Mars Science Laboratory Research Articles

Sub‐Diurnal Methane Variations on Mars Driven by Barometric Pumping and Planetary Boundary Layer Evolution

AbstractIn recent years, the Tunable Laser Spectrometer within the Sample Analysis at Mars (TLS‐SAM) instrument on board the Mars Science Laboratory (MSL) Curiosity rover has detected methane variations in the atmosphere at Gale crater. Methane concentrations appear to fluctuate seasonally as well as sub‐diurnally, which is difficult to reconcile with an as‐yet‐unknown transport mechanism delivering the gas from underground to the atmosphere. To potentially explain the fluctuations, we consider barometrically induced transport of methane from an underground source to the surface, modulated by temperature‐dependent adsorption. The subsurface fractured‐rock seepage model is coupled to a simplified 1‐D atmospheric mixing model to provide insights on the pattern of atmospheric methane concentrations in response to transient surface methane emissions, as well as to predict sub‐diurnal variation in methane abundance for the northern summer period, which is a candidate time frame for a MSL Curiosity sampling campaign. Our analysis suggests that there is a lower limit to the subsurface fracture density that can produce the observed methane patterns, below which the atmospheric methane variations would be out of phase with the observations. The best‐performing model scenarios indicate a significant, short‐lived methane pulse just prior to sunrise, the detection of which by TLS‐SAM would be a potential indicator of the contribution of barometric pumping to Mars' atmospheric methane variations.

ARAMIS: a Martian radiative environment model built from GEANT4 simulations

A new model of the Martian surface radiative environment has been built: Atmospheric RAdiation Model for Ionizing spectra on martian Surface (ARAMIS). Based on Monte Carlo calculations, it offers high computational flexibility for surface flux spectra with several GEANT4 physics lists tested for different exposures and mission scenarios. ARAMIS performs Monte Carlo simulations independently of any exposure scenario to determine a surface response function that can then be convolved to any input spectrum, avoiding simulation repetition while maintaining results accuracy, using a parametric atmosphere geometry. In particular, the adopted approach enables secondary spectra to be discriminated by type and origin, in order to observe the impact of different primary flux components on the surface dose calculation. The ARAMIS model has been validated with experimental measurements from the RAD (Radiation Assessment Detector) instrument on board the Mars Science Laboratory (MSL) Curiosity rover, and benchmarked against other models in the literature. Built using version 11.1.0 of the GEometry ANd Tracking (GEANT4) toolbox and established models of Galactic Cosmic Ray (GCR) or Solar Particle Event (SEP) spectra, the surface neutron and photon spectra provided by ARAMIS show a better agreement than other models with high-energy experimental data, reducing model uncertainty for radiation protection calculations.

Pressure Deficit in Gale Crater and a Larger Northern Polar Cap After the MY34 Global Dust Storm

AbstractWe describe the model‐independent analysis technique of Mars Science Laboratory (MSL) pressure and Mars Climate Sounder (MCS) data in de la Torre Juárez et al. (2019, https://doi.org/10.22541/essoar.169945479.90436599/v1) that compared multiple years of surface pressures on Gale before, during, and after the Global Dust Storm of Mars Year 34. The analysis found (a) representative pressure scale heights over Gale; (b) that the storm was followed by a pressure deficit at Gale; (c) the following C storms did not eliminate the deficit; (d) changes in the duration of the polar caps condensation seasons, with an early start of the North Polar (NP) ice cap growing season the year before the Great Dust Storm (GDS) and a late signature of the end of the expansion season thereafter, changes consistent with a larger growth phase of the NP cap; (e) MCS observed a larger than usual NP cap; and (f) cold temperature anomalies over the NP and warm over the Southern Pole after the storm. We also show that the analysis of observed MSL pressure data alone filters out effects on the pressure signal that are attributable to dynamical and orographic processes in a recent model analysis that makes similar interpretations as our 2019 study. One additional Mars year of observations is included to eliminate early concerns about sensor drifts. Noting that a similar NP anomaly was observed with MCS data after the last early GDS in MY25, and not the later GDS of MY27, the results suggest a possible unique effect of early GDSs.

Evolution of a Lake Margin Recorded in the Sutton Island Member of the Murray Formation, Gale Crater, Mars

AbstractThis study uses data from the Mars Science Laboratory Curiosity rover to document the facies of the Sutton Island member of the Murray formation, interpret paleoenvironments, and establish key stratigraphic transitions at Gale crater. Two facies associations were identified: Facies Association 1 (FA1) and Facies Association 2 (FA2). Individual facies in FA1 include planar‐laminated mudstone with minor intervals of planar sandstone, ripple cross‐laminated sandstone, cross‐stratified sandstone, and alternating laminated sandstone and mudstone. Meter‐thick packages of planar‐laminated mudstone in FA1 are interpreted to represent deposition in low‐energy ponded environments along the lake margin. Straight‐ and curve‐crested ripple cross‐laminated facies are interpreted to represent current‐influenced deposition. Cross‐stratified sandstone facies consist of dm‐thick sets that represent deposition in distal channels. Intercalated mm‐scale mudstone and sandstone laminae represent waning flow conditions and possible channel abandonment. Facies in FA1 collectively represent deposition in a distal delta plain. FA2 is comprised of planar‐laminated mudstone with minor sandstone and is interpreted to represent deposition in a lacustrine‐basin setting by suspension settling linked to density flows. FA1 transitions upward into FA2, defining a rapid transgression substantial enough to facilitate the deposition of distal lake facies above delta plain facies. The abrupt transition from FA2 back to FA1 deltaic deposits is suggestive of forced regression. Facies in FA1 and FA2 are consistent with the prevalence of aqueous environments recorded in other Murray formation members and extend our understanding of the dynamic sedimentary processes that characterized ancient lacustrine systems at Gale crater.

