Gravity Recovery And Interior Laboratory Research Articles

A potential subsurface cavity in the continuous ejecta deposits of the Ziwei crater discovered by the Chang\u2019E-3 mission

In the radargram obtained by the high-frequency lunar penetrating radar onboard the Chang’E-3 mission, we notice a potential subsurface cavity that has a smaller permittivity compared to the surrounding materials. The two-way travel time between the top and bottom boundaries of the potential cavity is ~ 21 ns, and the entire zone is located within the continuous ejecta deposits of the Ziwei crater, which generally have similar physical properties to typical lunar regolith. We carried out numerical simulations for electromagnetic wave propagation to investigate the nature of this low-permittivity zone. Assuming different shapes for this zone, a comprehensive comparison between our model results and the observed radargram suggests that the roof of this zone is convex and slightly inclined to the south. Modeling subsurface materials with different relative permittivities suggests that the low-permittivity zone is most likely formed due to a subsurface cavity. The maximum vertical dimension of this potential cavity is ~ 3.1 m. While the continuous ejecta deposits of Ziwei crater are largely composed of pre-impact regolith, competent mare basalts were also excavated, which is evident by the abundant meter-scale boulders on the wall and rim of Ziwei crater. We infer that the subsurface cavity is supported by excavated large boulders, which were stacked during the energetic emplacement of the continuous ejecta deposits. However, the exact geometry of this cavity (e.g., the width) cannot be constrained using the single two-dimensional radar profile. This discovery indicates that large voids formed during the emplacement of impact ejecta should be abundant on the Moon, which contributes to the high bulk porosity of the lunar shallow crust, as discovered by the GRAIL mission. Our results further suggest that ground penetrating radar is capable of detecting and deciphering subsurface cavities such as lava tubes, which can be applied in future lunar and deep space explorations.Subsurface cavities of the Moon are the ideal natural shelter for future lunar explorations since they provide ideal insulation from cosmic radiation, meteoroid impacts, temperature fluctuations, etc. In this paper, we first report that a potential subsurface cavity with a height of ~3.1 m is revealed by the lunar penetrating radar onboard Chang’E-3 Yutu Rover

Investigating the Influences of Crustal Thickness and Temperature on the Uplift of Mantle Materials Beneath Large Impact Craters on the Moon

AbstractIn this work, we examine variations in the mantle uplift associated with large lunar impact craters and basins between major terranes. This study is based on Bouguer gravity anomalies of 100–650‐km diameter impact craters using Gravity Recovery and Interior Laboratory (GRAIL) observations and the Lunar Orbiter Laser Altimeter (LOLA) crater database. The Bouguer gravity anomalies of 324 large impact craters analyzed herein are primarily controlled by the uplifted crust‐mantle (Moho) interface in the central region of these impact craters, while postimpact mare deposits that represent ∼25%–35% of the postimpact deposit column also contribute to the gravity anomalies of mare craters. The central uplift of the Moho interface is primarily controlled by impact energy and increases to ∼ 30 km for a 650‐km diameter crater. Analyses of nonmare craters in the Feldspathic Highlands Terrane (FHT) with varied crustal thickness (Tc) reveal that the onset crater diameter (Dmin) with an uplifted Moho interface is dependent on the local Tc: Dmin ∼ 150 + 1.3Tc (in a unit of km). This equation also provides a quantification of the depth‐dependent attenuation of impact‐induced structural uplift, using the Moho uplift as a proxy for the structural uplift. The Moho uplift of large craters in the South Pole‐Aitken (SPA) Terrane is not statistically different from the FHT craters, consistent with limited overall thermal difference between these two terranes and compensational thermal effects at crater collapse and viscoelastic relaxation stages.

