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Geophysical observations will provide key information about the inner structure of the planets and satellites and understanding the internal structure is a strong constraint on the bulk composition and thermal evolution of these bodies. Thus, geophysical observations are a key to uncovering the origin and evolution of the Moon. In this article, we propose the development of an autonomous lunar geophysical experiment package, composed of a suite of instruments and a central station with standardized interface, which can be installed on various future lunar missions. By fixing the interface between instruments and the central station, it would be possible to easily configure an appropriate experiment package for different missions. We describe here a series of geophysical instruments that may be included as part of the geophysical package: a seismometer, a magnetometer, a heat flow probe, and a laser reflector. These instruments will provide mechanical, thermal, and geodetic parameters of the Moon that are strongly related to the internal structure. We discuss the functionality required for future geophysical observations of the Moon, including the development of the central station that will be used commonly by different payloads.

SUMMARY Constraining initial conditions and parameters of mantle convection for a planet often requires running several hundred computationally expensive simulations in order to find those matching certain ‘observables’, such as crustal thickness, duration of volcanism, or radial contraction. A lower fidelity alternative is to use 1-D evolution models based on scaling laws that parametrize convective heat transfer. However, this approach is often limited in the amount of physics that scaling laws can accurately represent (e.g. temperature and pressure-dependent rheologies or mineralogical phase transitions can only be marginally simulated). We leverage neural networks to build a surrogate model that can predict the entire evolution (0–4.5 Gyr) of the 1-D temperature profile of a Mars-like planet for a wide range of values of five different parameters: reference viscosity, activation energy and activation volume of diffusion creep, enrichment factor of heat-producing elements in the crust and initial temperature of the mantle. The neural network we evaluate and present here has been trained from a subset of ∼10 000 evolution simulations of Mars ran on a 2-D quarter-cylindrical grid, from which we extracted laterally averaged 1-D temperature profiles. The temperature profiles predicted by this trained network match those of an unseen batch of 2-D simulations with an average accuracy of $99.7\, {\rm per~cent}$.

Ultra-short-period (USP) exoplanets have orbital periods shorter than one day. Precise masses and radii of USPs could provide constraints on their unknown formation and evolution processes. We report the detection and characterization of the USP planet GJ 367b using high precision photometry and radial velocity observations. GJ 367b orbits a bright (V-band magnitude = 10.2), nearby, red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of $0.718 \pm 0.054$ Earth-radii, a mass of $0.546 \pm 0.078$ Earth-masses, making it a sub-Earth. The corresponding bulk density is $8.106 \pm 2.165$ g cm$^-3$, close to that of iron. An interior structure model predicts the planet has an iron core radius fraction of $86 \pm 5\%$, similar to Mercury's interior., Comment: Note: "This is the author's version of the work. It is posted here by permission of the AAAS for personal use, not for redistribution. The definitive version was published in Science , (2021-12-03), doi: 10.1126/science.aay3253"

We use a large data set of 3D thermal evolution models to predict the distribution of present-day seismic velocities in the Martian interior. Our models show a difference between maximum and minimum S-wave velocity of up to 10% either below the crust, where thermal variations are largest, or at the depth of the olivine to wadsleyite phase transition, located at around 1000 – 1200 km depth. Models with thick lithospheres on average have weak low-velocity zones that extend deeper than 400 km, and seismic velocity variations in the uppermost 400 – 600 km that closely follow the crustal thickness pattern. For these cases the crust contains more than half of the total amount of heat producing elements. Models with limited crustal heat production have thinner lithospheres and shallower but prominent low-velocity zones that are incompatible with InSight observations. Seismic events suggested to originate in Cerberus Fossae indicate the absence of S-wave shadow zones in 25° - 30° epicentral distance. This result is compatible with previous best-fit models that require a large average lithospheric thickness and a crust containing more than half of the bulk amount of heat producing elements to be compatible with geological and geophysical constraints. Ongoing and future InSight measurements that will determine the existence of a weak low-velocity zone will directly bear on the crustal heat production. ISSN:0148-0227 ISSN:2169-9097 ISSN:2169-9100

