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.

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Planetary Radio Interferometry and Doppler Experiment (PRIDE) is a multi-purpose experimental technique aimed at enhancing the science return of planetary missions. The technique exploits the science payload and spacecraft service systems without requiring a dedicated onboard instrumentation or imposing on the existing instrumentation any special for PRIDE requirements. PRIDE is based on the near-field phase-referencing Very Long Baseline Interferometry (VLBI) and evaluation of the Doppler shift of the radio signal transmitted by spacecraft by observing it with multiple Earth-based radio telescopes. The methodology of PRIDE has been developed initially at the Joint Institute for VLBI ERIC (JIVE) for tracking the ESA’s Huygens Probe during its descent in the atmosphere of Titan in 2005. From that point on, the technique has been demonstrated for various planetary and other space science missions. The estimates of lateral position of the target spacecraft are done using the phase-referencing VLBI technique. Together with radial Doppler estimates, these observables can be used for a variety of applications, including improving the knowledge of the spacecraft state vector. The PRIDE measurements can be applied to a broad scope of research fields including studies of atmospheres through the use of radio occultations, the improvement of planetary and satellite ephemerides, as well as gravity field parameters and other geodetic properties of interest, and estimations of interplanetary plasma properties. This paper presents the implementation of PRIDE as a component of the ESA’s Jupiter Icy Moons Explorer (JUICE) mission.

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Long-term monitoring of global mass transport within the Earth system improves our ability to mitigate natural hazards and better understand their relations to climate change. Satellite gravity is widely used to monitor surface mass variations for its unprecedented spatial and temporal coverage. However, the gravity data contain signals from visco-elastic deformation in response to past ice sheet melting, preventing us from extracting signals of present-day surface mass trend (PDMT) directly. Here we present a global inversion scheme that separates PDMT and visco-elastic glacial isostatic adjustment (GIA) signatures by combining satellite gravimetry with satellite altimetry and ground observations. Our inversion provides global dual data coverage that enables a robust separation of PDMT and GIA spherical harmonic coefficients. It has the advantage of providing estimates of Earth's long wavelength deformation signatures and their uncertainties. Our GIA result, along with its uncertainty estimates, can be used in future GRACE processing to better assess the impact of GIA on surface mass change. Our GIA estimates include a rapid GIA uplift in the Southeast Alaska and the Amundsen Sea Embayment, due to the visco-elastic response to recent glacial unloading. We estimate the average surface mass change rate from 2002–2010 to be −203 ± 3 GT·a⁻¹ in Greenland, −126 ± 18 GT·a⁻¹ in Antarctica and, −62 ± 5 GT·a⁻¹ in Alaska. The GIA low degree spherical harmonic coefficients are sensitive to rheological properties in Earth's deep interior. Our low-degree GIA estimates include geocenter motion and (Formula presented.) which provide unique constraints to understand Earth's lower mantle and ice history.

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In this study, we focus on improved constraint of the glacial isostatic adjustment (GIA) signal at present-day, and its role as a contributor to present-day sea level budgets. The main study area extends from the coastal regions of northwestern Europe to northern Europe. Both Holocene relative sea level (RSL) data as well as vertical land motion (VLM) data are incorporated as constraints in a semi-empirical GIA model. 71 geological rates of GIA-driven RSL change are inferred from Holocene proxy data and 108 rates of vertical land motion from GNSS provide an additional measure of regional GIA deformation. Within the study area, the geological RSL data complement the spatial gaps of the VLM data and vice versa. Both data sets are inverted in a semi-empirical GIA model to yield updated estimates of regional present-day GIA deformations. A regional validation using tide gauges is presented for the North Sea, where the GIA signal may be complicated by lateral variations in Earth structure and existing predictions of regional and global GIA models show discrepancies. The model validation in the North Sea region suggests that geological data are needed to fit independent estimates of GIA-related RSL change inferred from tide gauge rates, indicating that geological rates from Holocene data do provide an important additional constraint for data-driven approaches to GIA estimation.