Variations of porosity in intermediate-sized lunar impact basins

The Moon is cratered with hundreds of well-preserved impact basins, and shared bombardment history with Earth makes lunar basins a good proxy for the processes affecting early Earth. Basin-forming impact events alter the bulk density and porosity of the targeted crust, and measurement of these quantities offers a means by which we can investigate the mechanisms of basin formation. In this work, we calculate the bulk density of the crust in the vicinity of 50 basins with diameters of 170–360 km—a size range that has been neglected by previous studies—with the goal of understanding the deformational mechanisms present during impact events. Our bulk density estimates are derived from gravity data from NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission and topography data from the Lunar Orbiter Laser Altimeter (LOLA) using a new technique similar to the Nettleton method in terrestrial gravimetry. By making assumptions about crustal compositions across the Moon, we can furthermore estimate porosity in and around the basins. Low porosity is observed in the interior of 76% of the basins studied, and this trend becomes more apparent when basins in the Feldspathic Highlands Terrane are observed alone. Overall, impact events appear to decrease porosity inside basins and increase porosity outside basins, suggesting the prevalence of impact melting within the basins and fracturing and ejecta deposition in the exteriors. Our results are seemingly inconsistent with previous studies that measured high porosity values inside basins from residual Bouguer anomalies. However, these disparate results may be reconciled if impact melting processes are confined to the uppermost kilometers of the lunar crust and are underlain by heavy impact-induced fracturing.

Crustal Porosity of Lunar Impact Basins

AbstractLateral variations in bulk density and porosity of the upper lunar highland crust are mapped using a high‐resolution Gravity Recovery and Interior Laboratory (GRAIL) gravity field model and Lunar Reconnaissance Orbiter (LRO) derived topography. With a higher spatial resolution gravity model than previous studies, we focus on individual impact basins with diameters greater than 200 km. The bulk density of the upper few kilometers of the lunar crust is estimated by minimizing the correlation between the topography and Bouguer gravity at short wavelengths that are unaffected by lithospheric flexure. Porosity is then derived using estimates of the grain density obtained from remote sensing data of the surface composition. The near surface crust in proximity to many large basins is found to exhibit distinct radial porosity signatures. Low porosities are found in the basin centers within the peak ring, whereas high porosities are identified near and just exterior to the main rim. The larger basins exhibit a more pronounced porosity signature than the smaller basins. Though the number of basins investigated in this study is limited, younger basins appear to be associated with the largest amplitude variations in porosity. For basins with increasing age the magnitude of the porosity variations decreases.

High‐Resolution Gravity Field Models from GRAIL Data and Implications for Models of the Density Structure of the Moon's Crust

AbstractWe present our latest high‐resolution lunar gravity field model of degree and order 1200 in spherical harmonics using Gravity Recovery and Interior Laboratory (GRAIL) data. In addition to a model with the standard spectral Kaula regularization constraint, we determine models by applying a constraint based on topography called rank‐minus‐one (RM1). The new models using this RM1 constraint have high correlations with topography over the entire degree range by design. The RM1 models allow the determination of apparent crustal densities at all spatial scales (called effective density) covered by the model, whereas the Kaula‐constrained model can only be used globally up to spherical harmonic degree 700. We find that the effective density spectrum has a smaller slope for the high degrees when compared to the medium degrees. We interpret this as indicative of a global average surface density, as opposed to an ever‐decreasing effective density as one approaches the surface. We use the RM1 models to derive maps of lateral and vertical density variations in the lunar crust. These models allow us to increase the resolution of this analysis compared to previous studies, by increasing the degree range over which to fit theoretical models of vertical density variations, and by decreasing the size of the spherical caps used in a localized analysis. Several regions on the Moon, such as South Pole‐Aitken and Mare Orientale, are distinct from their surroundings in terms of surface densities. The RM1 models are especially valuable in (localized) spectral studies of the structure of the lunar crust.

