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At least 613 records · Page 34

The Effect of Dust on the Martian Polar Vortices

The influence of atmospheric dust on the dynamics and stability of the martian polar vortices is examined, through analysis of Mars Climate Sounder observations and MarsWRF general circulation model simulations. We show that regional and global dust storms produce transient vortex warming events that partially or fully disrupt the northern winter polar vortex for brief periods. Increased atmospheric dust heating alters the Hadley circulation and shifts the downwelling branch of the circulation poleward, leading to a disruption of the polar vortex for a period of days to weeks. Through our simulations, we find this effect is dependent on the atmospheric heating rate, which can be changed by increasing the amount of dust in the atmosphere or by altering the dust optical properties (e.g., single scattering albedo). Despite this, our simulations show that some level of atmospheric dust is necessary to produce a distinct northern hemisphere winter polar vortex.

Guzewich, Scott D.↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO) [1,2,3]. PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) [4] CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) [5] program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield [6]. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem [7]. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Thermal Protection Systems↗

Martian thermal boundary layers: Subhourly variations induced by radiative-conductive heat transfer within the dust-laden atmosphere-ground system

Radiative-conductive heat transfer has been investigated for the ground-atmosphere system of the planet Mars. The basic goal was the quantitative determination of time dependent vertical distributions of temperature and static stability for Southern-Hemispheric summer season and middle and polar latitudes, for both dust-free and dust-laden atmospheric conditions. The numerical algorithm which models at high spatial and temporal resolution the thermal energy transports in the dual ground-atmosphere system, is based on solution of the applicable heating rate equation, including radiative and molecular-conductive heat transport terms. The two subsystems are coupled by an internal thermal boundary condition applied at the ground-atmosphere interface level. Initial data and input parameters are based on Mariner 4, 6, 7, and 9 measurements and the JPL Mars Scientific Model. Numerical experiments were run for dust-free and dust-laden conditions in the midlatitudes, as well as ice-free and ice-covered polar regions. Representative results and their interpretation are presented. Finally, the theoretical framework of the generalized problem with nonconservative Mie scattering and explicit thermal-convective heat transfer is formulated, and applicable solution algorithms are outlined.

Pallmann, A. J.↗

Keeping the Deal

On the 4th of July 1997, I lay on a blanket with my family at a fireworks display near our home in Los Angeles, California. The pyrotechnics, they tell me, were dazzling. I wouldn't know. My attention was fixed on a tiny orange dot in the sky - Mars. A month earlier, NASA had released an Announcement of Opportunity for a supplementary payload on the Mars Surveyor Lander mission scheduled for launch in 2001. The Human Exploration and Development of Space (HEDS) organization had been authorized to make the most preliminary of investigations into the feasibility of sending humans to Mars. Among the requested investigations was an opportunity to study the dust and soil of the Red Planet, emphasizing possible hazards to human explorers. I spent that summer of '97 working on a proposal for the project I would eventually lead, the Mars Environmental Compatibility Assessment (MECA). MECA was selected in February of '98. We promised to deliver four new instruments by April 2000 with a modest budget of $5M. This is a story about some of the people who created MECA.

Hecht, Michael↗

Wind abrasion on Mars

Aeolian activity was predicted for Mars from earth based observations of changing surface patterns that were interpreted as dust storms. Mariner 9 images showed conclusive evidence for aeolian processes in the form of active dust storms and various aeolian landforms including dunes and yardangs. Windspeeds to initiate particle movement are an order of magnitude higher on Mars than on Earth because of the low atmospheric density on Mars. In order to determine rates of abrasion by wind blown particles, knowledge of three factors is required: (1) particle parameters such as numbers and velocities of windblown grains as functions of windspeeds at various heights above the surface; (2) the susceptibility to abrasion of various rocks and minerals; and (3) wind frequencies and speeds. For estimates appropriate to Mars, data for the first two parameters can be determined through lab and wind tunnel tests; data for the last two factors are available directly from the Viking Lander meteorology experiments for the two landing sites.

Greeley, Ronald↗

Everyone Wins: A Mars-Impact Origin for Carbonaceous Phobos and Deimos

Discussions of Phobos' and Deimos' origin(s) tend to feature an orthogonally opposed pair of observations: dynamical studies which favor coalescence of the moons from an orbital debris ring arising from a large impact on Mars; and reflectance spectroscopy of the moons that indicate a carbonaceous composition that is not consistent with Martian surface materials. One way to reconcile this discrepancy is to consider the option of a Mars-impact origin for Phobos and Deimos, followed by surficial decoration of carbon-rich materials by interplanetary dust particles (IDP). The moons experience a high IDP flux because of their location in Mars' gravity well. Calculations show that accreted carbon is sufficient to produce a surface with reflectance spectra resembling carbonaceous chondrites.