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Tidal heating can play an important role in the formation and evolution of subsurface oceans of outer-planet moons. Up until now tidal heating has only been studied in subsurface oceans of spatially uniform thickness. We develop a numerical model to consider oceans of spatially variable thickness. We use the Laplace Tidal Equations for the ocean and model the ice shell using membrane theory. The problem is solved using the commercial Finite Element software Comsol Multiphysics®. We use this new model to study the tidal response of Enceladus' ocean with a twofold objective: to understand how ocean thickness variations modify the tidal response of a subsurface ocean and to assess if tidal dissipation in an Enceladan ocean with varying ocean thickness can explain the high heat flux emanating from Enceladus' South Polar Terrain and the perdurance of a subsurface ocean. We consider the effect of meridional ocean thickness changes of spherical harmonic degree two and three as suggested by topography and gravimetry data. We observe that an ocean with degree two topography responds with the same eigenmodes as an ocean of constant thickness but resonances occur for thicker oceans. However, resonant ocean thicknesses are still thin compared to current estimates for Enceladus ocean thickness. Rossby-Haurwitz waves, excited by the obliquity tide for thick oceans of constant thickness, are not excited at the tidal frequency when oceans of variable thickness are considered. This result implies that the role of the obliquity tide in ocean tidal-dissipation might have been overestimated for Enceladus and other icy worlds. An antisymmetric, degree-three ocean thickness variation mixes the ocean modes excited in a constant thickness ocean by the eccentricity and obliquity tide.

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Changes in ocean properties and circulation lead to a spatially non-uniform pattern of ocean dynamic sea-level change (DSLC). The projections of ocean dynamic sea level presented in the IPCC AR5 were constructed with global climate models (GCMs) from the Coupled Model Intercomparison Project 5 (CMIP5). Since CMIP5 GCMs have a relatively coarse resolution and exclude tides and surges it is unclear whether they are suitable for providing DSLC projections in shallow coastal regions such as the Northwestern European Shelf (NWES). One approach to addressing these shortcomings is dynamical downscaling – i.e. using a high-resolution regional model forced with output from GCMs. Here we use the regional shelf seas model AMM7 to show that, depending on the driving CMIP5 GCM, dynamical downscaling can have a large impact on DSLC simulations in the NWES region. For a business-as-usual greenhouse gas concentration scenario, we find that downscaled simulations of twenty-first century DSLC can be up to 15.5 cm smaller than DSLC in the GCM simulations along the North Sea coastline owing to unresolved processes in the GCM. Furthermore, dynamical downscaling affects the simulated time of emergence of sea-level change (SLC) above sea-level variability, and can result in differences in the projected change of the amplitude of the seasonal cycle of sea level of over 0.3 mm/yr. We find that the difference between GCM and downscaled results is of similar magnitude to the uncertainty of CMIP5 ensembles used for previous DSLC projections. Our results support a role for dynamical downscaling in future regional sea-level projections to aid coastal decision makers.

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Planetary Radio Interferometry and Doppler Experiment (PRIDE) will exploit the signal recording and processing technology developed originally for Very Lonag Baseline interferometric (VLBI). The essence of PRIDE is in observing the spacecraft radio signal with a network of Earth-based radio telescopes. The PRIDE technique developed at the Joint Institute for VLBI ERIC (JIVE) together with its partners was used for several experiments with several ESA planetary science missions. It has been chosen by ESA as one of the eleven experiments of the Jupiter Icy Moons Explorer (JUICE), the first Large-class mission in the ESA’s Cosmic Vision 2015–2025 program. The mission is scheduled for launch in 2022. @en

Tidal dissipation makes Jupiter's moon Io the most volcanically active body in the solar system. Most of the heat generated in the interior is lost through volcanic activity. In this study, we aim to answer the questions: Can convection and melt migration in the mantle explain the spatial characteristics of Io's observed volcanic pattern? And, if so, what constraints does this place on the viscosity and thickness of the convective layer? We examine three different spatial characteristics of Io's volcanic activity: (i) The presence of global volcanism, (ii) the presence of large-scale variations in Io's volcanic activity, and (iii) the number of Io's volcanic systems. Our study relies on the assumptions that melt in the mantle controls Io's global volcanism, that the large-scale variations of Io's volcanic activity are caused by nonuniform tidal heating, and that the spatial density of volcanoes correlates with the spatial density of convective anomalies in the mantle. The results show that the observed small and large-scale characteristics of Io's volcanic pattern can be explained by sublithospheric anomalies influenced and caused by convective flow. Solutions that allow for active volcanism and Io's specific large-scale variations in volcanic activity range from a thick mantle of a high viscosity ((Formula presented.) Pa s) to a thin asthenosphere of a low viscosity ((Formula presented.) Pa s). Provided that Io's volcanoes are induced by convective anomalies in the mantle, we find that more than 80% of Io's internal heat is transported by magmatic processes and that Io's upper mantle needs to be thicker than 50 km.