Feasibility of quasi-frozen, near-polar and extremely low-altitude lunar orbits

Designing long-duration lunar orbiter missions is challenging due to the Moon's highly nonlinear gravity field and the third-body perturbations induced by the Earth, Sun and other large bodies. The absence of a Lunar atmosphere has offered the possibility for mission designers to search for extremely low-altitude, quasi-stable lunar orbits. In addition to the reduced amount of propellant required for station-keeping maneuvers, these orbits present great opportunities for unique scientific studies such as high resolution imaging and characterization of the polar ice deposits in deep craters. Prior to the GRAIL mission, mission planning for Lunar orbiters had suffered from inaccuracies, mainly due to the lack of an accurate Lunar gravity model, which resulted in severe deviations with respect to the spacecraft's nominal orbit.We study station-keeping feasibility for spacecraft in near-polar and extremely low-altitude, quasi-frozen orbits around the Moon, that are perturbed by a high-fidelity lunar gravity model and third-body effects from the Earth and Sun. For several candidate orbits, we compare the trade-space between mission duration and ΔV budget, considering impulsive maneuvers applied once every ‘N∈{2,6,10,14,18}’ orbits at periselene or aposelene. Additionally, we investigate the propulsive cost for different orbit insertion dates, the location of impulsive corrections for arresting argument of periselene (ω) drift, and controlling periselene altitude.

Density Structure of the Von Kármán Crater in the Northwestern South Pole-Aitken Basin: Initial Subsurface Interpretation of the Chang'E-4 Landing Site Region.

The Von Kármán Crater, within the South Pole-Aitken (SPA) Basin, is the landing site of China’s Chang’E-4 mission. To complement the in situ exploration mission and provide initial subsurface interpretation, we applied a 3D density inversion using the Gravity Recovery and Interior Laboratory (GRAIL) gravity data. We constrain our inversion method using known geological and geophysical lunar parameters to reduce the non-uniqueness associated with gravity inversion. The 3D density models reveal vertical and lateral density variations, 2600–3200 kg/m3, assigned to the changing porosity beneath the Von Kármán Crater. We also identify two mass excess anomalies in the crust with a steep density contrast of 150 kg/m3, which were suggested to have been caused by multiple impact cratering. The anomalies from recovered near surface density models, together with the gravity derivative maps extending to the lower crust, are consistent with surface geological manifestation of excavated mantle materials from remote sensing studies. Therefore, we suggest that the density distribution of the Von Kármán Crater indicates multiple episodes of impact cratering that resulted in formation and destruction of ancient craters, with crustal reworking and excavation of mantle materials.

Magmatic intrusion-related processes in the upper lunar crust: The role of country rock porosity/permeability in magmatic percolation and thermal annealing, and implications for gravity signatures

Shallow crustal country rock on the Moon is demonstrably more fractured and porous than deeper crustal bedrock, and Gravity Recovery and Interior Laboratory (GRAIL) mission gravity data have shown that deeper crustal bedrock is more porous than previously thought. This raises the question of how crustal porosity and permeability will influence the nature of magmatic dike intrusions in terms of: 1) the ability of intruding magma to inject into and occupy this pore space (shallow magmatic percolation), 2) the influence of the intruded magma on annealing of this porosity and permeability (thermal annealing) both 1 and 2 densify the country rock), and 3) the effect of crustal porosity on favoring sill formation as a function of depth in the lunar crust. We analyze quantitatively the emplacement of basaltic dikes and sills on the Moon and assess these three factors in the context of the most recent data on micro- and macro-scale porosity of lunar crustal materials. For the range of plausible micro/macro-scale porosity and permeability determined by crack widths (mm to cm) and open crack lateral continuity (mm to tens of cm), we find that 1) rapid conductive cooling of injected magma due to the very large surface area to volume ratio restricts magmatic percolation to very limited zones (extending for at most several tens of cm) adjacent to the ascending dike or intruded sill, even in the upper several hundred meters of the lunar crust; 2) the conductive heat loss from intruded dikes and sills results in a thermal wave decay rate that is predicted to limit the extent of intrusion-adjacent thermal annealing to less than ~6% of the thickness of the intruded body; 3) the extremely rapid rise rate of magma in dikes originating from sources in the lunar mantle disfavors the lateral migration of dikes to form sills in the crust, except in specific shallow crustal locations influenced by impact crater-related environments (e.g., floor-fractured craters). We conclude that, although magmatic percolation and thermal annealing in association with lunar mare basalt magmatic dike and sill emplacement should be taken into consideration in interpreting gravity signatures, the effects are likely to be minor compared with the density contrast of the solidified basaltic magmatic intrusion itself.

