B.C. (Bart) Root, an Assistant Professor at Delft University of Technology, discusses pioneering efforts in quantum space exploration aimed at unlocking the secrets of Mars’ interior and atmosphere. The Mars Quantum Gravity Mission for Interior Structure and Atmosphere (MaQuIS) represents a transformative approach to understanding the Red Planet, uniting advanced quantum sensing technologies with a mission architecture proven through decades of successful satellite missions. By combining cutting-edge instrumentation with a robust spacecraft design, MaQuIS addresses one of the most compelling questions in planetary science: the internal structure, geodynamics, and atmospheric evolution of Mars.

The volcanic complex Tharsis Region on Mars is known for its numerous volcanoes on top of the crust, elevated topography (doming), and a long-wavelength gravity anomaly correlated with the region. Flexural modeling of the lithosphere has commonly been used to understand the relationship between observed topography, crustal structure, and gravity, but no conclusive answers have been obtained due to the ambiguity of these models. NASA's InSight mission has brought new information about the Martian lithosphere, which warrants a reanalysis of the support of the Tharsis Region. After analyzing the topography and gravity data, we found that a thin shell model of Mars matches both the observed gravity field for spherical harmonic degrees higher than 8 and the crustal thickness at Elysium determined by the InSight mission. Our thin shell flexure model uses an average crustal thickness of 55 km, crustal density of 3,050 kg/, average mantle density of 3,750 kg/, and an elastic thickness () of 100 km. The mismatch between modeled and observed gravity field for the long-wavelengths (between degrees) correlates with the Tharsis Region, suggesting active large-scale dynamic support of the volcanic region. After modeling this dynamic support, we concluded that a substantial negative mass anomaly (hot buoyant mantle material, or depleted mantle region) in the mid mantle underneath the Tharsis Rise can explain the long-wavelength gravity residual. The remaining short-scale gravity residual gives insight to the Martian crustal density distribution and seems to correlate with geological structures of Mars. Buried mass anomalies in the subsurface of the northern polar plains seem not to be related to any geological or surface expressions, suggesting a more complex geology of the northern Martian crust than is suggested by the surface topography.

The largest volcano in our solar system, Olympus Mons, is part of the Tharsis rise volcanic complex. Studies have shown that the free-air gravity anomaly at the Tharsis rise that goes up to 3,540 mGal at Olympus Mons, cannot only be explained by a flexure in the lithosphere and requires a substantial mass anomaly in the mantle to account for the heat needed to sustain Tharsis (Root et al., 2026; Redmond and King, 2004). Corroborating this, Le Maistre et al. (2023) detected a long-term acceleration in Mars' rotation rate from InSight's RISE experiment, suggesting ongoing redistribution of mass in the Martian interior that cannot be attributed to atmospheric processes alone, pointing to active internal dynamics.Previous work has demonstrated that time-variable gravity measurements from satellite tracking offer a promising path toward detecting active mantle flow on Mars. Low viscosity and deep plumes with high density contrast with the surrounding mantle produce the strongest gravity-rate signals, reaching up to ~20 nGal/year, values that are at the edge of current observational capabilities. However, the wide uncertainty range in plume and mantle properties, including size, temperature excess, depth, and viscosity structure, translates into a broad spread of predicted signals, preventing definitive interpretation.To move beyond this limitation, we investigate the long-term geodynamical evolution of the Tharsis mantle plume from its initiation to the present day. We model it as the product of a multi-billion-year thermal and dynamic history, to track how the plume head and tail develop, stall, and potentially persist as a thermal anomaly in the Martian mantle. The signal detectable by satellites tracking today does not necessarily reflect an actively rising mantle plume. Instead, it could be an imprint of a residue structure, whose characteristics are shaped by Mars' long thermal history.A central focus of our study is the role of mantle viscosity, which governs the timescales of thermal diffusion, the longevity of plume structures, and the amplitude of time-variable gravity signals. We systematically explore a range of depth-dependent viscosity scenarios based on the literature, to assess how sensitively the present-day plume state depends on these assumptions, and to identify which configurations remain consistent with existing observational constraints from InSight and orbital gravity data.By forward-modeling the gravity-rate signatures of different plume evolution scenarios, we narrow the plausible parameter space of present-day plume states and evaluate their detectability with current and future satellite missions. Our results provide refined constraints on the physical characteristics of a possible Martian mantle plume or its remnant and offer an explanation of the gravity anomaly of the Tharsis rise. This work advances our understanding of the present-day thermal and geodynamic state of Mars, with broader implications for the long-term interior evolution of terrestrial planets.Bibliography:Alkahal, R., Root, B. C., Dirkx, D., Thieulot, C., Fayolle, S., Goossens, S. (under review) Investigating gravity trends from realistic simulated satellite orbits. Icarus.Le Maistre, S., et al. (2023). Spin state and deep interior structure of Mars from InSight radio tracking. Nature, 619, 733–737. https://doi.org/10.1038/s41586-023-06150-0Redmond, H. L., and King, S. D. (2004). A numerical study of a mantle plume beneath the Tharsis Rise: Reconciling dynamic uplift and lithospheric support models. Journal of Geophysical Research: Planets, 109, E09008. https://doi.org/10.1029/2003JE002228Root, B. C., Qin, W., van der Tang, Y., Thieulot, C. (2026). Describing the global gravity field of Mars with lithospheric flexure and deep mantle flow. Journal of Geophysical Research: Planets, 131, https://doi.org/10.1029/2024JE008765

Why quantum satellite gravimetry? B.C. (Bart) Root, an Assistant Professor at Delft University of Technology, investigates the significance of quantum satellite gravimetry in this intriguing analysis. Quantum technologies in space are the next engineering frontier. Especially in space gravimetry, it will be a game- changer for monitoring global mass transport processes, such as hydrology and solid-Earth processes. Classical space technology is optimally developed but at its operational limits. To go beyond is to use quantum sensing, achieving higher precision and extreme stabile observations, which would result in smaller-scale and shorter temporal signature detection.