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A growing number of satellites in the outer solar system likely have global oceans beneath their outer icy shells. While the presence of liquid water makes these ocean worlds compelling astrobiological targets, the exchange of heat and materials between the deep interior and the surface also plays a critical role in promoting habitable environments. In this article, we combine geophysical, geochemical, and geological observations of the Jovian satellites Europa, Ganymede, and Callisto as well as the Saturnian satellites Enceladus and Titan to summarize our current state of understanding of their interiors and surface exchange processes. Potential mechanisms for driving exchange processes upward from the ocean floor and downward from the satellite surface are then reviewed, which are primarily based on numerical models of ice shell and ocean dynamics and complemented by terrestrial analog studies. Future missions to explore these exo-oceans will further revolutionize our understanding of ice-ocean exchange processes and their implications for the habitability of these worlds.

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Satellite and recent Earth-based observations of Io's surface reveal a specific spatial pattern of persisting hotspots and sudden high-intensity events. Io's major heat producing mechanism is tidal dissipation, which is thought to be non-uniformly distributed within Io's mantle and asthenosphere. The question arises to what extent Io's non-homogeneous heat production can cause long-wavelength variations in the interior and volcanic activity at the surface. We investigate dissipation patterns resulting from two different initially spherical symmetric visco-elastic rheological structures, which are consistent with geodetic observations. The spatial distributions of the time-averaged tidal heat production are computed by a finite element model. Whereas for the first rheological structure heat is produced only in the upper viscous layer (asthenosphere-heating model), the second rheological structure results in a more evenly distributed dissipation pattern (mixed-heating model) with tidal heating occurring in the deep mantle and the asthenosphere. To relate the heat production to the interior temperature and melt distribution, we use steady-state scaling laws of mantle convection and a simple melt migration model. The resulting long-wavelength thermal heterogeneities strongly depend on the initial tidal dissipation pattern, the thickness of the convective layer, the mantle viscosity, and the ratio between magmatic and convective heat transport. While for the asthenosphere-heating model a strong lateral temperature signal with up to 190 K peak-to-peak difference can remain, convection within a thick convective layer, as for the mixed-heating model, can reduce the lateral temperature variation to <1 K, if the mantle viscosity is sufficiently low. Models with a dominating magma heat transport preserve the long-wavelength pattern of tidal dissipation much better and are favoured, because they are better to explain Io's thick crust. The approach presented here can also be applied to investigate the effect of an arbitrary interior heating pattern on Io's volcanic activity pattern.

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Some of the moons of the outer solar system harbour subsurface liquid oceans. Tidal dissipation plays an important role in preventing these oceans from freezing. In the past, most studies considered only tidal dissipation in the solid layers of these bodies (rock and ice). Recently, new studies considering tidal dissipation in the oceans of these moons have appeared. All of them make use of the shallow water approximation. However, the use of this approximation might not be adequate. Here we consider the linear non-hydrostatic three dimensional response of these oceans to tidal forcing with the full Coriolis force. To do so we consider an ocean of homogeneous density contained within a perfectly spherical shell and neglect the effect of the ice shell. We force the ocean with a time changing tidal potential and observe patterns of periodic inertial waves that take energy from the global tidal forcing and focus it along thin shear layers that propagate in the fluid. We focus on Europa and Enceladus, showing that inertial waves result in fluid flows of significant amplitude (a few cm/s). Nevertheless, we find that under the previously mentioned assumptions tidal dissipation due to inertial waves is several orders of magnitude smaller than Europa's radiogenic heating and Enceladus’ observed heat flux. Finally, we propose additional dissipation mechanisms that might play a relevant role in Europa and Enceladus and could be further investigated.