Improving the geometry of Kaguya extended mission data through refined orbit determination using laser altimetry

The Japan Aerospace Exploration Agency’s (JAXA) Kaguya spacecraft carried a suite of instruments to map the Moon and its environment globally. During its extended mission, the average altitude was 50 km or lower, and Kaguya science products using these data hence have an increased spatial resolution. However, the geodetic position quality of these products is much worse than that of those acquired during the primary mission (at an altitude of 100 km) because of reduced radiometric tracking and frequent thrusting to maintain spacecraft attitude after the loss of momentum wheels. We have analyzed the Kaguya tracking data using gravity models based on the Gravity Recovery and Interior Laboratory (GRAIL) mission, and by making use of a new data type based on laser altimeter data collected by Kaguya: we adjust the spacecraft orbit such that the altimetry tracks fit a precise topographic basemap based on the Lunar Reconnaissance Orbiter’s (LRO) Lunar Orbiter Laser Altimeter (LOLA) data. This results in geodetically accurate orbits tied to the precise LOLA/LRO frame. Whereas previously archived orbits show errors at the level of several kilometers, the inclusion of altimetry greatly improves the orbit precision, to a level of several tens of meters. When altimetry data are not available, the combination of GRAIL gravity and radio tracking results in an orbit precision of around several hundreds of meters for the low-altitude phase of the extended mission. Our greatly improved orbits result in better geolocation of the Kaguya extended mission data set.

Relativistic celestial mechanics at sub-microarcsecond accuracy level

Einstein stated two dictums, so that more experimental facts can replace the previously adopted hypotheses and General Relativity (GR) can evolve to “grand aim” or perfection. In the absence of appropriate experimental facts during pre-CEREPAC (Century-long Experience of Relativity-related Experiments on Physics, Astronomy and Celestial-mechanics) era, Einstein found no “escape” from the consequence of non-Euclidean geometry, while keeping all frames permissible based on contemporary knowledge. Bergmann also stated in 1968 that the “principle of general covariance” has brought about serious complication in GR. During CEREPAC, relativists and mathematical-astronomers invariably identified the appropriate “nature’s preferred-frame,” which was later found essential for operation of conservation laws. Based on CEREPAC, replacing the experimentally unverifiable hypotheses with experimentally proven principles, and improving upon the GR-astronomers model (developed by JPL, USA, as an evolved-version of GR-conventional model) in two successive stages, GR was remodeled to what became evident as Evolved GR (EGR), after it enabled the elimination of all earlier-adopted ad-hoc methods or approaches, and of the problems, paradoxes and anomalies, associated with the applications of GR, during CEREPAC, and after it unraveled the “General-relativistic nature of speed-of-light (c)” which links the variable c r with F r, the local Gravitational Red-Shift Factor (as stated by Einstein between 1911‐1921). As a consequence of the space-age developments in numerical simulation and in the availability of precision observational data, it got proven that nature itself operates the conservation laws of energy, and of linear and angular momentums (both magnitudes and directions), with respect to the appropriate “nature’s preferred frame”; this provided sufficient reason for giving up the “relativity of all frames,” bringing back Euclidean geometry in EGR. Euclidean space in EGR enabled development of a Prototype of future Ephemerides, leading to five orders-of-magnitude improvement in accuracy of computation of precession of celestial orbits, using three independent methods; this methodology of Prototype Ephemeris and “three-methods-match” can also be applied while remaining exclusively within the precincts of GR, by using one alternative mode of running the EGR program for planetary and Lunar orbits, by opting for GRTOPT=Y; this mode utilizes exclusively the GR equations instead of EGR equations; in fact, this mode is the GR-astronomers (modified) model that was really an intermediate stage of evolution (as mentioned above) between the GR-astronomers model and the EGR model. This model incorporates: (1) All good (and, experimentally proven) features from the three generations of GR models (Einstein’s original, Bergmann’s and Misner-Thorne-Wheeler or MTW), and (2) The “Nature-adopted” real orbital model (as proven from comparison of the computed precession values at Micro-arcsecond {μas} level using the “three-methods-match”) for its Methodology for Conservation of Linear and Orbital Angular Momentums, in a polar coordinate system (r, , Φ). This model computes: (1) Precession of celestial orbits at nearly the same accuracy as that done using the EGR model, and (2) About three digit more accurate (than reported by Folkner in 2014, from fitting lunar laser ranging data with an updated lunar gravity field from the GRAIL mission, etc.) orbits of inner planets and the Moon.