With the plans of the MAGIC/NGGM mission approved, there will be several decades of satellite gravity data available. Both periodic and secular mass changes can be studied with this data, mostly surface mass changes like hydrology, ice melt, glacial isostatic adjustment, and large earthquakes. With the increasing time period of the gravity data set, smaller processes in the signal can be detected. Therefore, we conduct sensitivity analysis on small temporal gravity signals which can be related to mass change due to mantle convection.We perform various sensitivity analysis studies to understand the added benefit of detecting mantle flow with satellite gravity change observations. A fast stoke solver (FLAPS) is developed that is based on an axisymmetric half annulus geometry. The model evolves over 50 years after which the difference between the initial and final state to compute the rate of change. Realistic Earth models (PREM) as well as synthetic models are tested to better understand the sensitivity of the gravity change data. To understand 3D variations in structure and viscosity, we use the open-source mantle flow software ASPECT and incorporate interior models related to ESA's 4D Dynamic Earth project. For the upper mantle the WINTERC-G model incorporates multi data types information in a joint inversion. New analysis show data sensitivity down to the transition zone. For the lower mantle, we use available global tomography models.The gravity change observations are sensitive to the absolute viscosity state of the mantle. This is contrary to dynamic topography and geoid data, which do not have this sensitivity and studies using these data always have an ambiguity wrt. viscosity state. Moreover, it seems that the gravity change data is more sensitive to the lower mantle of the Earth. 3D calculations need HPC resources and we show that the mesh resolution needs high computational demands to consistently account for the temporal gravity due to mantle flow. Nevertheless, the modelled magnitude of the gravity change linked to global mantle convection seems to be larger than the formal error estimates of the GRACE and GRACE-FO instrumentation. A longer acquisition period will reduce the secular errors in the ocean, atmosphere and tidal correction models, such that eventually mantle convection can be studied directly by satellite gravimetry.

Due to the limited availability of seismic data from Mars, the current best source of information about the internal structure of the planet is from the measurements of the gravitational field. In this work, the lateral density variations in the lithosphere are studied using a simulation-based approach linking the planetary model and measurements of gravity. A two-layer planetary model is implemented, where we study lateral density distributions in the crust and the mantle. However, gravity data is known for its insensitivity to depth-related information. Therefore, we parameterize the two layered model using a Matérn covariance function to simulate realistic distributions and reduce the number of freedoms. The question we aim to answer is; what can we learn about the Matérn parameters governing these distributions? We simulate various synthetic 2-layer crust-mantle models from a multivariate normal distribution. The synthetic models are inputted in a Bayesian inference and probabilistic modelling is performed using a Normalising Flow neural network techniques. From the inference results, we can learn about the scale and structure of density variations in the lithosphere, as well as the relationships between the parameters governing these distributions in the two layers, and the sensitivity of available gravity data to this information. We have then used the available gravity data of the Martian gravity field to estimate the Matérn covariance parameters for a two layered density model. These parameters give insight the the subsurface density distribution in the form of variance of crustal and mantle anomalies, their spatial correlation, and any smoothing effects. The results of this study can inform future gravity inversion efforts and provide a stepping stone to the development of a global density map of the lithosphere of Mars.

A planet in motion: Understanding Earth’s changing gravity field B.C. (Bart) Root, Assistant Professor at Delft University of Technology explores how Earth’s gravity field is constantly changing and what these variations reveal about our planet. Everyone has experienced gravity, heard about the falling apple, and knows that gravity governs the motion of planets around our Sun. A static phenomenon that is always present, constant and not changing at all. You could not be further from the truth! Our Earth’s gravity field is full of regions with high and low gravitational attraction. Moreover, this field changes over time. Scientists use these characteristics to probe deep inside our home planet to reveal the inner workings of Earth.

With the GRACE-FO mission well underway and the plans of the MAGIC/NGGM mission in the future, there will be several decades of satellite gravity change data available. Both periodic and secular mass changes are studied with this data, mostly surface mass changes like hydrology, ice melt, Glacial Isostatic Adjustment, and large Earthquakes. With the increasing time period of the gravity data set, smaller variation in the signal can be detected, especially linear secular changes. One of the processes that would result in small secular gravity rate is the mass change due to mantle convection. We perform various sensitivity analysis studies to understand the added benefit of detecting mantle convection with satellite gravity change observations. A fast stoke solver (FLAPS) is developed that is based on an axisymmetric half annulus geometry. A density and viscosity structure can inserted as well as test anomalies to understand the effect of the mantle flow on the gravity change observations. The model evolves over 50 years after which the difference between the initial and final state is computed. This will also give the rate of change information. Realistic Earth models (PREM) as well as synthetic models are tested to better understand the sensitivity of the gravity change data. The gravity change observations are sensitive to the absolute viscosity state of the mantle. This is contrary to dynamic topography and geoid data, which do not have this sensitivity and studies using these data always have an ambiguity wrt. viscosity state. Moreover, it seems that the gravity change data is more sensitive to the lower mantle of the Earth. This sensitivity can be very helpful in further exploration of Core-Mantle Boundary structures. The modelled magnitude of the gravity change linked to global mantle convection seems to be larger then the formal error estimates of the GRACE and GRACE-FO instrumentation. A longer acquisition period will reduce the secular errors in the ocean, atmosphere and tidal correction models, such that eventually mantle convection can be studied directly by satellite gravimetry.