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In past studies, the reorientation or true polar wander (TPW) of visco-elastic bodies has been studied with approximated solutions. Two types of methods are commonly adopted: those based on the quasi-fluid approximation e.g. Ricard et al., 1993 and those based on the fluid limit approximation which only consider the final orientation (e.g. Matsuyama and Nimmo, 2007). Recently, Hu et al., (2017b) established a method which provides a dynamic solution for calculating the reorientation of tidally deformed bodies. However, they did not provide the links between the complete solution and the fluid limit solution. This paper provides a semi-analytical method for calculating the reorientation of tidally deformed bodies and shows the relation between the complete and the approximated solutions. Furthermore, we provide a criterion, the fluid limit process number F, to test for a given model and estimated TPW speed if the quasi-fluid approximation or fluid limit solution is valid. This number is a quantitative description of how close the body stays in hydrostatic equilibrium during a reorientation process. We use this number to obtain the largest allowed TPW speed of Mars as a function of viscosity, for which the approximated solutions may be used.@en

Existing lineaments on the surface of the Jovian moon Europa are thought to be the result of ongoing brittle crack formation in the elastic regime. Arcuate features are called cycloids and can be modeled using linear elastic fracture mechanics. Here, we build on existing terrestrial models of rift propagation and extend them to cycloids on the moon. We propose that these cracks tend to grow as a series of nearly instantaneous events, spaced by periods of inactivity. The behavior is similar to what is observed on Antarctic ice shelves, where rifts can remain dormant for years. We argue that dormant periods between growth events could explain the presence of cycloids on Europa even without invoking secular motion of the crust. Furthermore, being able to model propagation events and their timing should help future missions exploring the moon.

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Undergoing extreme tidal dissipation, Io serves as an archetype of tidally heated rocky exoplanets and exomoons. Therefore, understanding Io’s dissipative processes and their interactions with Io's interior provides insights into the evolution of these tidally heated bodies. Tidal dissipation depends on Io’s rheological structure and is thought to be radially and laterally non-uniformly distributed within Io’s interior. We explore whether the heterogeneous nature of tidal heating causes regional variations of Io's temperature-dependent melt fraction and rheology. Furthermore, we investigate to which extent these regional variations in turn change Io’s tidal dissipation pattern. To study the spatial effect of the heterogeneous heat production on Io's interior structure we developed a model that couples Io's non-uniform heating pattern with Io's main heat transport mechanisms [1]. The initial tidal heating pattern is calculated from a 1-dimensional rheological structure. From the resulting temperature and melt distribution we derive the regionally varying viscosity and rigidity structure. In a second step, we use a finite-element model to re-calculate Io’s tidal dissipation pattern using the updated tidally induced three-dimensional viscosity and rigidity distribution. Our results reveal that for models with a magma-dominating heat transport peak-to-peak variations in the global temperature field of up to 190 K arise. However, for models with a convection-dominating heat transport and low reference viscosities of the convective layer, variations are fully damped. In particular for models with strong tidally-induced lateral variations, the newly obtained dissipation patterns strongly differ from the initial dissipation patterns resulting from 1-dimensional structures. The updated patterns show asymmetric contributions towards the 0°/180°W/E plane and contain additional spherical components with degrees > 4. Our results show that three-dimensional structures are inevitable for bodies with strong tidal dissipation, and 3D modelling approaches for the computation of thermal heat transport and tidal dissipation are necessary. [1] Steinke, T., et al.,2019, Icarus, Tidally induced lateral variations of Io's interior. @en

Planetary Radio Interferometry and Doppler Experiment (PRIDE) is a multi-purpose experimental technique aimed at enhancing the science return of planetary missions. It is based on, the near-field phase-referencing VLBI (Very Long Baseline Interferometry) and radial Doppler measurements. It has been developed initially by the Joint Institute for VLBI ERIC (JIVE) for tracking the ESA’s Huygens Probe during its descent in the atmosphere of Titan in 2005 and from that point forward actualized for various planetary science missions. It was selected by ESA as one of the eleven experiments of the ESA’s L-class JUpiter ICy moons Explorer mission (JUICE) mission, planned for launch in 2022.@en