Ebb and Flow

In 2012 NASA’s two Gravity Recovery and Interior Laboratory (GRAIL) spacecraft – Ebb (GRAIL-A) and Flow (GRAIL-B) – produced the most detailed lunar gravity map to date (shown).

Effect of thermal state on the chemical composition of the mantle and the sizes of the moon’s core

Based on the joint inversion of seismic and gravity data in combination with the Gibbs free energy minimization method for calculating phase equilibria in the framework of the Na2O-TiO2-CaO-FeO-MgO-Al2O3-SiO2 system, the influence of the thermal state on the chemical composition models of the mantle and the sizes of the Fe-S core of the Moon has been studied. The boundary conditions used are seismic models from Apollo experiments, mass and moment of inertia from the GRAIL mission. As a result of solving the inverse problem, constraints on the chemical composition (concentration of rock-forming oxides) and the mineralogy of a three-layer mantle are obtained. It is shown that regardless of the temperature distribution, the FeO content of 11–14 wt.% and magnesian number MG# 80–83 are approximately the same in the upper, middle and lower mantle of the Moon, but differ sharply from that for the bulk composition of the silicate Earth (Bulk Silicate Earth = BSE, FeO ~8 wt% and MG# 89). On the contrary, estimates of the Al2O3 content in the mantle rather noticeably depend on the temperature distribution. For the considered scenarios of the thermal state with a difference in temperature of 100–200°C at different depths, Al2O3 concentrations increase from 1–5% in the upper and middle mantles to 4–7 wt.% in the lower mantle with garnet amounts up to 20 wt.%. For the “cold” models, the bulk abundance of aluminum oxide in the Moonis Al2O3 ~1–1.2 × BSE, and for the “hot” models it can be in the range of 1.3–1.7 × BSE. Concentrations of SiO2 to a lesser extent depend on the temperature distribution and constitute 50–55% in the upper and 45–50 wt.% in the lower mantle; orthopyroxene, rather than olivine, is the dominant mineral of the upper mantle. Based on the modeling of the density of Fe-S melts at high Р-Т parameters, the sizes of the lunar core are estimated. The Fe-S core radii with an average density of 7.1 g/cm3 and a sulfur content of 3.5–6 wt.% are in the range of 50–350 km with a most likely value of about 300 km and rather weakly depend on the thermal regime of the Moon. The simulation results suggest that a lunar mantle is stratified by chemical composition and indicate significant differences in the compositions of the Earth and its satellite.