The thermal and convective evolution of terrestrial planets like Mars is governed by a number of initial conditions and parameters, which are poorly constrained. We use Mixture Density Networks (MDN) to invert various sets of synthetic present‐day observables and infer five parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. The data set comes from 6,130 two‐dimensional simulations of the thermal evolution of Mars' interior. We quantify the possibility of constraining a parameter using the log‐likelihood value from the MDN. Reference viscosity can be constrained to within 32% of its entire range (1019 − 1022 Pa s), when all the observables are available: core‐mantle‐boundary heat flux, surface heat flux, radial contraction, melt produced, and duration of volcanism. Furthermore, crustal enrichment factor (1–50) can be constrained, at best, to within 15%, and the activation energy (105 − 5 × 105 J mol−1) to within 80%. Initial mantle temperature can be constrained to within 39% of its range (1,600–1,800 K). Using the full present‐day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4 × 10−6 − 10 × 10−6 m3 mol−1) cannot be constrained. We also tested different levels of uncertainty in the observables and found that constraints on different parameters loosen differently, with initial temperature being the most sensitive. Finally, we present how a joint probability model for all parameters can be obtained from the MDN., Plain Language Summary: The mantle of rocky planets like Mars behaves like a highly viscous fluid over geological time scales. Key parameters and initial conditions for the non‐linear partial differential equations governing mantle flow are poorly known. Machine Learning (ML) can help us avoid running several thousand computationally expensive fluid dynamic simulations each time to determine if an observable can constrain a parameter. Using an ML approach, we invert a set of synthetic observables such as present‐day surface heat flux, duration of volcanism and radial contraction to constrain important parameters controlling the long‐term evolution of the planet's interior, such as the reference mantle viscosity or the partitioning of radiogenic heat sources between mantle and crust. We demonstrate that by training a probabilistic ML algorithm on the data and applying it, we can quantify the constraints on parameters. This provides a high‐dimensional framework for analyzing inverse problems in geodynamics., Key Points: Mixture Density Networks provide a probabilistic framework for inverting observables to infer parameters of Mars' interior evolution Reference viscosity, crustal enrichment in heat‐producing elements and initial mantle temperature can be well constrained Activation energy of diffusion creep can be weakly constrained; constraining activation volume requires new observational signatures, Helmholtz Einstein International Berlin Research School in Data Science (HEIBRiDS), Berlin Institute for the Foundations of Learning and Data (BIFOLD), Deutsche Forschungsgemeinschaft (DFG) Research Unit FOR 2440

The Martian mantle probably experienced an early global magma ocean stage. The crystallization and the fractionation and overturn of such a magma ocean likely led to the formation of a compositionally distinct layer at the bottom of the mantle. This layer would have been heavily enriched in iron and in heat-producing elements (HPE). The significant iron enrichment can lead to long-term stability with little mixing between the layer and the overlying mantle. We studied the influence of such an enriched basal layer on the thermal and chemical evolution of the Martian mantle using both 2-D finite-volume modeling at mantle scale, and a parameterized convection approach at the entire planetary scale. The basal layer is most likely stably stratified because of its moderate thickness and/or its gradual enrichment in iron with depth that prevents the development of convection in this region. We explored a wide parameter space in our parameterized models, including the layer thickness and the mantle rheology. We show that the presence of an enriched basal layer has a dramatic influence on the thermo-chemical evolution of Mars, strongly delaying deep cooling, and significantly affecting nearly all present-day characteristics of the planet (heat flux, thermal state, crustal and lithospheric thickness, Love number and tidal dissipation). In particular, the enrichment of the layer in iron and HPE generates large volumes of stable melt near the core-mantle boundary. Due to their intrinsic low viscosity and seismic velocities, these regions of silicate melt could be erroneously interpreted as core material.