Fries, M.↗

Numerical Predictions of Dust-Induced Heat Flux Augmentation in Hypersonic Blunt-Body Flows Using a Discontinuous Galerkin Multiphase Flow Solver

Recent interest in human-scale missions to Mars has motivated the need for high-fidelity simulations of reentry flows. During a dust storm, there can be high levels of suspended dust in the Martian atmosphere, which cannot only enhance erosion of thermal protection systems but also transfer energy and momentum to the shock layer, thereby significantly augmenting the surface heat flux. Second-order finite-volume schemes are typically employed for hypersonic flow simulations, but such schemes suffer from a number of disadvantages. An attractive alternative is discontinuous Galerkin methods, which benefit from arbitrarily high spatial order of accuracy, geometric flexibility, and other properties. To enable accurate computations of high-speed particle-laden flows, an Euler-Lagrange methodology was developed in which the Eulerian field of the carrier gas is calculated using a discontinuous Galerkin scheme while the disperse phase is treated with Lagrangian particle tracking. We discuss challenges associated with coupling these two formulations and how to handle them. Momentum and energy transfer between the carrier gas and the particle phase is considered, and the importance of accounting for interparticle collisions is assessed. In addition, we describe the physical model of the particle phase and examine effects of its uncertainties on the numerical solution. We demonstrate the performance of the Euler-Lagrange method in representative testcases, with focus on the accurate prediction of particle trajectories and heating augmentation. Quantitative comparisons with experiments are provided.

Ching, Eric J.↗

A Crew and Logistics Lander for the Common Habitat Architecture

The Common Habitat Architecture is a conceptual study that explores the use of a large habitat derived from the Space Launch System (SLS) liquid oxygen tank as a core habitation element that can be used for crew missions or training in 0g, 1/6g, 3/8g, and 1g. This is not part of current NASA Artemis mission planning, but instead represents an architecture that could potentially follow after the Artemis missions and initial human Mars landings. This architecture leverages Starship-derived vehicles for crew landing on and ascent from the Moon and Mars in support of long-duration surface missions with pressurized crew transfer baselined as a nominal capability. This is not the Human Landing System variant of Starship but represents a number of modifications to enable long-duration surface missions with an eight-person crew size. A rapid brainstorming study was conducted in February of 2021, using only public data, to identify options to deliver the 90-ton Common Habitat to the surface and emplace it at the intended habitation site. This study compared three lunar lander concepts and three Mars lander concepts before ultimately selecting the SpaceX Starship as the most viable lander. The Common Habitat Architecture assumes that this Starship variant can further be modified for crew and cargo delivery, assuming that the use of a common system will lead to cost benefits. It is assumed that the Starship will expend too much propellant in landing crew and logistics to be able to launch, given the assumed absence of surface propellant production. Consequently, a separable ascent stage is used for crew ascent. The pressurized elements of this modified Starship are discussed: Starship Ascent Module, Airlock, Transfer Tunnel, Pressurized Crew Transfer Module, and Logistics Modules. For each element, a description, dimensions, rough mass estimates, core capabilities, and design features are presented. Key mechanisms and internal structures of the starship are also discussed. This will include flame diverters for the ascend module, the orbital docking hatch, Pressurized Crew Transfer Module Garage door, Starship Ascent Module fairing, flame diverter blow-out panels, Pressurized Crew Transfer Module lift system, logistics module lift system, contingency crew ascent via the logistics module lift system, internal catwalks, and structural interfaces. Concept of Operations will be discussed for both Moon and Mars. This will include in-space crew rendezvous and transfer, crewed landing, shirtsleeve crew transfer, crew departure, contingency surface operations, and final element disposition. Key differences for Mars will be discussed, such as the Martian atmosphere, dust storms, the absence of crew handover, and Deep Space Exploration Vehicle rendezvous. Contingency microgravity maintenance access will also be discussed. This work will demonstrate viable pressurized crew transfer with a Starship-based lander architecture. Forward work includes Garage lighting and camera systems, Starship Ascent Module propulsion system and docking port trades, contingency habitation trades, and mass/power equipment estimation. Finally, forward work includes developing a heavy cargo return system derived from the Crew and Logistics Starship. The goal of this system is the return of at least 10,000 kg payloads from the surfaces of the Moon and Mars.