Several orbiters and landers at Mars have allowed to unravel valuable knowledge about its surface and interior. Tracking of the satellites MGS, MRO, and Odyssey have provided us with detailed knowledge about the gravitational field of Mars, revealing the presence of subsurface structures in crust and mantle. With the InSight mission, seismic waves have indicated the presence of more frequent Marsquakes than assumed before the mission. This raises questions regarding the planet's formation and why Mars is more geologically active than was expected. Another important milestone in studying the interior of Mars is not only the recovery of static gravity field models but addition the seasonal variations, providing information on the periodic behavior of the polar ice caps. With the longer time-period of gravity variation could the secular time varying gravity field be linked to the solid deformation of the planet?In this study, we focus on a new method for estimating the secular variations of Mars' gravity field using available Deep Space Network (DSN) tracking data with an open-source orbit estimation tool called TUDAT (TU Delft Astrodynamics Toolbox). We have constructed an orbit simulation, including realistic environmental models like the Mars-DTM atmosphere model, that has an orbital accuracy within 2 meters of SPICE kernels.With this orbital simulator, we conduct sensitivity analyses to study the decoupling of secular gravity variations from other disturbing acceleration signals. These analyses incorporate all relevant dynamic forces acting on the satellite. We perform covariance analysis for various estimation parameters, including the satellite's initial state, atmospheric drag, static, periodic, as well as global versus arc-wise secular gravity coefficients.By evaluating the formal errors of the estimated parameters and the correlations between them, we aim to identify scenarios where we can effectively separate the atmospheric signal from the gravitational changes of solid Mars. This investigation will contribute to addressing the unresolved question of Martian interior activity.

The lateral and vertical thermochemical heterogeneity in the mantle is a long-standing question in geodynamics. The forces that control mantle flow and therefore Plate Tectonics arise from the density and viscosity lateral and vertical variations. Satellite gravity data are a unique source of information on the density structure of the Earth due to its global and relatively uniform coverage, which complements gravimetric terrestrial measurements. Gravity data (geoid, gravity, gravity gradients) sense subsurface mass anomalies have proven to be helpful in determining the Earth’s thermochemical field in virtue of density’s relatively stronger dependence on rock composition compared to seismic velocities. However, the inversion of gravity data alone for the density distribution within the Earth is an ill-posed problem with a highly non-unique solution that requires regularization and smoothing, implying additional and independent constraints. A common approach to estimate the density field for geodynamical purposes is to simply convert seismic tomography anomalies sometimes assuming constraints from mineral physics. Such converted density field does not match in general with the observed gravity field, typically predicting anomalies the amplitudes of which are too large. Furthermore, a complete description of the Earth’s gravity field must include the internal density distribution and must satisfy the requirement of mechanical equilibrium as well. Therefore, the deformation of the density contrast interfaces (surface of the Earth and Core Mantle Boundary-CMB, primarily) must be consistent with the 3D mass distribution for a given rheological structure of the Earth. With the current resolution of modern tomography models and integrated geophysical-petrological modelling it is possible to consistently predict the topography of the mineral phase transitions across the transition zone (i.e., olivine à wadsleyite, and ringwoodite+majorite à perovskite+ ferropericlase) based on a temperature and chemical description of the Earth. However, for a consistent representation of the gravity field such thermochemical (i.e., density) 3D models must be compatible with the mantle flow arising from the equilibrium equations that explains both the surface topography (dynamic + isostatic-lithospheric components) and the CMB topography. Here we present a new inversion scheme to image the global thermochemical structure of the whole mantle constrained by state-of-the-art seismic waveform inversion, satellite gravity (geoid and gravity anomalies and gradiometric measurements from ESA's GOCE mission) and surface heat flow data, plus surface and CMB dynamic topography (Stokes flow). The model is based upon an integrated geophysical-petrological approach where mantle seismic velocities and density are computed within a thermodynamically self-consistent framework, allowing for a direct parameterization in terms of the temperature and composition variables.