Introduction: The lunar surface is characterized by large impact basins that formed in the early history of the Moon. To better understand how basin size and their corresponding gravity signature are related to the impactor size and the thermal history of the Moon, we investigated how properties of impactor and target could affect this formation process. Impactor properties are defined by its size, density, and impactor velocity. The target is characterized by the crustal thickness and the thermal state. Previous studies (e.g.[1],[2],[3],[4]) revealed that thermal conditions in crust and mantle rocks affected the crater formation process, the final basin structure, and the gravity signature. Here, we present numerical simulations for 16 basins located on the lunar farside. The simulations are constrained by gravity data from the Gravity Recovery and Interior Laboratory (GRAIL) mission, and differ in impactor size, crustal thickness and target temperature as a function of depth. We established a relationship between the observed gravity, the geometry of the basin and the pre-impact thermal conditions of the target. These observations lead to a better understanding on how the thermal evolution of the Moon is related to changes in the formation of basins. Methods: We used the iSALE2D shock physics code to simulate the basin formation process ([5],[6],[7],[8]). We used impactor sizes of 20km to 100km in diameter. The impactor speed was set to 13km/s. The resolution of all models was set to 25 cells per projectile radius (grid cell sizes from 400m to 2000m). The target was composed of a basaltic crust on top of a dunitic mantle. We changed the target properties by using two different crustal thicknesses (40km, 60km) and three temperature profiles which represent the Moon’s thermal states at 4.4, 4.1, and 3.8 billion years ago [9]. Gravity data from GRAIL mission [10] provides detailed information about the deep structure of lunar basins. By combining the most recent GRAIL gravity model GL1500E [11] with LOLA derived topography [12], we obtained a highly resolved Bouguer gravity field. We assumed constant densities in both crust and mantle to calculate Bouguer gravity anomalies from the basin formation models. This approach can be understood as a simple way to mimic the density distribution after a long-term cooling process in the basin. The shape of the gravity signal preserves information about the position of the crust-mantle boundary and, therefore, assuming constant densities is useful in order to verify the geometry of the model. Results: For all 54 models we determined the diameter of the largest crustal thickness (DLCT) as a measure of the size of the basins. Figure 1 shows the relationship between impactor sizes and the DLCT for different temperature profiles and initial crustal thicknesses. The results show similar basin diameters for small impactors independently from the thermal profile. For impactor sizes larger than 40km (Fig.1A) or 30km (Fig.1B), the diameters of the hotter profile are significantly higher than those of the cold and intermediate profiles. We present Hertzsprung and Orientale basin as two examples for gravity modeling. In the formation model of Hertzsprung (Fig. 2A), we used the thermal profile corresponding to an age of 4.1Ga [13]. Figure 2 shows our best-fit model assuming an impactor size of 60km, and a crustal density of 2950kg/m3. The results for Orientale are shown in Figure 2B. In the best-fit model the impactor is 80km in diameter, crustal density is 2750kg/m3 and we assume a cold thermal profile corresponding to an age of 3.8Ga [13]. Gravity profiles from the formation models show that the position of Bouguerminima correlate with the DLCT. The ratio of Bouguerdiameter and DLCT evaluates the fit of the models. A ratio of one indicates that the Bouguerminimum is close to the DLCT. Conclusion: Our results agree with previous studies [4] in terms of the importance of the thermal state of the target material. Final crater morphologies are sensitive to the thermal conditions in the target material. In our study, temperature effects are visible in simulations with impactors larger than 40km and the change from intermediate to hot thermal states. Isostatic relaxation processes might further modify the initial gravity signature over time. The correlation between basin size and the position of the minimum in observed gravity is a powerful tool to predict impactor diameters without extensive modeling studies. Acknowledgments: We gratefully acknowledge the developers of iSALE. Topography and gravity data are available at NASA’s PDS. This work is funded by the DFG-grant SFB-TRR 170 (A4). Katarina Miljković research is funded by the Australian Research Council. References: [1]Ivanov, B., Melosh, H., and Pierazzo, E. (2010) Large Meteorite Impacts and Planet. Evol. IV,29-49. [2]Potter, R. W. K. et al. (2013) JGR:Planets,118,963-979. [3]Zhu, M.-H., Wünnemann, K. and Potter, R. W. K. (2015) JGR:Planets,120,2118-2134. [4]Miljković, K. et al. (2016) JGR:Planets,121,1695-1712. [5]Collins, G. S., Melosh, H. J. and Ivanov, B. A., (2004) Meteoritics & Planet.Sci.,39,217-231. [6]Wünnemann, K., Collins, G. and Melosh, H. (2006) Icarus,180,514- 527. [7]Thompson, S. L. (1990) Sandia National Laboratories Albuquerque, SAND89-2951. [8]Melosh, H. J. (2007) Meteoritics & Planet.Sci.,42,2079–2098. [9]Padovan, S. et al. (2018) EPSC,Abstract#755. [10]Zuber, M. T. et al. (2013) Science,339,668-671. [11]Park, R. S. et al. (2015) AGU Fall Meeting,Abstract#G41-B01. [12]Smith, D. E. et al. (2017) Icarus,283,70-9. [13]Orgel, C. et al. (2017) JGR:Planets,123,1-15.