Lunar Lander↗

Jet Propulsion Laboratory: Annual Report 2003

If you stepped outdoors on the final evening of 2003 and looked up into the night sky, many celestial events were taking place. A hundred million miles away from Earth, a dust storm swirled across the terracotta peaks and gullies of Mars, as two six-wheeled robots bore down on the planet. They were soon to join two orbital sentries already stationed there. A few hops across the inner solar system, another spacecraft was closing in on a ball of ice and rock spewing forth a hailstorm of dust grains, heated as it swung in toward the Sun. Closer in, two newly lofted space telescopes scanned the skies, their mirrors gathering photons that had crossed the empty vastness of space for billions of years, recording ancient events in unimaginably distant galaxies. And streaking overhead every few minutes directly above our home planet, a handful of satellites was recording the unfolding events of a tropical cyclone off the east coast of Africa and a blizzard that carpeted the northwestern United States. As 2003 drew to a close, the Jet Propulsion Laboratory was on the cusp of an extraordinarily busy period, a time when JPL will execute more fly-bys, landings, sample returns and other milestones than at any other time in its history. The exploration we undertake is important for its own sake. And it serves other purposes, none more important than inspiring the next generation of explorers. If the United States wishes to retain its status as a world leader, it must maintain the technological edge of its workforce. What we do here is the stuff of dreams that will inspire a new generation to continue the American legacy of exploration.

Jet Propulsion Laboratory (JPL)↗

Mid-infrared spectroscopy of Pahala ash palagonite and implications for remote sensing studies of Mars

The mid-IR (7-20 micron range) spectral properties of Pahala ash palagonite and the effect of thin dustings of the palagonite on reflectance characteristics of quartzite and basalt were investigated. Unlike the reflectance of quartzite and basalt, the reflectance of the palagonite is flat and low (1-2 percent). It was found that a dusting of 1-20 micron palagonite particles and 20-250 micron particle clumps, covering 50 percent of the quartzite of the basalt host reduced the quartizite mid-IR reflectance by about 50 percent. The reflectance of the underlying rock was found to be linearly related to the exposed surface area even for extremely small amounts of palagonite (2-100 micron thickness, averaging 5 microns), indicating that mid-IR remote sensing of rocks on Mars will be practical only for dust-free areas.

Crisp, Joy↗

Real-Time Detection of Dust Devils from Pressure Readings

A method for real-time detection of dust devils at a given location is based on identifying the abrupt, temporary decreases in atmospheric pressure that are characteristic of dust devils as they travel through that location. The method was conceived for use in a study of dust devils on the Martian surface, where bandwidth limitations encourage the transmission of only those blocks of data that are most likely to contain information about features of interest, such as dust devils. The method, which is a form of intelligent data compression, could readily be adapted to use for the same purpose in scientific investigation of dust devils on Earth. In this method, the readings of an atmospheric- pressure sensor are repeatedly digitized, recorded, and processed by an algorithm that looks for extreme deviations from a continually updated model of the current pressure environment. The question in formulating the algorithm is how to model current normal observations and what minimum magnitude deviation can be considered sufficiently anomalous as to indicate the presence of a dust devil. There is no single, simple answer to this question: any answer necessarily entails a compromise between false detections and misses. For the original Mars application, the answer was sought through analysis of sliding time windows of digitized pressure readings. Windows of 5-, 10-, and 15-minute durations were considered. The windows were advanced in increments of 30 seconds. Increments of other sizes can also be used, but computational cost increases as the increment decreases and analysis is performed more frequently. Pressure models were defined using a polynomial fit to the data within the windows. For example, the figure depicts pressure readings from a 10-minute window wherein the model was defined by a third-degree polynomial fit to the readings and dust devils were identified as negative deviations larger than both 3 standard deviations (from the mean) and 0.05 mbar in magnitude. An algorithm embodying the detection scheme of this example was found to yield a miss rate of just 8 percent and a false-detection rate of 57 percent when evaluated on historical pressure-sensor data collected by the Mars Pathfinder lander. Since dust devils occur infrequently over the course of a mission, prioritizing observations that contain successful detections could greatly conserve bandwidth allocated to a given mission. This technique can be used on future Mars landers and rovers, such as Mars Phoenix and the Mars Science Laboratory.

Wagstaff, Kiri↗

Martian Global Surface Mineralogy from the Thermal Emission Spectrometer: Surface Emissivity, Mineral Map, and Spectral Endmember Data Products

One of the primary goals of the Thermal Emission Spectrometer experiment on the Mars Global Surveyor is to determine the mineralogy of the Martian surface. This information has been used to place constraints on the range of igneous processes present. The extent of water related processes on Mars has been significantly constrained by the TES experiment. The mineralogy of the Martian dust has also been refined using TES data. These mineralogical results have made a significant contribution towards determining the development of Mars, complimenting other datasets and existing information. Mineralogical determination requires the isolation of surface emissivity from the measured radiance and a variety of techniques have been developed for this purpose. Additionally, deconvolution techniques have been developed and extensively tested to separate the individual mineral contributions to the surface emissivity. These methods and techniques have produced a variety of data products that are currently available through http://tes.asu.edu/