Effect of Thermal State on the Mantle Composition and Core Sizes of the Moon

Based on the joint inversion of seismic and gravity data in combination with phase equilibrium calculations within the Na2O–TiO2–CaO–FeO–MgO–Al2O3–SiO2 system using the method of Gibbs free energy minimization, we estimated the influence of the thermal state on the model chemical composition of the lunar mantle and the size of the Fe–S lunar core. Models based on the Apollo seismic data and mass and moment of inertia estimates from the data of the GRAIL mission were used as boundary conditions. The solution of the inverse problem provided constraints on the chemical composition (major oxide abundances) and mineralogy of the three-layer mantle. It was shown that, independent of temperature distribution, the FeO contents (~11–14 wt %) and MG# values (80–83) of the upper, middle, and lower mantle of the Moon are approximately equal and strongly different from those of the bulk silicate Earth (BSE): FeO ~ 8% and MG# ~ 89. In contrast, the estimates of Al2O3 content in the mantle are sensitive to temperature distribution. The analysis of thermal state models with temperature differences of 100–200°C at different depths showed that the Al2O3 content increases from 1–5 wt % in the upper and middle mantle to 4–7 wt % in the lower mantle containing up to 20 wt % garnet. The lunar abundance of Al2O3 is ~(1.0–1.2) × BSE for “cold” models and may be as high as (1.3–1.7) × BSE for “hot” models. The abundance of SiO2 is less sensitive to temperature distribution and is 50–55 wt % in the upper mantle and 45–50 wt % in the lower mantle. Orthopyroxene rather than olivine is the dominant mineral of the upper mantle. Based on the modeling of Fe–S melt density at high P and T, the size of the lunar core was estimated. The radius of the Fe–S core having a mean density of 7.1 g/cm3 and a sulfur content of 3.5–6.0 wt % lies within the range 50–350 km with the most probable value of approximately 300 km and depends weakly on the thermal regime of the Moon. The results of modeling imply that the lunar mantle is chemically stratified and the compositions of the Earth and its satellite are significantly different.

GRAIL-identified gravity anomalies in Oceanus Procellarum: Insight into subsurface impact and magmatic structures on the Moon

Four, quasi-circular, positive Bouguer gravity anomalies (PBGAs) that are similar in diameter (~90–190 km) and gravitational amplitude (>140 mGal contrast) are identified within the central Oceanus Procellarum region of the Moon. These spatially associated PBGAs are located south of Aristarchus Plateau, north of Flamsteed crater, and two are within the Marius Hills volcanic complex (north and south). Each is characterized by distinct surface geologic features suggestive of ancient impact craters and/or volcanic/plutonic activity. Here, we combine geologic analyses with forward modeling of high-resolution gravity data from the Gravity Recovery and Interior Laboratory (GRAIL) mission in order to constrain the subsurface structures that contribute to these four PBGAs. The GRAIL data presented here, at spherical harmonic degrees 6–660, permit higher resolution analyses of these anomalies than previously reported, and reveal new information about subsurface structures. Specifically, we find that the amplitudes of the four PBGAs cannot be explained solely by mare-flooded craters, as suggested in previous work; an additional density contrast is required to explain the high-amplitude of the PBGAs. For Northern Flamsteed (190 km diameter), the additional density contrast may be provided by impact-related mantle uplift. If the local crust has a density ~2800 kg/m3, then ~7 km of uplift is required for this anomaly, although less uplift is required if the local crust has a lower mean density of ~2500 kg/m3. For the Northern and Southern Marius Hills anomalies, the additional density contrast is consistent with the presence of a crustal complex of vertical dikes that occupies up to ~50% of the regionally thin crust. The structure of Southern Aristarchus Plateau (90 km diameter), an anomaly with crater-related topographic structures, remains ambiguous. Based on the relatively small size of the anomaly, we do not favor mantle uplift; however, understanding mantle response in a region of especially thin crust needs to be better resolved. It is more likely that this anomaly is due to subsurface magmatic material given the abundance of volcanic material in the surrounding region. Overall, the four PBGAs analyzed here are important in understanding the impact and volcanic/plutonic history of the Moon, specifically in a region of thin crust and elevated temperatures characteristic of the Procellarum KREEP Terrane.

Constraints on Lunar Crustal Porosity From the Gravitational Signature of Impact Craters

