions and analysis. Suggestions for space measurements to discriminate between different scenarios concerning the formation, evolution and internal state of the Saturnian system are given.
1. Uncover the evolution of Mars by studying interior dynamics, detailed structure and composition of the planet's lithosphere and deep mantle.
2. Capture Mars' climate history by monitoring the density of the planet's upper atmosphere and uncover the monthly, seasonal, and long-term changes.
3. Explore potential scenarios for the fate and sequestration pathways of Mars' surface liquid water.
These primary mission goals will have profound and long-lasting impacts on the study of Mars, shedding new light on Mars' geologic evolution and ongoing interior and atmosphere activity.
Activities are ongoing to increase the TRL-level of the instrument technology. Both improved systems for the main instruments are being developed. LRI link acquisition is being developed to improve the initialisation phases. Also, other laser frequencies are being looked at to be able to share laser sources for the LRI and CAI accelerometers. Improvements of the internal layout of the CAI instrumentation help in detecting bottlenecks in the new technology. Mission design studies are improving the understanding of the impact of certain orbit choices to the precission and coverage of the observations. Finally we will also present some preliminary CFD studies performed on the whole mission design, highlighting that the mission is technological feasible and will provide excellent data to improve our understanding of Mars. ...
1. Uncover the evolution of Mars by studying interior dynamics, detailed structure and composition of the planet's lithosphere and deep mantle.
2. Capture Mars' climate history by monitoring the density of the planet's upper atmosphere and uncover the monthly, seasonal, and long-term changes.
3. Explore potential scenarios for the fate and sequestration pathways of Mars' surface liquid water.
These primary mission goals will have profound and long-lasting impacts on the study of Mars, shedding new light on Mars' geologic evolution and ongoing interior and atmosphere activity.
Activities are ongoing to increase the TRL-level of the instrument technology. Both improved systems for the main instruments are being developed. LRI link acquisition is being developed to improve the initialisation phases. Also, other laser frequencies are being looked at to be able to share laser sources for the LRI and CAI accelerometers. Improvements of the internal layout of the CAI instrumentation help in detecting bottlenecks in the new technology. Mission design studies are improving the understanding of the impact of certain orbit choices to the precission and coverage of the observations. Finally we will also present some preliminary CFD studies performed on the whole mission design, highlighting that the mission is technological feasible and will provide excellent data to improve our understanding of Mars.
High-precision inter-satellite ranging is critical for formation flying, autonomous navigation, and scientific measurements in small-satellite missions. Laser communication terminals (LCTs) offer an opportunity to perform both data transfer and ranging, but their dual-use imposes stringent requirements on onboard clocks and timing electronics. This paper investigates the impact of clock-induced timing errors on two-way LCT-based ranging between CubeSats operating around the near-Earth asteroid 99942 Apophis. A methodology is developed to unify clock noise specifications provided in datasheets, generating realistic timing errors across microsecond-to-hour integration periods. Using high-fidelity orbital simulations, two orbital configurations—coplanar and non-coplanar—are analyzed to evaluate how relative satellite geometry influences the propagation of clock errors into range measurements, orbit determination, and the estimation of Apophis’ gravitational parameter. Results demonstrate that inter-satellite links (ISLs) can reduce orbit determination errors along directions weakly constrained by Earth-based Doppler—from 1–3 m to 0.1–0.3 m in coplanar formations, and even further in non-coplanar formations—corresponding to improvements of one to two orders of magnitude. Subsystem-level noise, such as detector jitter and time tagging, can still limit achievable precision, even with high-performance clocks. The methodology provides a framework applicable to a broad range of small-satellite missions, guiding the selection of clocks, formation geometry, and system design to optimize both navigation performance and science return.