Aeolian bedrock ridges in Gale crater, Mars

Fields of parallel, regularly-spaced, bedrock ridges observed on Mars and rarely on Earth have been interpreted as aeolian surface features oriented perpendicular to a formative wind. The exact formation process for these ridges, however, including the role of aeolian erosion versus deposition, continues to be debated. We identified forty fields of bedrock ridges on and within the sedimentary strata of Gale crater's central mound, Aeolis Mons. To better constrain the development of these landforms and the winds responsible for their formation, we characterized ridge morphology, orientation, geographic distribution, stratigraphic relationships, and interactions with other aeolian landforms. The study area of Aeolis Mons was chosen to leverage the extensive high-resolution image coverage from orbit, as well as to build upon the detailed stratigraphy compiled from in situ exploration with the Mars Science Laboratory Curiosity rover. Using the orientation of the ridges, we present a wind vector map of Aeolis Mons. The orientation of bedrock ridges in the Mound Skirting Unit, which unconformably drapes Aeolis Mons, suggests the average wind direction in Gale crater may have remained consistent since that unit was emplaced (∼3.8–3.1 Ga). This study explores the implications of these ridges for the history of wind, deposition, and erosion in Gale crater.

Martian Equatorial Atmospheric Tides From Surface Observations

AbstractDiurnal solar radiation causes global oscillations in pressure, temperature, and wind fields, known as atmospheric tides, which are further modified by topography, surface properties, and atmospheric dust loading. Hence, the tides are a combination of sun‐synchronous and non sun‐synchronous tides that propagate around the planet both eastward and westward. In the Martian tropics, atmospheric tides dominate daily pressure variations on the surface. Therefore, surface observing platforms are extremely useful for detailed analysis of atmospheric tides. In this investigation, we analyze diurnal and semi‐diurnal components of atmospheric surface pressure measured by the simultaneously operating InSight and Mars Science Laboratory (MSL) payloads. We utilize observations of the time period from Martian year (MY) 34 solar longitude 296° to MY 36 solar longitude 53°. The diurnal tide average amplitude is 17 Pa with an average phase of 03:39 local true solar time (LTST), while the semi‐diurnal tide average amplitude and phase are 7 Pa and 09:34 LTST for the InSight. The corresponding values for the MSL are 33 Pa with 04:25 LTST for the diurnal and 10 Pa with 09:36 LTST for the semi‐diurnal component. Thermo‐topographic lateral hydrostatic adjustment flow generated by topography causes the higher diurnal amplitude observed by MSL. Both platforms observe a similar response between these harmonic components and dust loading. Furthermore, amplitudes obtained from a Mars Climate Database mimic the observations well. Our study provides for the first time a comparison of atmospheric tides at two simultaneously observing tropical surface platforms for more than 1 MY.

Dust Lifting Observations With the Mars Science Laboratory Navigation Cameras

AbstractMartian dust lifting is believed to occur through two primary mechanisms: dust devils and wind stress forced dust lifting. Gale Crater's varied terrain and meteorology provide a unique in situ perspective on Martian dust lifting, with the Mars Science Laboratory Curiosity rover passing through both conditions and locations detrimental to dust lifting (e.g., the crater floor) and those with active sand motion and frequent dust lifting (e.g., the Bagnold Dunes). Between Ls = 248° in Mars Year 33 and Ls = 51° in Mars Year 37, over ∼3.5 Mars years and 2,300 sols, the rover's Navigation Cameras took 1,260 dedicated image sequences to search for dust lifting. Approximately 42.7% of all sequences, and 9.5% of the total images have shown active dust lifting, both dust devils and linear/straight‐line wind stress dust lifting. 79% of dust lifting events are classified as dust devils, while ∼16% are linear wind stress dust lifting and the remainder are of an indeterminate type. We analyze this large catalog of dust lifting events to provide ground truth on theoretical and model expectations of dust lifting and show that dust lifting in Gale Crater occurs throughout the Martian year, is strongly peaked in frequency near solar noon (even after accounting for observational biases), and that dust lifting shows an affinity for sand‐covered surfaces which highlights the importance of saltating sand grains for Martian dust lifting in both dust devils and wind stress forced lifting.