AbstractBased on Gravity Recovery and Interior Laboratory (GRAIL) observations and the Lunar Orbiter Laser Altimeter (LOLA) crater database, we constrain the spatial variations in the Moon's crustal porosity (ϕc) to a depth of several kilometers using the gravity anomalies of 4,864 midsized craters (those with a diameter of 20–100 km). For each crater, we estimated the local ϕc by quantifying the gravitational effects of impact‐induced porosity change and postimpact breccia infill. The crustal porosity model was uniquely determined assuming a global mean ϕc of 12%, although a trade‐off exists between the porosity of postimpact breccia infill and the (preimpact) crustal porosity that results in zero net porosity change underlying the crater floor. At this crustal porosity the effects of impact bulking and compaction compensate each other to yield zero crater residual Bouguer anomaly (RBA), when the effect of postimpact infill is excluded. For lower crustal porosities, bulking dominates to produce a negative RBA; for higher crustal porosities, compaction dominates to produce a positive RBA. Spatial kriging and statistical tests suggest lower‐than‐average ϕc in the western nearside maria and southern South Pole‐Aitken (SP‐A) basin, in contrast to higher‐than‐average values in the southwestern periphery of the nearside maria. Most of the large impact basins, presumably formed before the majority of the midsized craters we analyzed, show reduced porosities relative to their immediate surroundings.

Comparison and analysis on lunar rotation with lunar gravity field models

Understanding the structure of and dynamic processes in the deep interior of planets is crucial for understanding their origin and evolution. An effective way to constrain them is through observation of rotation and subsequent simulation. In this paper, a numerical model of the Moon’s rotation and orbital motion is developed based on previous studies and implemented independently. The Moon is modeled as an anelastic body with a liquid core. The equations of the rotation were nonlinear and the Euler angles are cross coupled. We solve them numerically via the Runge-Kutta-Fehlberg (RKF) and multi-steps Adams-Bashforth-Moulton (ABM) predictor-corrector numerical integration. We have found that adequate accuracy is maintained by taking twelve steps per day using eleventh differences in the integrating polynomial. The lunar orbital and rotational equations are strongly coupled, so we integrated the rotation and motion simultaneously. We refer to other planetary informations from the newest planetary and lunar ephemeris INPOP17a, which is reported had fitted the longest LLR (Lunar Laser Ranging) observation data. Using the model GL660B from GRAIL (Gravity Recovery and Interior Laboratory) mission, we firstly compare our numerical results with the INPOP17a to prove the reasonability of our model. After that we apply the lunar gravity model CEGM02 determined from Chang’E-1 mission and SGM100h from SELENE mission to our model, the difference between results from CEGM02 and GL660B are less than $-0.20 \sim0.15$ arc-second, and $-0.25 \sim0.20$ arc-second for GL660B and SGM100h. Compared to SGM100h, the results show that the low degree and order coefficients (less than 6 from this paper) of lunar gravity field were improved in CEGM02 as expected. It is the first time to demonstrate that these models can be applied to lunar rotation model. These results manifest that a development of the gravity field measure will help us to know the rotation motion more precisely.

First independent Graz Lunar Gravity Model derived from GRAIL

The twin satellite mission Gravity Recovery and Interior Laboratory (GRAIL) aims to recover the lunar gravity field by means of Ka-band ranging observations. In order to exploit the potential of the inter-satellite range variations, absolute position information of the two probes is required. Hitherto, the Graz lunar gravity field models (GrazLGM) relied on the official science orbit products provided by NASA. In this contribution, we present for the first time a completely independent Graz Lunar Gravity Model based on Primary Mission data. The models are resolved up to spherical harmonic degree and order 420. The orbits of the two probes are determined using variational equations following a batch least squares differential adjustment process implemented in the in-house developed software package ORCA (Orbit Re-Construction Application). These orbits are based on S-band radiometric tracking data collected by the Deep Space Network (DSN) and are used for the independent GRAIL gravity field recovery. To reveal a highly accurate lunar gravity field, an integral equation approach using short orbital arcs is adopted to process the Ka-band data, where no regularization or Kaula constraint is applied. The correlation of gravity with lunar topography as well as the Bouguer spectrum of our solutions is comparable to the models officially released by the GRAIL Science Team.