High resolution gravity field measurements from GRAIL [1], in-situ heat flux [2] and seismic measurements from Apollo [3,4], surface composition from Clementine and Lunar Prospector [5,6], and the analysis of lunar samples have provided a wealth of information about the thermal evolution of the Moon [7]. Constraints on the present-day thermal state of the lunar interior come from the Apollo surface heat flux measurements: 21±3 mW m-2 at the Apollo 15 and 14±2 mW m-2 at the Apollo 17 landing sites [2]. A peak heat flux of ~180 mW m-2 was recently inferred by [8] from the Chang’E 1 and 2 data at the Compton-Belkovich location, a Thorium anomaly feature on the lunar farside. A lower bound for the lunar heat flux of only ~6 mW m-2 has been suggested, for the so-called Region 5, by measurements of the Diviner Lunar Radiometer Experiment onboard LRO [9]. Additionally, thermal expansion/contraction estimates [10] provide secondary constraints on the thermal state of the interior throughout lunar history. Here, we model the interior dynamics of the Moon to infer plausible distributions of heat producing elements (HPEs) that, in turn, are directly linked to surface heat flux variations. To this end, we compare the present-day surface heat flux obtained in our models with the above constraints. Similar to [11], we combine global geodynamical models [12] with crustal thickness models derived from gravity and topography data [13]. We include higher HPEs abundances in the Procellarum KREEP Terrane (PKT) and crust compared to the mantle, and a mantle rheology similar to [14]. We test both constant and pressure/temperature dependent thermal conductivity scenarios. In addition to present-day heat flux, we compute the thermal expansion/contraction based on the interior thermal state obtained from our models at different times during lunar evolution and compare these values with available estimates to select best-fit models. We find that variations in crustal thickness and the distribution of HPEs in the crust, mantle, and PKT region predominantly affect the convection pattern in the lunar interior and the surface heat flux. Models best compatible with the heat fluxes in the Apollo regions and Region 5 show an average Thorium abundance in the PKT region of ~2.4 ppm, smaller than the observed surface values [6], suggesting a strong Thorium enrichment close to the surface. These models have a crustal thermal conductivity of ~1.2 W/(mK), ~3 times lower than that of the mantle. None of our models matches the heat flux estimated at the Compton-Belkovich location, indicating either specific local processes [8] or large measurement uncertainties. References: [1] Zuber et al., 2013; [2] Langseth et al., 1976; [3] Garcia et al., 2019; [4] Nunn et al., 2020; [5] McEwen et al., 1997; [6] Lawrence at al., 2003; [7] Jaumann et al., 2012; [8] Siegler et al., 2023; [9] Paige & Siegler, 2016; [10] Andrews-Hanna et al. 2013; [11] Plesa et al., 2016; [12] Hüttig et al., 2013; [13] Broquet & Andrews-Hanna, 2023; [14] Laneuville et al., 2013.

NASA’s InSight mission has brought new information about the Martian lithosphere (Banerdt et al. 2020), which warrants a re-analysis of the support of the crustal and sub-crustal masses. Furthermore, the discovery of a possible mantle plume underneath the region south of Elysium Mons (Broquet et al. 2023), gives evidence for recent magmatic activity underneath the crust of Mars causing dynamic support to volcanic structures.The goal of this study is to combine a global flexural model combined with mantle convection modelling to study the different uncertainties in the geophysical parameters that dictate crustal (short-scale) and mantle (large-scale) mass anomalies. After conducting spectral analysis on the gravitational signal of we found that the Martian lithosphere can be best modelled by an elastic thin shell with the following physical parameters: crustal thickness of 60 ±10 km, crustal density of 3050 ±50 kg/m3, mantle density of 3550 ±100 kg/m3, and the elastic thickness (Te) is found to be 80 ±5 km.Figure 1: Crustal density from short scale gravity anomalies inversion. The flexural model is not able to represent to perfect isostasy ate Hellas Basin (and assumed present also at Utopia basin). Therefore, high crustal density is seen reflecting a shallower crust-mantle interface. Isidis and Argyle basin also show high mass regions that could be interpreted as shallow crust-mantle boundary or magmatic intrusions in the crust. Other high mass features are related to volcanoes and large impact craters. Finally, the northern polar planes show also anomalous high mass regions.By using this spectral analysis, we were able to isolate the remaining long-wavelength signal that cannot be realistically modelled by a flexure model. The location of the residual anomaly correlates with the Tharsis Rise, which suggests active large-scale dynamic support of the volcanic region. A negative mass anomaly in the mantle underneath the Tharsis Region explains the remaining gravity residual. This anomaly could be interpreted as underplating of the lithosphere, a phase transition anomaly at 1000 km depth, or an rising mantle plume. Could mantle convection is still be active in Mars explaining the relatively young geologic surface volcanism?The remaining short scale gravity residuals give insight in Martian crustal density distributions (Figure 1). Flexure models cannot account for these structures as the lithosphere is strong enough to reduce/negate any topographic signature. Especially in the northern polar plains several buried mass anomalies have been detected (Figure 2). The nature of these anomalies is unclear, as they could be interpreted with a volcanic origin, impact related structures, or tectonic orogeny that would all be buried be the sedimentary layer that is observed on the surface of the northern hemisphere. If these structures are interpreted as impact craters this would suggest of an older crustal age of the northern hemisphere of Mars than is now considered. New gravity satellite missions towards Mars are needed to uncover the nature of these subsurface mass anomalies (Wörner et al 2023, Genova et al 2020).Figure 2: Contours of the high mass anomalies in the nortern polar plains. These high mass anomalies seem to have no topograohic signature. Topography is shown in the colorscale and taken from the MOLA dataset.References:Banerdt, W. B., Smrekar, S. E., Banfield, D., Giardini, D., Golombek, M., Johnson, C. L., … Wieczorek, M. (2020, March). Initial results from the InSight mission on Mars. Nature Geoscience, 13 (3), 183–189. Broquet, A., & Andrews-Hanna, J. C. (2023). Geophysical evidence for an active mantle plume underneath Elysium Planitia on Mars. Nature Astronomy, 7 (2),160–169. Genova, A. (2020), ORACLE: A mission concept to study Mars’ climate, surface and interior, Acta Astronautica, 166, 317-329. Wörner, L., B.C. Root, P. Bouyer, C. Braxmaier, D. Dirkx, J. Encarnação, E. Hauber, H. Hussmann, Ö. Karatekin, A. Koch, L. Kumanchik, F. Migliaccio, M. Reguzzoni, B. Ritter, M. Schilling, C. Schubert, C. Thieulot, W.v. Klitzing, O. Witasse (2023), MaQuIs—Concept for a Mars Quantum Gravity Mission, Planetary and Space Science, 239, 105800.