J L Bandfield↗

Meteorites on Mars

Four types of meteoritic material should be found on Mars: (1) micrometeorites, many of which will survive atmospheric entry unmelted, which should fall relatively uniformly over the planet's surface, (2) ablation products from larger meteorites which ablate, break up and burn up in the Mars atmosphere, (3) debris from large, crater forming objects, which, by analogy to terrestrial and lunar impact events, will be concentrated in the crater ejecta blankets (except for rare, large events, such as the proposed C-T event on earth, which can distribute debris on a planetary scale), and (4) debris from the early, intense bombardment, which, in many areas of the planet, may now be incorporated into rocks by geologic processes subsequent to the intense bombardment era. To estimate the extent of meteoritic addition to indigenous Martian material, the meteoritic flux on Mars must be known. It is estimated that the overall flux is twice that for the Moon and 1.33 that for Earth. For small particles, whose orbital evolution is dominated by Poynting Robertson drag, the flux at Mars can be estimated from the Earth flux. The smaller Martian gravitational enhancement as well as the decrease in the spatial density of interplanetary dust with increasing heliocentric distance should reduce the flux of small particles at Mars to about 0.33 times the flux at Earth. Because of the smaller planetary cross-section the total infalling mass at Mars is then estimated to be 0.09 time the infalling mass in the micrometeorite size range at Earth.

Flynn, G. J.↗

Infrared spectroscopy experiment on Mariner 9: Preliminary results

The Mariner 9 infrared spectroscopy experiment has provided good quality spectra of many areas of Mars, predominantly in the Southern Hemisphere. Large portions of the thermal emission spectra are significantly affected by dust with a silicon oxide content approximately corresponding to that of an intermediate igneous rock, implying that Mars has undergone a substantial geochemical differentiation. Derived temperature profiles indicate a warm daytime upper atmosphere with a strong warming over the south polar cap. Atmospheric water vapor is clearly observed over the south polar area and less strongly over other regions.

Hanel, R. A.↗

Factors governing water condensation in the Martian atmosphere

Modeling results are presented suggesting a diurnal condensation cycle at high altitudes at some seasons and latitudes. In a previous paper, the use of atmospheric optical depth measurements at the Viking lander site to show diurnal variability of water condensation at different seasons of the Mars year was described. Factors influencing the amount of condensation include latitude, season, atmospheric dust content and water vapor content at the observation site. A one-dimensional radiative-convective model is used herein based on the diabatic heating routines under development for the Mars General Circulation Model. The model predicts atmospheric temperature profiles at any latitude, season, time of day and dust load. From these profiles and an estimate of the water vapor, one can estimate the maximum occurring at an early morning hour (AM) and the minimum in the late afternoon (PM). Measured variations in the atmospheric optical density between AM and PM measurements were interpreted as differences in AM and PM condensation.

Colburn, David S.↗

Physical properties of Oxia/Lunae Planum and Arabia-type units in the central equatorial region of Mars

Classification and mapping of surficial units in the central equatorial region of Mars Consortium data identified the relatively dark but 'red' materials that cover Lunae Planum and surround the Meridiani materials of Oxia Palus inertia region of Arabia. Oxia Province consists of the regions dominated by the characteristically dark 'red' Oxia materials, but it includes darker streaks and splotches of relatively 'blue' Meridiani materials and brighter 'red' deposits of dust belonging to Eos Province (the bright 'red' border between Oxia and regional Meridiani deposits to the south) and Xanthe Province (the moderately bright 'red' dust deposits in western Chryse Planitia and its vicinity, including the VL-1 landing site). Two Oxia units were recognized: a darker unit present on Lunae Planum and east of Oxia Palus that have intermediate to high inertias. Oxia Province surrounds the extremely low thermal inertia Arabia Province in the east part of the study area, and occurs as isolated patches within Arabia (often including splotches of Meridiani materials within the Oxia patches). Arabia Province's materials have been widely interpreted as unconsolidated dust deposits which are currently forming at this stage of Mars' precessional climate cycle, although the persistence of stable, moderately strong albedo contracts among Arabia materials has not been addressed in those models. A systematic interpretation of Oxia and Arabia Province materials based on currently available remote sensing data is given.

Strickland, Edwin L., III↗

Drill/borescope System for the Mars Polar Pathfinder

The primary goals of the Mars Polar Pathfinder (MPP) Discovery Mission are to characterize the composition and structure of Mars' north polar ice cap, and to determine whether a climate record may be preserved in layers of ice and dust. The MPP would land as close as possible to the geographic north pole of Mars and use a set of instruments similar to those used by glaciologists to study polar ice caps on Earth: a radar sounder, a drill/borescope system, and a thermal probe. The drill/borescope system will drill approximately 50 cm into the surface and image the sides of the hole at 10 micron resolution for compositional and stratigraphic analysis. Several uncertainties have guided the development of this instrument, and they are discussed.

Paige, D. A.↗