The overturn of mantle cumulates following the crystallization of the lunar magma ocean -- particularly the sinking of ilmenite-bearing cumulates (IBC) -- provides an explanation for several aspect...

The parameters and initial conditions governing mantle convection in terrestrial planets like Mars are poorly known meaning that one often needs to randomly vary several parameters to test which ones satisfy observational constraints. However, running forward models in 2D or 3D is computationally intensive to the point that it might prohibit a thorough scan of the entire parameter space. We propose using Machine Learning to find a low-dimensional mapping from input parameters to outputs. We use about 10,000 thermal evolution simulations with Mars-like parameters run on a 2D quarter cylindrical grid to train a fully-connected Neural Network (NN). We use the code GAIA (Hüttig et al., 2013) to solve the conservation equations of mantle convection for a fluid with Newtonian rheology and infinite Prandtl number under the Extended Boussinesq Approximation. The viscosity is calculated according to the Arrhenius law of diffusion creep (Hirth & Kohlstedt, 2003). The model also considers the effects of partial melting on the energy balance, including mantle depletion of heat producing-elements (Padovan et., 2017), as well as major phase transitions in the olivine system. To generate the dataset, we randomly vary 5 different parameters with respect to each other: thermal Rayleigh number, internal heating Rayleigh number, activation energy, activation volume and a depletion factor for heat-producing elements in the mantle. In order to train in time, we take the simplest possible approach, i.e., we treat time as another variable in our input vector. 80% of the dataset is used to train our NN, 10% is used to test different architectures and to avoid over-fitting, and the remaining 10% is used as test set to evaluate the error of the predictions. For given values of the five parameters, our NN can predict the resulting horizontally-averaged temperature profile at any time in the evolution, spanning 4.5 Ga with an average error under 0.3% on the test set. Tests indicate that with as few as 5% of the training samples (= simulations x time steps), one can achieve a test-error below 0.5%, suggesting that for this setup, one can potentially learn the mapping from fewer simulations. Finally, we ran a fourth batch of GAIA simulations and compared them to the output of our NN. In almost all cases, the instantaneous predictions of the 1D temperature profiles from the NN match those of the computationally expensive simulations extremely well, with an error below 0.5%.