The surface heat flux provides important constraints on the present-day thermal state of the lunar interior. In situ surface heat flux measurements, performed during the Apollo program, obtained surface heat flux values of 21±3 and 14±2 mW/m2 at the landing sites of Apollo 15 and 17, respectively [1]. Recently, a peak heat flux of ~180 mW/m2 was inferred by [2] from the Chang’E 1 and 2 data at the Compton-Belkovich location. A lower bound for global lunar heat flux of ~6 mW/m2, based on measurements of the Diviner Lunar Radiometer Experiment onboard LRO, has been suggested for Region 5, a location at the eastern edge of Haworth crater [3]. In addition to heat flux measurements, global thermal expansion/contraction estimates can be used to constrain the thermal state of the interior throughout lunar history [4].Differences between the surface heat flux measurements, even for geographically close regions, indicate a high heat flux variability on the Moon. Previous work investigated regional combinations of crustal thermophysical properties (thickness, density, thermal conductivity), distribution of heat producing elements (HPEs), and heat flux coming from the mantle to explain the differences between the two Apollo measurements [5,6]. The results of these regional-scale models suggested heat-flux values of 7-13 mW/m2 and 12-14 mW/m2 at the crust-mantle interface and for the global average, respectively. These studies also highlighted the need to include regional-scale scenarios within global thermal evolution models and investigate key aspects (e.g., the geographical extent of a subsurface KREEP layer), in order to relate local heat flux measurements and regional-scale estimates to the global properties of the Moon. Here, we construct 3D thermal evolution models using the fluid solver GAIA [7]. The interior dynamics of the Moon are simulated over 4.5 billion years, by solving the conservation equations of mass, linear momentum and thermal energy. Similar to [8], we account for spatially variable crustal thickness, derived from gravity and topography data [9] (Fig. 1a). We consider higher HPEs abundances in the PKT and crust compared to the mantle, and compute the interior dynamics (Fig. 1b) using an Arrhenius viscosity for diffusion creep similar to [11]. This setup is designed to allow for an extensive investigation of lunar crustal properties and their spatial variability.In our models we vary critical parameters such as the location, size, thermal conductivity, and HPE enrichment of the PKT region, but also the location of a putative KREEP layer (i.e., within or below the crust). Finally, we consider various thermal conductivity values and HPE enrichment of the anorthositic crust, and initial temperature profile of the interior. In addition to present-day surface heat flux, we compute the heat flux at the crust-mantle interface and also estimate the time-variable thermal expansion/contraction during lunar evolution. These values are compared to all available constraints [1-6] to select best-fit models.Our models that are best compatible with the Apollo measurements are in agreement with [5] and [6]. These models have a bulk uranium content of 25 ppb [11], and show average and standard deviation surface and crust-mantle interface heat flux values of ~14±5 and ~8±1 mW/m2, respectively (Fig. 2a and b). For the Compton-Belkovich anomaly, none of our models can reproduce the high heat flux value proposed by [2]. Therefore, we conclude that the inferred heat flux value of ~180 mW/m2 indicates either very specific local processes (e.g., overly high radiogenic enrichment) [2] or large measurement uncertainties.We find that, without considering 3D lateral variability in thermal conductivity across the lunar surface, measurably lower heat flux values at Region 5 [3] with respect to Apollo 15 & 17 require for KREEP material to extend at least partly beneath mare Serenitatis. In this case, the Apollo 15 measurement would be representative of the PKT average heat flux, while Apollo 17 would lie on its edge (Fig. 2c). On the other hand, a smaller PKT could imply that the low heat flux at Region 5 is caused by different phenomena, for instance a laterally variable thermal conductivity. Heat flux measurements that will be performed by the Farside Seismic Suite [12] at Schrödinger crater, if successful, will provide key information that would help to exclude one of these two scenarios, and thus potentially constrain the extent on the KREEP layer underneath PKT region.The full spatial variations of the surface heat flux on the Moon obtained by our models are an important step forward towards understanding the thermal history and present-day state of the lunar interior. Such models can help to put current and future heat flux measurements into a global context and to constrain the distribution of the KREEP layer beneath the PKT region. Future work will include a laterally variable thermal conductivity of the crust to test the effects of the spatial distribution of lunar regolith on the surface heat flow and subsurface temperature variations.References:[1] Langseth et al., 1976; [2] Siegler et al., 2023; [3] Paige & Siegler, 2016; [4] Andrews-Hanna et al. 2013; [5] Siegler and Smrekar, 2013; [6] Warren and Rasmussen, 1987; [7] Hüttig et al., 2013; [8] Plesa et al., 2016; [9] Broquet & Andrews-Hanna, 2023; [11] Laneuville et al., 2013 [12] Panning et al., LPSC 2024.