In 2031 the JUICE spacecraft will perform a multi-flyby tour of the Jovian system. Next to the radiometric tracking that is performed for navigation operations, the dedicated radio science instrument (3GM) collects high-accuracy radiometric measurements during the flybys. We investigate the capability of the radio science data to provide improved moon state knowledge during navigational operations. We introduce ephemeris updates from radio science data into our simulated navigation operations and examine the potential savings of statistical ΔV for corrective manoeuvres. A navigation orbit determination (OD) solution was simulated for the multi-flyby tour of JUICE, including the resulting state knowledge evolution of the Galilean moons. The OD was extended by an interface for external moon ephemeris updates, which was used to evaluate the impact of radio science generated external ephemerides on the statistical ΔV budgets for post-flyby cleanup manoeuvres. The moon state knowledge evolution during navigation operation showed a rapid reduction of the a-priori moon state uncertainty, for which the navigational tracking data coverage of the long, early tour arcs was identified as the driving factor. As a result of the longer tracking arcs, the moon state knowledge from navigation data results improves more quickly during the initial phase of the tour. Since the impact of moon state knowledge on the corrective manoeuvres is largest in this initial phase, the comparative analysis of the statistical ΔV cost shows that the adoption of radio science ephemeris products does not effectuate significant ΔV savings. Instead we showed that in order to achieve substantial ΔV savings improvements of Europa's and Ganymede's ephemerides are required ahead of JUICE's arrival. While the analysis concludes that data synergies are unlikely to benefit the navigational operations, it highlights other potential synergies between the navigation and radio science data. A comparatively strong signature of Io's dynamics was found in the simulated navigation data along the long early tour arcs, which could be leveraged for the benefit of the new global moon ephemeris solutions after JUICE.
Context. Upcoming science missions to Phobos will potentially provide unprecedented observations of Phobos’s orbit in the form of orbiter and/or lander tracking data. This will likely require an updating of the dynamical models currently used to invert this data, with the coupling between the satellite’s orbit and rotation being of particular importance. State-of-the-art ephemerides estimations for tidally locked satellites rely on a decoupled approach where translational models are combined with a simplified analytical representation of the moon’s rotation (typically a single-frequency periodic variation superimposed to a synchronous rotation). Aims. This paper investigates the coupled propagation of Phobos’s translational and rotational dynamics, and assesses the extent to which the most commonly used uncoupled model can emulate the results of the coupled integration, and what consequences the mismodeling has on the products of data inversion. Methods. We considered two models: a coupled model that propagates Phobos’s translational and rotational dynamics simultaneously, and an uncoupled model that assumes Phobos to be in a fully locked configuration with a once-per-orbit longitudinal libration. By simulating the dynamics for about ten years, first in a coupled and then in an uncoupled manner, we compared the results and used the coupled trajectory as simulated observations for an estimation of the different parameters using uncoupled translational dynamics. Results. For identical initial states, differences between the coupled and uncoupled trajectories were found to accumulate to 40 m, most predominantly in Phobos’s direction of motion. Longitudinal librations were misrepresented by the uncoupled model particularly around the frequencies of the normal mode, where forcings are amplified up to 3.6 × 10−3 degrees. Long-term latitudinal librations also arise from forcings due to coupling-induced changes in orbital inclination. The use of uncoupled models in data inversion results in true errors in the estimated parameters. In this case, we performed estimations of different lengths up to 1000 days to estimate Phobos’s initial state, once-per-orbit libration amplitude, and harmonic coefficients C2,0 and C2,2. Errors in dynamical parameters were found to be on the order of 10−3 degrees for the physical libration amplitude and of 10−5 for the harmonic coefficients (relative errors of around 0.1%). Conclusions. These true errors are one to three orders of magnitude above the formal errors expected from laser ranging measurements to a Phobos lander, which indicates that the typical single-frequency uncoupled model is not suitable for the proper inversion of such data. Refined rotation models will therefore be required, either by expanding the uncoupled model to multiple frequencies or by performing a fully coupled orbital-rotational propagation as proposed in this paper. We discuss the theoretical and practical limitations of an extended analytical parametrization in the specific case of tidally locked satellites, and advocate for the use of a fully coupled approach.
Juice (JUpiter ICy moons Explorer) 3GM Radio Science Experiment will map the gravitational field of Ganymede with unprecedented accuracy and measure tidally-induced variations. These measurements will allow the characterization of its putative ocean and may resolve lateral variations in internal structure. Lateral variations cause an additional tidal signal that depends on their wavelength and amplitude. We show that shell thickness variations of (Formula presented.) the mean thickness produce an additional tidal signal (Formula presented.) times smaller than the main tidal signal, detectable given the accuracy of Juice. Using a Bayesian framework, we show that measuring differences between (Formula presented.) and (Formula presented.) constrain equator to pole shell thickness differences. Also measuring the degree-3 spherical harmonic signal due to degree 2 forcing constrain degree-1 and degree-3 structure. This demonstrates tidal tomography's potential to map three dimensional structure and supports its consideration for future missions.