A conceptual design is presented for a low complexity, heritage-based flyby mission to Io, Jupiter’s innermost Galilean satellite and the most volcanically active body in the Solar System. The design addresses the 2011 Decadal Surveys recommendation for a New Frontiers class mission to Io and is based upon the result of the June 2012 NASA-JPL Planetary Science Summer School. A science payload is proposed to investigate the link between the structure of Io’s interior, it’s volcanic activity, it’s surface composition, and it’s tectonics. A study of Io’s atmospheric processes and Io’s role in the Jovian magnetosphere is also planned. The instrument suite includes a visible/near IR imager, a magnetic field and plasma suite, a dust analyzer and a gimbaled high gain antenna to perform radio science investigations. Payload activity and spacecraft operations would be powered by three Advanced Stirling Radioisotope Generators (ASRG). The primary mission includes 10 flybys with close-encounter altitudes as low as 100 km. The mission risks are mitigated by ensuring that relevant components are radiation tolerant and by using redundancy and flight-proven parts in the design. The spacecraft would be launched on an Atlas V rocket with a delta-v of 1.3 km/s. Three gravity assists (Venus, Earth, Earth) would be used to reach the Jupiter system in a 6-year cruise. The resulting concept demonstrates the rich scientific return of a flyby mission to Io.

The InSight mission [1] landed in November 2018 in the Elysium Planitia region [2] bringing the first geophysical observatory to Mars. Since February 2019 the seismometer SEIS [3] has continuously ...

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures., 14 pages, 7 figures, accepted for publication in ApJ

Author(s): Margot, JL; Hauck, SA; Mazarico, E; Padovan, S; Peale, SJ | Abstract: We describe the current state of knowledge about Mercury's interior structure. We review the available observational constraints, including mass, size, density, gravity field, spin state, composition, and tidal response. These data enable the construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial profiles of the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamics and the influence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discuss the wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in a unique spin-orbit resonance, and magnetic field generation.

We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k2. Based on these constraints we predict the tidal Love number h2 to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase-lag is predicted to be 4° at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16 mW/m2. We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h2 and k2 provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700 km, and with the expected determination of h2 from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase-lag with an accuracy better than ≈0.5° would further allow constraining the temperature at the core-mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core.

Context. The mass and radius of a planet directly provide its bulk density, which can be interpreted in terms of its overall composition. Any measure of the radial mass distribution provides a first step in constraining the interior structure. The fluid Love number $k_2$ provides such a measure, and estimates of $k_2$ for extrasolar planets are expected to be available in the coming years thanks to improved observational facilities and the ever-extending temporal baseline of extrasolar planet observations. Aims. We derive a method for calculating the Love numbers $k_n$ of any object given its density profile, which is routinely calculated from interior structure codes. Methods. We used the matrix-propagator technique, a method frequently used in the geophysical community. Results. We detail the calculation and apply it to the case of GJ 436b, a classical example of the degeneracy of mass-radius relationships, to illustrate how measurements of $k_2$ can improve our understanding of the interior structure of extrasolar planets. We implemented the method in a code that is fast, freely available, and easy to combine with preexisting interior structure codes. While the linear approach presented here for the calculation of the Love numbers cannot treat the presence of nonlinear effects that may arise under certain dynamical conditions, it is applicable to close-in gaseous extrasolar planets like hot Jupiters, likely the first targets for which $k_2$ will be measured., Comment: 10 pages, 9 figures

Mercury’s crust is mostly the result of partial melting in the mantle associated with solid-state convection. Large impacts induce additional melting by generating subsurface thermal anomalies. By numerically investigating the geodynamical effects of impacts, here we show that impact-generated thermal anomalies interact with the underlying convection modifying the source depth of melt and inducing volcanism that can significantly postdate the impact depending on the impact time and location with respect to the underlying convection pattern. We can reproduce the volume and time of emplacement of the melt sheets in the interior of Caloris and Rembrandt if at about 3.7–3.8 Ga convection in the mantle of Mercury was weak, an inference corroborated by the dating of the youngest large volcanic provinces. The source depth of the melt sheets is located in the stagnant lid, a volume of the mantle that never participated in convection and may contain pristine mantle material., Mantle partial melting produced the volcanic crust of Mercury. Here, the authors numerically model the formation of post-impact melt sheets and find that mantle convection was weak at around 3.7–3.8 Ga and that the melt sheets of Caloris and Rembrandt may contain partial melting of pristine mantle material.