1. Introduction With the increasing interest in the Solar System's smaller bodies, quite a few missions have been sent to comets and asteroids, and more will be send in the near future. Due to the large distances involved, communication to command mission parameters takes a long time, which has a negative impact on operational safety. Autonomous navigation would be one of the key technologies that can make asteroid missions more robust, safe, and cost effective. This is especially true if one considers the unknown flight environment when the spacecraft is first encountering the body. Most asteroids and comets have a very irregular shape and unknown mass distribution. Therefore, knowledge about its irregular gravity field will be directly beneficial as input to orbital corrections and manoeuvre planning. 2. Methodology Based on a detailed ``real-world'' simulator, orbits around a small body, here the asteroid Eros-433, can be simulated that are perturbed by non-linear gravity effects, as well as solar-radiation pressure and third-body perturbations. Measuring land marks on the small-body's surface, processed (in a preliminary mission phase with Earth in the loop) to a detailed land-mark database, can be subsequently used to determine the (relative) position and velocity of the spacecraft with respect to the body. A next step would be to use measurements of orbital perturbations to estimate as many components of the body's gravity field as possible. Detailed knowledge about the gravity field can then be used for planning science and mission operations, such as orbital corrections. An in-house code is used to determine the spherical-harmonics coefficients Cnm and Snm, assuming an average asteroid density of 2.6212 g/cm3. Part of the navigation system are simplified sensors, which provide noisy position and/or velocity measurements. Interfacing with more realistic sensors is possible, but left as future work. The core of the navigation system is an augmented state estimator, based on the unscented Kalman filter for its applicability to highly non-linear systems. 3. Results Eros-433 is an elongated body, roughly resembling an ellipsoid, with dimensions of 33 by 13 by 13 km, and rotates with an approximate constant rate in 5.27 hours. For the ``real-world'' asteroid model, a gravity field up to order and degree 16 has been determined, see Figure 1. The results shown are the deviations from the point-mass model and thus highlighting the irregularities of Eros' gravity field. With increasing altitude these irregularities are much more ``smeared out'' and will thus be harder to estimate. The first simulations that were done aimed at estimating the central-field parameter, μ, and the first zonal harmonic, J2 = C2,0. To do so, several orbital altitudes ranging from 1500 down to 150 km were chosen. In terms of measurements data, it was assumed that only noisy position and velocity data were available at a frequency of 1 Hz. Figure 2 shows the estimates of μ. The remaining error is well below 0.1% for the different altitudes. With the estimated value of μ substituted in the filter, the estimate of J2 is seen to converge best at an altitude of 45 km: at higher altitudes the J2 effect starts to decrease and becomes less noticeable, whereas at lower altitudes the effect of the higher-order terms start dominating. The remaining error is about 6%. The last part of the research focusses on the estimation of higher-order coefficients. Idealised noisy position (noise level 10 m, which would be possible with current sensor technology) and velocity measurements are used, supported by ideal range measurements at 2 Hz. Figure 3a displays the errors of the full 8 degree and order coefficients for the estimation at an orbital height of 50 km. The coefficients of degree 6 and higher have significant errors, but the coefficients up to degree and order 5 can be estimated within errors of less than 30%. However, once μ and J2 have been estimated and subsequently put to constant values in the estimator, the estimation accuracy significantly improves, but only when the orbit is lowered to 35 km and the measurement time is extended to 10 days (Figure 3b). The average error is about 10%, with a few outliers. These errors are quite small, because of the relatively ideal measurements. Follow-on research should therefore focus on realistic sensor modelling and including instrument errors to the augmented state.

Earth has been the only known habitable world and thus used as a reference to understand habitability. The origin of life on Earth is not yet clearly understood, but known traces are up-to the Archean (∼ 3.5Ga, Ga-billion years). Earth had water and continents from the Hadean Earth (> 4.0Ga), which had different atmospheric conditions compared to the Archean Earth. Similarly, the current state and composition of atmosphere does not represent its future state. Climate changes are partly attributed to feedback mechanism between the internal processes and the atmosphere. And as such, each atmospheric state is depictive of an instance a long a trajectory path of a coupled evolution of Earth system. Venus was thought to be habitable until into the 1960s, when its surface was observed to be oven-hot with surface pressure a hundred times that of Earth. Why and when the evolutionary paths of Venus and Earth, which are similarly sized and should have similar internal compositions, started to diverge? Moreover, known exoplanets, planets and moons have very different geophysical characteristic from Earth. This implies exotic life might vary substantially from what we know. As a result, understanding evolution of rocky planets, that is their interior structure, atmospheres and climate regardless of their habitability is of great importance. In this work we study the relation between a rocky planet’s internal properties and its observable surface and atmosphere properties over time. We explore the different convection regimes (stagnant lid, episodic-lid and tectonic), studying the relation between a planet’s viscous state, its interior composition and structure. Focusing on the effects of mantle convection on volatile recycling processes such as CO2 outgassing that influence the atmospheric state and climatic conditions over time. The computed models are then used to compute observables, that ultimately can be tested with observations.