Preferred design and error analysis for the future dedicated deep-space Mars-SST satellite gravity mission

Because the precise measurement of the Martian gravitational field plays a significant role in the future Mars exploration program, the future dedicated Mars satellite-to-satellite tracking (Mars-SST) gravity mission in China is investigated in detail for producing the next generation of the Mars gravity field model with high accuracy. Firstly, a new semi-numerical synthetical error model of the cumulative Martian geoid height influenced by the major error sources of the space-borne instruments is precisely established and efficiently verified. Secondly, the deep space network in combination with the satellite-to-satellite tracking in the low-low (DSN-SST-LL) mode is a preferred design owing to the high precision determination of the gravity maps, the low technical complexity of the satellite system and the successful experiences with the Earth’s Gravity Recovery and Climate Experiment (GRACE) projects and the lunar Gravity Recovery and Interior Laboratory (GRAIL) program. Finally, the future twin Mars-SST satellites plan to adopt the optimal matching accuracy indices of the satellite-equipped sensors (e.g., $10^{-7}$ m/s in the inter-satellite range-rate from the interferometric laser ranging system (ILRS), 35 m in the orbital position tracked by the DSN and $3\times 10^{-11}$ m/s2 in the non-conservative force from the drag-free control system (DFCS)) and the preferred orbital parameters (e.g., the orbital altitude of $100\pm 50$ km and the inter-satellite range of $50\pm 10$ km).

Fractional crystallization of the lunar magma ocean: Updating the dominant paradigm

AbstractWe report results of systematic experimental simulation of fractional crystallization of a lunar magma ocean (LMO) with the Lunar Primitive Upper Mantle bulk composition. These results complement prior work that simulated equilibrium crystallization. In contrast to previous numerical models for investigating magma ocean solidification processes and implications, our combined program simulates these processes directly using petrologic experimentation. Our experiments mimic LMO crystallization that is fractional throughout the process, rather than switching from initially equilibrium to fractional crystallization partway through. To do this, we adopted an iterative approach in which the starting material for each run is synthesized using the composition of the melt phase from the prior run. We compare our results to those from long‐standing numerical models of LMO crystallization and show that although some features of those models are broadly reproduced, there are key differences in liquid lines of descent and the cumulate lithologies generated. Our results can be used to estimate the possible thickness of a primordial lunar crust formed from flotation of plagioclase during magma ocean solidification. Our estimate is greater than that from the recent Gravity Recovery and Interior Laboratory (GRAIL) mission, but consistent with the criteria on which the starting bulk composition was originally calculated. It assumes perfectly efficient separation of all plagioclase formed from the crystallizing magma ocean, which is likely not the case. We also demonstrate that a non‐chondritic bulk composition, with respect to trace elements, is not required in order to generate a KREEP (potassium, rare earth elements, and phosphorus) signature from magma ocean crystallization.

Gravity anomalies and crustal structure of the Lunar far side highlands

The far side of the lunar hemisphere is dominated by a large number of impact craters having a smaller diameter and few Mare basins compared to the near side of the Moon. This study presents a detailed analyses of gravity anomalies derived from Gravity Recovery and Interior Laboratory (GRAIL) mission and topography over the central equatorial region of Lunar far side covering the major impact basins such as Dirichlet-Jackson, Korolev, Hertzsprung and adjoining regions of the highlands, to understand sub-surface structure. Bouguer gravity anomaly map of the region is prepared using the density of 2.7 g/cc, which is estimated using fractals based approach. The spectral analyses using Maximum Entropy Method of calculated Bouguer anomaly and topography provided an estimated of Effective Elastic Thickness (Te) as 19 km and also a cut-off wavelength of 270 km for separating Regional and residual Bouguer gravity anomalies. Further a crustal thickness of this region of Moon is estimated by inversion of regional Bouguer gravity anomalies, which varies from 20 to 71 km.An estimated crustal thickness of Dirichlet Jackson and Hertzpsrung, Korolev basins varies between 39 and 65 km, 20–65 km and 39–64 km, respectively. The residual gravity anomaly map shows symmetric gravity highs and lows in Dirichlet-Jackson, Hertzsprung and Korolev basins. These gravity highs can be attributed to high-density mare basalts within inner rims of these basins. The observed nature of gravity anomalies and crustal thickness map can be attributed to the buried impact crater under this region.