Data from transit light curves, radial velocity and transit timing observations can be used to probe the interiors of exoplanets beyond the mean density, by measuring the Love numbers $h_2$ and $k_2$. The first indirect estimate of $k_2$ for an exoplanet from radial velocity and transit timing variations observations has been performed by taking advantage of the years-spanning baseline. Not a single measurement of $h_2$ has been achieved from transit light curves, mostly because the photometric precision of current observing facilities is still too low. We show that the Imaging Spectrograph instrument on-board the Hubble Space Telescope could measure $h_2$ of the hot Jupiter WASP-121b if only few more observations were gathered. We show that a careful treatment of the noise and stellar limb darkening must be carried out to achieve a measurement of $h_2$. In particular, we find that the impact of the noise modelling on the estimation of $h_2$ is stronger than the impact of the limb darkening modelling. In addition, we emphasize that the wavelet method for correlated noise analysis can mask limb brightening. Finally, using presently available data, we briefly discuss the tentative measurement of $h_2 = 1.39^{+0.71}_{-0.81}$ in terms of interior structure. Additional observations would further constrain the interior of WASP-121b and possibly provide insights on the physics of inflation. The possibility of using the approach presented here with the Hubble Space Telescope provides a bridge before the high-quality data to be returned by the James Webb Space Telescope and PLATO telescope in the coming decade., Comment: Accepted for publication in ApJ

The combination of the radio tracking of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft and Earth-based radar measurements of the planet's spin state gives three fundamental quantities for the determination of the interior structure of Mercury: mean density �� , moment of inertia C, and moment of inertia of the outer solid shell C m . This work focuses on the additional information that can be gained by a determination of the change in gravitational potential due to planetary tides, as parameterized by the tidal potential Love number k2. We investigate the tidal response for sets of interior models that are compatible with the available constraints (�� , C, and Cm). We show that the tidal response correlates with the size of the liquid core and the mean density of material below the outer solid shell and that it is affected by the rheology of the outer solid shell of the planet, which depends on its temperature and mineralogy. For a mantle grain size of 1 cm, we calculate that the tidal k2 of Mercury is in the range 0.45 to 0.52. Some of the current models for the interior structure of Mercury are compatible with the existence of a solid FeS layer at the top of the core. Such a layer, if present, would increase the tidal response of the planet.

International audience; The present-day thermal state, interior structure, composition, and rheology of Mars can be constrained by comparing the results of thermal history calculations with geophysical, petrological, and geological observations. Using the largest-to-date set of 3-D thermal evolution models, we find that a limited set of models can satisfy all available constraints simultaneously. These models require a core radius strictly larger than 1,800 km, a crust with an average thickness between 48.8 and 87.1 km containing more than half of the planet's bulk abundance of heat producing elements, and a dry mantle rheology. A strong pressure dependence of the viscosity leads to the formation of prominent mantle plumes producing melt underneath Tharsis up to the present time. Heat flow and core size estimates derived from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission will increase the set of constraining data and help to confine the range of admissible models. Plain Language Summary We constrain the thermal state and interior structure of Mars by combining a large number of observations with thermal evolution models. Models that match the available observations require a core radius larger that half the planetary radius and a crust thicker than 48.8 km but thinner than 87.1 km on average. All best-fit models suggest that more than half of the planet's bulk abundance of heat producing elements is located in the crust. Mantle plumes may still be active today in the interior of Mars and produce partial melt underneath the Tharsis volcanic province. Our results have important implications for the thermal evolution of Mars. Future data from the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) mission can be used to validate our models and further improve our understanding of the thermal evolution of Mars.