In the past few decades, Mars-oriented orbiters and landers have allowed to unravel valuable knowledge about Mars’ surface and interior. With the InSight mission, seismic waves have indicated the presence of more frequent Marsquakes than assumed before the mission (Banerdt et al. 2020). Moreover, active mantle plume is considered below the Elysium Region (Broquet and Andrews-Hanna, 2023). This raises questions regarding the planet's formation and whether Mars is more geologically active than was considered.An important milestone in studying the interior of Mars is the recovery of static gravity field models. These models have been accomplished using data from the three recent Mars orbiting missions, namely, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). In addition to the static gravity field, seasonal variations of Mars’ gravity field have been observed, providing information regarding the periodic behavior of the polar ice caps (Konopliv et al. 2016, Genova et al. 2016). However, the secular variation of the gravity field and its link to the solid deformation of the planet has been limited studied.In general, the estimation of the time variations of the gravity field in the very long wavelength can provide insights into activity of the mantle (Wörner et al. 2023). Le Maistre et al., (2023) have studied the spin rate of Mars and its connection to interior mantle flow or atmospheric changes. By analyzing measurements from the Viking and InSight landers, they estimated a long-term change of the rotation rate of Mars and its moment of inertia. The obtained rotation rate change, along with the J2 coefficient variation over one Martian year, suggests factors such as atmospheric changes, glacial rebound of the polar ice caps (GIA, Glacial Isostatic Adjustment), or substantial deep mantle flow. Therefore, decoupling atmospheric signal from solid Mars deformations in the gravity signal is essential. In this study, we focus on a new way of estimating secular variations of the gravity field of Mars from the available tracking data with an open-source orbit estimation tool: TUDAT (TU Delft Astrodynamics Toolbox). First, we review the state-of-the-art literature on studying the plume-lithosphere interaction and model the gravity-rate signal that would come from mantle flow. Then, we perform a sensitivity analysis for decoupling the secular variations from other signals, such as, the atmospheric density variations and ongoing GIA of the polar ice caps. We do this by simulating one-way and two-way Doppler observations of a Mars-orbiting satellite. We include all possible dynamic forces impacting the satellite. Some of these forces are the static and temporal gravity field, the third body gravitation, the solar radiation pressure, the atmospheric drag, and other forces. For the atmospheric drag, we use the Mars-DTM atmosphere density model that models the static, daily, and yearly variations that affect the drag of the satellite (Bruinsma and Lemoine, 2002). We determined the sensitivity of the estimation process for different parameters including: the initial state, the atmospheric drag and the solar radiation coefficients, and the global vs. arc-wise time varying coefficients. Finally, we perform a correlation analysis of these parameters to determine in which estimation scenario we are able to separate the atmospheric signal from the solid Mars gravity changes. This sensitivity analysis will help in decoupling the gravity-rate signal in order to answer the unresolved question about the activity of the Martian interior.References: Banerdt, W.B., Smrekar, S.E., Banfield, D. et al. Initial results from the InSight mission on Mars. Nat. Geosci. 13, 183–189 (2020). https://doi.org/10.1038/s41561-020-0544-yBroquet, A., Andrews-Hanna, J.C. Geophysical evidence for an active mantle plume underneath Elysium Planitia on Mars. Nat Astron 7, 160–169 (2023). https://doi.org/10.1038/s41550-022-01836-3Bruinsma, S., & Lemoine, F. G. (2002). A preliminary semiempirical thermosphere499model of mars: Dtm-mars. Journal of Geophysical Research: Planets, 107 (E10). doi: https://doi.org/10.1029/2001JE001508Genova, A., Goossens, S., Lemoine, F.G., Mazarico, E., Neumann, G.A., Smith, D.E., Zuber, M.T., 2016. Seasonal and static gravity field of Mars from MGS, Mars Odyssey and MRO radio science. Icarus 272, 228–245. http://dx.doi.org/10.1016/j.icarus.2016.02.050Konopliv, A.S., Park, R.S., Folkner, W.M., 2016. An improved JPL Mars gravity field and orientation from Mars orbiter and lander tracking data. Icarus 274, 253–260. http://dx.doi.org/10.1016/j.icarus.2016.02.052.Le Maistre, S., Rivoldini, A., Caldiero, A. et al. Spin state and deep interior structure of Mars from InSight radio tracking. Nature 619, 733–737 (2023). https://doi.org/10.1038/s41586-023-06150-0Wörner, L., Root, B. C., Bouyer, P., Braxmaier, C., Dirkx, D., Encarnação, J., Hauber, E., Hussmann, H., Karatekin, Ö., Koch, A., Kumanchik, L., Migliaccio, F., Reguzzoni, M., Ritter, B., Schilling, M., Schubert, C., Thieulot, C., Klitzing, W. v., & Witasse, O. (2023). MaQuIs—Concept for a Mars Quantum Gravity Mission. Planetary and Space Science, 239, 105800. https://doi.org/10.1016/j.pss.2023.1058