Rising sea levels due to climate change can have severe consequences for coastal populations and ecosystems all around the world. Understanding and projecting sea-level rise is especially important for low-lying countries such as the Netherlands. It is of specific interest for vulnerable ecological and morphodynamic regions, such as the Wadden Sea UNESCO World Heritage region. Here we provide an overview of sea-level projections for the 21st century for the Wadden Sea region and a condensed review of the scientific data, understanding and uncertainties underpinning the projections. The sea-level projections are formulated in the framework of the geological history of the Wadden Sea region and are based on the regional sea-level projections published in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5). These IPCC AR5 projections are compared against updates derived from more recent literature and evaluated for the Wadden Sea region. The projections are further put into perspective by including interannual variability based on long-Term tide-gauge records from observing stations at Den Helder and Delfzijl. We consider three climate scenarios, following the Representative Concentration Pathways (RCPs), as defined in IPCC AR5: The RCP2.6 scenario assumes that greenhouse gas (GHG) emissions decline after 2020; the RCP4.5 scenario assumes that GHG emissions peak at 2040 and decline thereafter; and the RCP8.5 scenario represents a continued rise of GHG emissions throughout the 21st century. For RCP8.5, we also evaluate several scenarios from recent literature where the mass loss in Antarctica accelerates at rates exceeding those presented in IPCC AR5. For the Dutch Wadden Sea, the IPCC AR5-based projected sea-level rise is 0.07±0.06m for the RCP4.5 scenario for the period 2018-30 (uncertainties representing 5-95%), with the RCP2.6 and RCP8.5 scenarios projecting 0.01m less and more, respectively. The projected rates of sea-level change in 2030 range between 2.6mma^-1 for the 5th percentile of the RCP2.6 scenario to 9.1mma^-1 for the 95th percentile of the RCP8.5 scenario. For the period 2018-50, the differences between the scenarios increase, with projected changes of 0.16±0.12m for RCP2.6, 0.19±0.11m for RCP4.5 and 0.23±0.12m for RCP8.5. The accompanying rates of change range between 2.3 and 12.4mma^-1 in 2050. The differences between the scenarios amplify for the 2018-2100 period, with projected total changes of 0.41±0.25m for RCP2.6, 0.52±0.27m for RCP4.5 and 0.76±0.36m for RCP8.5. The projections for the RCP8.5 scenario are larger than the high-end projections presented in the 2008 Delta Commission Report (0.74m for 1990-2100) when the differences in time period are considered. The sea-level change rates range from 2.2 to 18.3mma^-1 for the year 2100. We also assess the effect of accelerated ice mass loss on the sea-level projections under the RCP8.5 scenario, as recent literature suggests that there may be a larger contribution from Antarctica than presented in IPCC AR5 (potentially exceeding 1m in 2100). Changes in episodic extreme events, such as storm surges, and periodic (tidal) contributions on (sub-)daily timescales, have not been included in these sea-level projections. However, the potential impacts of these processes on sea-level change rates have been assessed in the report.

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Sea-level indicators dated to the Last Interglacial, or Marine Isotope Stage (MIS) 5e, have a twofold value. First, they can be used to constrain the melting of Greenland and Antarctic Ice Sheets in response to global warming scenarios. Second, they can be used to calculate the vertical crustal rates at active margins. For both applications, the contribution of glacio- and hydro-isostatic adjustment (GIA) to vertical displacement of sea-level indicators must be calculated. In this paper, we re-assess MIS 5e sea-level indicators at 11 Mediterranean sites that have been generally considered tectonically stable or affected by mild tectonics. These are found within a range of elevations of 2–10 m above modern mean sea level. Four sites are characterized by two separate sea-level stands, which suggest a two-step sea-level highstand during MIS 5e. Comparing field data with numerical modeling we show that (i) GIA is an important contributor to the spatial and temporal variability of the sea-level highstand during MIS 5e, (ii) the isostatic imbalance from the melting of the MIS 6 ice sheet can produce a >2.0 m sea-level highstand, and (iii) a two-step melting phase for the Greenland and Antarctic Ice Sheets reduces the differences between observations and predictions. Our results show that assumptions of tectonic stability on the basis of the MIS 5e records carry intrinsically large uncertainties, stemming either from uncertainties in field data and GIA models. The latter are propagated to either Holocene or Pleistocene sea-level reconstructions if tectonic rates are considered linear through time.