We are witness to a great and increasing interest in internal structure, composition and evolution of exoplanets. However, direct measurements of exoplanetary mass and radius cannot be uniquely interpreted in terms of interior structure, justifying the need for an additional observable. The second degree fluid Love number, $k_2$, is proportional to the concentration of mass towards the body's center, hence providing valuable additional information about the internal structure. When hydrostatic equilibrium is assumed for the planetary interior, $k_2$ is a direct function of the planetary shape. Previous attempts were made to link the observed tidally and rotationally induced planetary oblateness in photometric light curves to $k_2$ using ellipsoidal shape models. Here, we construct an analytical 3D shape model function of the true planetary mean radius, that properly accounts for tidal and rotational deformations. Measuring the true planetary mean radius is critical when one wishes to compare the measured $k_2$ to interior theoretical expectations. We illustrate the feasibility of our method and show, by applying a Differential Evolution Markov Chain to synthetic data of WASP-121b, that a precision $\leq$ 65 ppm/$\sqrt{2\,min}$ is required to reliably retrieve $k_2$ with present understanding of stellar limb darkening, therefore improving recent results based on ellipsoidal shape models. Any improvement on stellar limb darkening would increase such performance., Comment: Accepted for publication in The Astrophysical Journal

United States. National Aeronautics and Space Administration (NASA MESSENGER Participating Scientist grant NNX07AR77G)

©2015. American Geophysical Union Mercury experiences an uneven insolation that leads to significant latitudinal and longitudinal variations of its surface temperature. These variations, which are predominantly of spherical harmonic degrees 2 and 4, propagate to depth, imposing a long‐wavelength thermal perturbation throughout the mantle. We computed the accompanying density distribution and used it to calculate the mechanical and gravitational response of a spherical elastic shell overlying a quasi‐hydrostatic mantle. We then compared the resulting geoid and surface deformation at degrees 2 and 4 with Mercury's geoid and topography derived from the MErcury, Surface, Space ENvironment, GEochemistry, and Ranging spacecraft. More than 95% of the data can be accounted for if the thickness of the elastic lithosphere were between 110 and 180 km when the thermal anomaly was imposed. The obtained elastic thickness implies that Mercury became locked into its present 3:2 spin orbit resonance later than about 1 Gyr after planetary formation.

The Galileo mission has indicated the possibility of the existence of a subsurface ocean on Europa. The measurement of the surface deformation in response to the tidal forcing and the measurement of the amplitude and frequency of the librations of Europa around a 1:1 spin-orbit resonant state is considered as the best indirect verification of both the existence and approximate depth of such an ocean. Previous studies have separately dealt with the detection of a global liquid ocean beneath the icy crust of Europa with altimeter measurements, and through the detection of the libration amplitudes from Earth-based radio tracking. The purpose of the present study is to simulate the combined detection of bodily tides and librations with the use of altimeter data from a low-altitude Europa orbiter and radio tracking from the Earth. The analysis thus provides some insight into the sensitivity of the orbit geometry to the direct altimetric measurement and the indirect sensing through the analysis of the orbit perturbations due to the tidal mass displacement and the Europan librations. The results indicate that orbits of at least 70 inclination are required, although polar orbits are not necessary. A formal error propagation also indicates that the Love numbers of Europa can be determined with an error of a few percent from measurement arcs spanning just a few days. This information can be of value for the preliminary planning phase of future Europa exploration missions, like the LAPLACE mission recently considered by the ESA Cosmic Vision program and similar missions under study by NASA and other space agencies.

©2015. American Geophysical Union. All Rights Reserved. To gain insight into the thickness of the crust of Mercury, we use gravity and topography data acquired by the MErcury Surface, Space ENvironment, GEochemistry, and Ranging spacecraft to calculate geoid-to-topography ratios over the northern hemisphere of the planet. For an Airy model for isostatic compensation of variations in topography, we infer an average crustal thickness of 35 ± 18 km. Combined with the value of the radius of the core of Mercury, this crustal thickness implies that Mercury had the highest efficiency of crustal production among the terrestrial planets. From the measured abundance of heat-producing elements on the surface, we calculate that the heat production in the mantle from long-lived radioactive elements at 4.45 Ga was greater than 5.4 ×10-12W/kg. By analogy with the Moon, the relatively thin crust of Mercury allows for the possibility that major impact events, such as the one that formed the Caloris basin, excavated material from Mercury's mantle.