The radio telescopes of the European VLBI Network (EVN) and the University of Tasmania (UTAS) conducted an extensive observation campaign of the European Space Agency's (ESA) Mars Express (MEX) spacecraft between 2013 and 2020. The campaign, carried out under the Planetary Radio Interferometry and Doppler Experiment (PRIDE) framework, aimed to study interplanetary phase scintillation and assess the noise budget in the closed-loop Doppler observations. The average closed-loop Doppler noise was determined to be approximately 10 mHz at a 10-s integration time, reaffirming the technique's suitability for radio science experiments. We evaluated how different observational parameters such as the solar elongation, antenna size, and elevation angle impact the Doppler noise. A key part of the analysis involved comparing results from co-located telescopes to investigate system noise effects. Co-located telescopes at both Wettzell and Hobart provided highly consistent results, with any deviations serving as diagnostic tools to identify station-dependent issues. Additionally, the use of phase calibration tones during spacecraft tracking showed that the instrumental noise contribution is of the order of 5 of the total noise. This study provides a detailed noise budget for closed-loop Doppler observations with VLBI telescopes while emphasizing the effectiveness of the co-location method in isolating system-level noise. These findings are important for optimizing future radio science and VLBI tracking missions using stations outside the the Deep Space Network (DSN) and European Space Tracking (ESTRACK) network.
To quantify the contribution of JUICE astrometry, we have performed the inversion of simulated optical astrometric observations by JUICE, using suitable a priori covariance to represent the radio science-only solution. Incorporating the astrometry into the ephemeris solution requires the consideration of the offset between Io’s centre-of-figure (COF, which astrometry measures) and the centre-of-mass (COM, which the ephemeris solution requires). We explicitly account for the offset between COF and COM as an estimated parameter in our model.
We assess the contribution of the optical observations to the ephemeris solution as a function of the radio science true-to-formal-error ratio (describing the statistical realism of the simulated radio science solution), as well as optical data quantity and planning. From this, we discuss to which extent space-based astrometry could help to validate the radio science solution, and under which conditions the data could improve the orbital solution of Io.
Significant contributions of astrometry to Io’s orbital solution occur for radio science true-to-formal-error ratios of 4 and higher (for the along-track and normal direction). This shows that optical space-based astrometry can improve and/or validate the radio science solution. Reductions in the obtainable uncertainties for the COF-COM-offset range from about 20 to 50 per cent – depending on the number of observations – using suitable algorithms to select the epochs at which observations are to be simulated. In particular, observations during the high-inclination phase have proven especially beneficial.
Our results show that constraints on the COM-COF offset of Io could be obtained from astrometry at the level 100 m – 1 km, depending on the quantity and planning of the observations. This could provide a novel data point to constrain Io’s interior. Moreover, the astrometric data will provide independent validation – and possibly improvement – of the orbital solution of Io. ...
To quantify the contribution of JUICE astrometry, we have performed the inversion of simulated optical astrometric observations by JUICE, using suitable a priori covariance to represent the radio science-only solution. Incorporating the astrometry into the ephemeris solution requires the consideration of the offset between Io’s centre-of-figure (COF, which astrometry measures) and the centre-of-mass (COM, which the ephemeris solution requires). We explicitly account for the offset between COF and COM as an estimated parameter in our model.
We assess the contribution of the optical observations to the ephemeris solution as a function of the radio science true-to-formal-error ratio (describing the statistical realism of the simulated radio science solution), as well as optical data quantity and planning. From this, we discuss to which extent space-based astrometry could help to validate the radio science solution, and under which conditions the data could improve the orbital solution of Io.
Significant contributions of astrometry to Io’s orbital solution occur for radio science true-to-formal-error ratios of 4 and higher (for the along-track and normal direction). This shows that optical space-based astrometry can improve and/or validate the radio science solution. Reductions in the obtainable uncertainties for the COF-COM-offset range from about 20 to 50 per cent – depending on the number of observations – using suitable algorithms to select the epochs at which observations are to be simulated. In particular, observations during the high-inclination phase have proven especially beneficial.