Introduction: The response of a planet to loading is intimately linked to its interior structure. On Earth, studying the time-variable response of the lithosphere to the growth and decay of large ice sheets, or glacial isostatic adjustment (GIA), has been the standard approach to constrain the mantle structure [1]. However, such models have rarely been applied to the other terrestrial planets because of a lack of observational data [2].Mars harbors two geologically young (60°N) is discretized into 68 constant-thickness layers with given viscosity, density, and rigidity, from the core to the surface (Fig. 2). The time evolution of the deformation for these models is predicted using ALMA and the polar cap load potential [5,7]. Our model assumes that the ice cap formed instantly at a given time in Martian history. We also estimate the rate of deformation and the associated time-variable degree-2 zonal gravity coefficient (J2). A model is deemed acceptable if the predicted viscoelastic deformation matches radar observations [5].Results and conclusions: The present-day interior structure beneath the northern cap shows mantle viscosities ranging from 1021 to 1024 Pa s (Fig. 2). Given the large interior viscosity, the equilibrium response of the interior to loading is achieved over long-timescales (>100 Myr). The north polar cap is young (150 km), and large mantle viscosity (>1022 Pa s). A thick crust is consistent with the independent reassessment of InSight seismic data [16]. Models with a higher crustal heat production cool faster, have higher mantle viscosities, slower interior response to loading and thus better fit radar observations. For accepted models, GIA in the polar regions show rates >10-3 mm/year and strain rates >10-20 s-1.Our analysis further constrains the bulk of the northern cap to have formed no more than 7 Myr ago, which is in remarkable agreement with independent Global Climate Model [15]. Models with a linear ice cap formation would imply even younger ages. If the mantle viscosity were precisely known, our framework could be used to place constraints on the formation history of the ice cap.GIA affects the long-wavelength gravity field. Over the last 20 years, J2 may have varied by up to 10-11 m s-2. Together, our results implies that GIA could be measured from precise laser ranging or with a dedicated GRAIL-like gravity mission to Mars [17,18]. Alternatively, reanalyses and extended collection of radio tracking data could enable discerning a trend in the gravity field.References: [1] Peltier W. R. (1974). [2] Greve R., et al. (2003) [3] Byrne S. (2009). [4] Phillips R. et al. (2008). [5] Broquet A. et al. (2020). [6] Broquet A. (2020) AB-Ares/Te_HF_Conversion [7] Broquet A. et al. (2021) JGR:Planets. [8] Khan A. et al. (2021). [9] Plesa A.-C. et al. (2022). [10] Voigt J. R. C. et al. (2023). [11] Broquet A. & Andrews-Hanna J. C. (2023). [12] Wieczorek M. A. et al. (2022). [13] Hahn B. C. et al. (2011). [14] Spada G. (2008). [15] Levrard B. et al. (2007). [16] Kim D. et al. (2023). [17] Genova A. (2020). [18] Wörner L. et al. (2023).

<p>Flexural isostasy is commonly used to understand the relationship between the observed topography, the crustal structure, and the gravity. Compared to local isostasy, flexural models behave like low-pass filters on the crust-mantle interface. Using this methodology different internal structures are revealed showing the geometry of crustal and lithospheric structures. In the current flexure studies it is assumed that the lithosphere has uniform densities. The misfit between this method and the observed gravity data could be used to invert for lateral densities in the lithosphere.  </p> <p>In this study spectral analysis on the topographic and gravity results from the flexural models is performed to study the effect of lateral variations. For the inversion we use the full tensor of the gravity gradient as they show more sensitivity to the lithosphere structures. The inversion technique is based on spectral kernel models that are able to depict the sensitivity of satellite gravity data. Extensive synthetic analysis is been performed to acquire the best inversion settings and to study the uncertainty of the inversion results with respect to the chosen flexural model. A two-layer lateral density model (crust – upper mantle) is applied to the Sunda Subduction zone to yield more insights into the density structure of the subducting plate.</p>

<p><span lang="en-GB">The Tharsis Region has been an interest of study for many years due to its large impact on the long wavelength gravity field and topography of Mars. The leading theory on the origin of the volcanic region is a combination of both isostatic flexure of a thickened crust and a small contribution due to a (possible) large superplume residing in the upper mantle. The isostatic balance, on which previous studies have relied, does not adequately explain the long-wavelength gravity field spectra. These long-wavelength signals contribute to large scale features in the mantle. We consider the presence of a dynamic mass anomaly below the Tharsis Region. This could help explain the geological surveys of the relative young lava flows. By looking at mantle dynamic models we can explore the effect of a superplume that is actively rising in the mantle and changing the geoid over time. </span></p> <p><span lang="en-GB">We ran a series of instantaneous axisymmetric finite element models of Mars with varying plume and subsurface structural variables constrained by InSight. We run the model for 50 years, thereby accounting for the total duration of satellite data acquisition. The deformation in the model allows us to calculate the change in dynamic topography and gravity anomaly.</span></p> <p><span lang="en-GB">Our preliminary results show dynamic topography rates of a few centimetres per year and gravity rates in the order of 0.1 </span><span lang="en-GB">μ</span><span lang="en-GB">Gal per year. These gravity rates should fall within the precision of the Mars Reconnaissance Orbiter gravity field estimates, but are masked by other geological surface mass changes. Our results show that with longer and dedicated gravity observations, we should be able to observe the large scale mantle dynamics of Mars. </span></p>

The largest volcanos in our Solar System are part of a huge volcanic complex, named Tharsis Rise, which is located on the Martian surface several kilometers higher than the average topography. Moreover, the gravitational field of Mars shows a strong and large signal centered on top of the region, a positive anomaly (+300 mGal) surrounded by a negative ring (-300 mGal). Flexural theory is commonly used to understand the relationship between observed topography, crustal structure and gravity, revealing structures that support the volcanic complex.The new information about the Martian lithosphere thanks to NASA’s Insight mission deserves a re-analysis of the lithosphere flexure models. The Martian lithosphere can be modeled by infinite plate and the thin shell flexure models. The latter takes into account the curvature effect responsible for supporting extra surface loads. We see that the need for compensation based on buoyancy is even lower at long wavelength than that of the classic infinite plate model. This has consequences for the interpretation of density structure underneath the volcanic regions.After conducting spectral analysis on the topographic and gravity results from the flexural models, we found that the gravitational signal of Martian topography with thin shell compensation fits well with the observed free-air anomaly for degrees n≥2 . The best-fit elastic thickness (Te) is found to be 105 ±5 km and we observe a crustal density of 3050 ± 50 kg/m3. Despite the use of the thin shell flexure model, we notice a mismatch between modeled and observed gravity field between n=2-4 degrees, which suggests an active large-scale dynamic support of the Tharsis Rise. This could explain relatively the young geologic evidence for surface volcanism on Mars.