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At present, tracking data for planetary missions largely consists of radio observables: range-rate (Doppler), range and angular position (VLBI/Δ DOR). Future planetary missions may use Interplanetary Laser Ranging (ILR) as a tracking observable. Two-way ILR will provide range data that are about 2 orders of magnitude more accurate than radio-based range data. ILR does not produce Doppler data, however. In this article, we compare the relative strength of radio Doppler and laser range data for the retrieval of parameters of interest in planetary missions, to clarify and quantify the science case of ILR, with a focus on geodetic observables. We first provide an overview of the near-term attainable quality of ILR, in terms of both the realization of the observable and the models used to process the measurements. Subsequently, we analyse the sensitivity of radio Doppler and laser range measurements in representative mission scenarios for parameters of interest. We use both an analytical approximation and numerical analyses of the relative sensitivity of ILR and radio Doppler observables for more general cases. We show that mm-precise range normal points are feasible for ILR, but mm-level accuracy and stability in the full analysis chain are unlikely to be attained, due to a combination of instrumental and model errors. We find that ILR has the potential for superior performance in observing signatures in the data with a characteristic period of greater than 0.33–1.65 hours (assuming 2–10 mm uncertainty for range and 10 μ m/s at 60 s for Doppler). This indicates that Doppler tracking will typically remain the method of choice for gravity field determination and spacecraft orbit determination in planetary missions. ILR data will be able to supplement the orbiter tracking data used for the estimation of parameters with a once-per-orbit signal. Laser ranging data, however, are shown to have a significant advantage for the retrieval of rotational and tidal characteristics from landers. Similarly, laser ranging data will be superior for the construction of planetary ephemerides and the improvement of solar system tests of gravitation, both for orbiter and for lander missions.

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Recent Earth-based observations of Io reveal a specific distribution of persistent hotspots and sudden highintensity events. The volcanic pattern is commonly associated with the heat flux originating from Io’s tidally heated mantle and asthenosphere. Io’s interior state is a complex system of heat production, heat transport, melt, and temperature-dependent rheology. The spatial pattern of dissipated heat, for example, depends on the interior rheology but at the same time the heating influences the rheology, in particular due to the temperature-dependence of the mantle viscosity. We present an iterative procedure to investigate the strength and characteristics of this specific feedback. The tidal dissipation is calculated by a viscoelastic model of a spherical body disturbed by a tidal force. The model is based on finite elements so it can deal with lateral variations of the viscosity. We use simple scaling laws to relate the temperature-dependent viscosity distribution to the spatial heat production and heat transport by mantle convection. In an iterative procedure, the viscosity distribution is updated and a new heat dissipation pattern is calculated until convergence is found. The results show that the heat in Io’s interior and consequently the heat flux at the surface are strongly smoothed. The comparison of the converged models and the initial models of different Rayleigh numbers and types of mantle rheology reveals a diverge characteristics of the feedback. This possibly changes the way the observed distribution of volcanos on Io’s surface is related to Io’s interior properties. @en

During true polar wander (TPW), the rotational axis and the axis of the maximum moment of inertia (AoM) of the body do not coincide any more. Thus, equatorial bulge readjustment happens which causes the AoM to follow the rotational axis. Strictly speaking, during TPW the body is not in hydrostatic equilibrium. However, if the speed of TPW is very slow or the viscosity of the planetary body is low enough which makes the equatorial bulge readjustment fast enough, then the body can be assumed to be in hydrostatic equilibrium. If the body is in hydrostatic equilibrium than the following approximate methods for TPW are valid: • method which assumes that the AoM and the rotational axis coincide during TPW (e.g. Nakada, 2007). • method which is based on the quasi-fluid approximation (e.g. Ricard et al, 1993). • method which is based on the fluid-limit assumption (e.g. Matsuyama & Nimmo, 2007). However, it is not clear how slow the TPW needs to be and how low the viscosity of the body needs to be to safely assume hydrostatic equilibrium. Here we present a quantitative criterion to test for a give interior model and TPW speed, if these approximations can be adopted. We define a dimensionless fluid limit process number F, which depends on the visco-elastic Love numbers, the maximum polar wander speed and a tidal deformation factor (which is 0 for negligible tidal bulges such as for Earth and Mars). @en