Our results show that constraints on the COM-COF offset of Io could be obtained from astrometry at the level 100 m – 1 km, depending on the quantity and planning of the observations. This could provide a novel data point to constrain Io’s interior. Moreover, the astrometric data will provide independent validation – and possibly improvement – of the orbital solution of Io.
In the coming decade, JUICE and Europa Clipper radio-science will yield the most accurate estimation to date of the Galilean moons’ physical parameters and ephemerides. JUICE's PRIDE (Planetary Radio Interferometry and Doppler Experiment) will help achieve such a solution by providing VLBI (Very Long Baseline Interferometry) observations of the spacecraft's lateral position, complementing nominal radio-science measurements. In this paper, we quantify how PRIDE VLBI can contribute to the moons’ ephemerides determination, in terms of attainable solution improvement and validation opportunities. To this end, we simulated VLBI data for JUICE, but also investigated the possibility to perform simultaneous tracking of JUICE and Europa Clipper, thus ultimately generating both single- and dual-spacecraft VLBI. We considered various tracking and data quality scenarios for both VLBI types, and compared the formal uncertainties provided by covariance analyses with and without VLBI. These analyses were performed for both global and local (i.e. per-flyby) estimations of the moons’ states, as eventually achieving a global solution first requires proceeding arc-per-arc. We showed that both single- and multi-spacecraft VLBI measurements only bring limited improvement to the global state estimation, but significantly contribute to the moons’ normal points (i.e. local states at flyby times), most notably in the out-of-plane direction. Additionally, we designed a validation plan exploiting PRIDE VLBI to progressively validate the classical radio-science solution, whose robustness and statistical realism is sensitive to modelling inconsistencies. By improving the local state estimations and offering various validation opportunities, PRIDE will be invaluable in overcoming possible dynamical challenges. It can therefore play a key role in reconstructing a global solution for the Galilean moons’ dynamics with the uncertainty levels promised by JUICE-Europa Clipper analyses. This, in turn, is critical to the accurate characterisation of tidal dissipation in the Jovian system, holding the key to the long-term evolution of the Galilean moons.
The JUpiter ICy moons Explorer (JUICE) of ESA was launched on 14 April 2023 and will arrive at Jupiter and its moons in July 2031. In this review article, we describe how JUICE will investigate the interior of the three icy Galilean moons, Ganymede, Callisto and Europa, during its Jupiter orbital tour and the final orbital phase around Ganymede. Detailed geophysical observations about the interior of the moons can only be performed from close distances to the moons, and best estimates of signatures of the interior, such as an induced magnetic field, tides and rotation variations, and radar reflections, will be obtained during flybys of the moons with altitudes of about 1000 km or less and during the Ganymede orbital phase at an average altitude of 490 km. The 9-month long orbital phase around Ganymede, the first of its kind around another moon than our Moon, will allow an unprecedented and detailed insight into the moon’s interior, from the central regions where a magnetic field is generated to the internal ocean and outer ice shell. Multiple flybys of Callisto will clarify the differences in evolution compared to Ganymede and will provide key constraints on the origin and evolution of the Jupiter system. JUICE will visit Europa only during two close flybys and the geophysical investigations will focus on selected areas of the ice shell. A prime goal of JUICE is the characterisation of the ice shell and ocean of the Galilean moons, and we here specifically emphasise the synergistic aspects of the different geophysical investigations, showing how different instruments will work together to probe the hydrosphere. We also describe how synergies between JUICE instruments will contribute to the assessment of the deep interior of the moons, their internal differentiation, dynamics and evolution. In situ measurements and remote sensing observations will support the geophysical instruments to achieve these goals, but will also, together with subsurface radar sounding, provide information about tectonics, potential plumes, and the composition of the surface, which will help understanding the composition of the interior, the structure of the ice shell, and exchange processes between ocean, ice and surface. Accurate tracking of the JUICE spacecraft all along the mission will strongly improve our knowledge of the changing orbital motions of the moons and will provide additional insight into the dissipative processes in the Jupiter system. Finally, we present an overview of how the geophysical investigations will be performed and describe the operational synergies and challenges.
China will launch the “Tianwen-IV” mission around 2030, focusing on the orbiting exploration of Jupiter and Callisto, a moon of Jupiter. As part of this ambitious mission, a main satellite will carry another satellite that will be released in the Jupiter system to continue its journey toward Uranus. Considering the current mission planning, we propose an inter-satellite radio-observation mode that differs from the conventional observation mode of tracking from Earth to precisely determine the orbit of the satellites. Given the significance of the Callisto gravity field model in both science objectives and satellite navigation, we have conducted a series of simulation experiments to evaluate the potential of this inter-satellite range-rate data for accurately estimating the Callisto gravity field. The results obtained from the analysis demonstrate that by utilizing 40 days of ground station observations, it is possible to estimate the gravity field model of Callisto up to a degree of 70. Remarkably, when combining these ground station observations with inter-satellite observations, a comparable level of accuracy can be achieved with just 10 days of observations. Furthermore, with reduced inter-satellite observation noise, accuracy improves, enabling estimation up to 80 degrees or higher. Initial inter-satellite distance selection impacts estimation accuracy. These findings serve as a valuable test bed for the future “Tianwen-IV” mission to perform precise orbit determination and gravity field model estimation to reduce reliance on deep space stations.
Aims. We investigate whether volcanic exomoons can be detected in thermal wavelength light curves due to their phase variability along their orbit. The method we use is based on the photometric signal variability that volcanic features or hotspots would cause in infrared (IR) wavelengths, when they are inhomogeneously distributed on the surface of a tidally heated exomoon (THEM). Methods. We simulated satellites of various sizes around an isolated planet and modeled the system’s variability in two IR wavelengths, taking into account photon shot noise. The moon’s periodic signal as it orbits the planet introduces a peak in the frequency space of the system’s time-variable flux. We investigated the THEM and system properties that would make a moon stand out in the frequency space of its host’s variable flux. Results. The moon’s signal can produce a prominent feature in its host’s flux periodogram at shorter IR wavelengths for hotspots with temperatures similar to the ones seen on the Jovian moon, Io, while the same moon would not be identifiable in longer IR wavelengths. By comparing observations at two different wavelengths, we are able to disentangle the signal of an exomoon with transiting and non-transiting orbital inclinations from the planet’s signal in the frequency domain for system distances up to ∼10 pc for Mars-sized exomoons and even further for Earth-sized ones. Conclusions. This method enlarges the parameter space of detectable exomoons around isolated planetary mass objects and directly imaged exoplanets, as it is sensitive to Io- to Earth-sized exomoons with hot volcanic features for a wide range of non-transiting orbital inclinations. Exomoon transits and the detection of outgassed volcanic molecules can subsequently confirm a putative detection.
We present an overview of the operations and engineering interface for Planetary Radio Interferometry and Doppler Experiment (PRIDE) radio astronomy observations as a scientific component of the ESA’s Jupiter Icy Moons Explorer (JUICE) mission, as well as other prospective planetary and space science missions. The article discusses advanced scheduling and planning methods that make it possible to create observing schedules for observations of specific spacecraft in concurrence with observations of natural radio sources. In order to put this into practice and find suitable natural background calibrator sources for PRIDE of JUICE mission, we developed planning and scheduling software. The conventional scheduling software for natural celestial radio sources is not set up to include spacecraft as observation targets in the necessary control files. Therefore, difficulties already arise during observation planning. We report on the development of new and the adaptation of existing routines used in astrophysical and geodetic VLBI for satellite scheduling and planning. The analysis of the PRIDE science observations led to improved observational planning, and the mission’s scheduling methodologies were studied using a systems engineering approach. In addition, we highlighted the new procedures, like finding charts for selecting calibrator radio sources over a range of frequency bands and the outcomes of those strategies for science operation planning. A simulation of the flyby of Venus during the cruise phase of the JUICE spacecraft, based on the Tudat software, is also presented, resulting in a promising opportunity to test PRIDE techniques and evaluate the improvements that PRIDE observables can make to natural bodies’ ephemerides. The first K a-band (32 GHz) observations of the ESA’s BepiColombo by a radio telescope in the VLBI network, which employs a similar radio communications system as JUICE, were also demonstrated as a test case. The primary objective of these activities is to serve as a practice run for the upcoming operational PRIDE JUICE operations. We showcase the capabilities of the planning and scheduling software for other space missions.