The Mars Science Laboratory record of optical depth measurements via solar imaging

The Mars Science Laboratory Curiosity rover has monitored the Martian environment in Gale crater since landing in 2012. This study reports the record of optical depth derived from visible and near-infrared images of the Sun. Aerosol optical depth, which is mostly due to dust but also includes ice, dominates the record, with gas optical depth too small to measure. The optical depth record includes the effects of regional dust storms and one planet-encircling dust event, showing the expected peaks during southern spring and summer and relatively lower and more stable optical depth in fall and winter. The measurements show that there is a seasonally varying diurnal change in dust load, with the optical depth peaking in the morning during southern spring and summer, correlated with thermotidal pressure changes. However, there was no systematic diurnal change during autumn and winter, except after one regional storm. There were indications that the dust was relatively enhanced at high altitudes during high-optical-depth periods and that high-altitude ice was significant during winter. The observations did not provide much information about particle size or composition, but they were consistent with a smaller particle size after aphelion (in southern winter). No scattering halos were seen in associated sky images, even when there was visual evidence of ice hazes or clouds, which suggests small or amorphous ice particles. Unexpectedly, the measurement campaign revealed that the cameras collected saltating sand in their sunshades 1.97 m above the surface. As a result, the measurement strategy had to be adjusted to avoid high-elevation imaging to avoid sand covering the optics.

Mechanical properties of terrestrial analogs to calcium sulfate veins on Gale crater, Mars

The MSL (Mars Science Lab) Curiosity rover has documented the presence of natural fractures at the Gale crater on Mars. Through the utilization of the ChemCam instrument, the chemical composition of the veins on Mars has been analyzed, revealing their mineralogy as calcium sulfate. However, there is limited knowledge regarding the mechanical properties of these veins, which hinders a deeper understanding of their origin. This work aims to characterize the mechanical properties of gypsiferous Triassic Moenkopi mudrocks as the terrestrial rock analog to Mars. The Digital Image Correlation (DIC) technique was used in tandem with the Indirect Tensile Strength test to acquire the required spatial full-field strain maps for characterizing the fracture propagation with complex geometries in addition to the derived mechanical properties. The effect of the primary vein orientation on the exerted load on the load-strain profile, fracture initiation and propagation, and tensile strength was established. The dynamic spatial horizontal, vertical, and shear strains' progression was distinguished through DIC imaging. The key findings include: (1) Different failure modes were observed in samples with and without calcium sulfate veins, with higher tensile strength perpendicular to lamination; (2) Most samples with veins exhibited reduced tensile strength, except when oriented 90° to the load; (3) Fracture paths were influenced by the orientation angle, with irregular paths at certain angles and more regular paths for centrally located veins; (4) Digital image correlation revealed a fracture process zone before macro-crack initiation and subsequent shear crack propagation; (5) Shear strain accumulation preceded shear crack propagation, with potential initiation of tensile cracks.

A decade of quantitative mineralogy on Mars: results from the CheMin X-ray diffractometer on the Mars Science Laboratory rover Curiosity

A decade of quantitative mineralogy on Mars: results from the CheMin X-ray diffractometer on the Mars Science Laboratory rover Curiosity

Unfolding the Neutron Flux Spectrum on the Surface of Mars Using the MSL‐RAD and Odyssey‐HEND Data

AbstractUnderstanding the long‐term radiation environment at the surface of Mars allows us to estimate the exposure for future robotic and crewed missions. Typically, the radiation environment includes charged particles (i.e., protons and heavier ions) and neutral particles (i.e., gamma rays and secondary neutrons). Previous studies used in‐situ measurements, models, or both to determine the characteristics of the radiation at Mars. For example, the Mars Science Laboratory instrument, the Radiation Assessment Detector (RAD), has provided invaluable in‐situ data since landing in 2012. However, the RAD instrument is only sensitive to neutrons with energies > ∼6 MeV and therefore misses what is expected to be a substantial flux of lower‐energy neutrons. To address this gap, we have developed an approach to derive the surface neutron spectrum using the MSL RAD data augmented by orbital data from the High Energy Neutron Detector (HEND) onboard Mars Odyssey (neutron energy < ∼10 MeV). Using a power law fit, we determine neutron flux spectra that reproduce the measurements recorded by both RAD and HEND. Our approach involves a series of Monte Carlo simulations to develop a set of atmospheric transmission functions that enables us to convert the on‐orbit HEND data to their corresponding surface neutron flux spectra. The combined RAD—HEND data present a unique opportunity to obtain a complete picture of the surface neutron environment.

Effectiveness of radiation shields constructed from Martian regolith and different polymers for human habitat on Mars using MULASSIS/GEANT4 and OLTARIS

Mars exploration and the possibility of future Martian colonization have generated much interest in recent years. However, several problems make long-term permanence on Mars challenging, one of which is the radiation environment of the red planet. To ensure long-term durability on the Mars surface against the deleterious effects due to radiation, effective radiation shields are compulsory. This paper presents the effectiveness of radiation shields made of Martian regolith and light, hydrogenous polymers to protect astronauts on the Martian surface. Monte Carlo simulations were performed using a Geant4-based tool, Multi-layered shielding simulation software. The shielding properties were studied using low energy charged particle spectra from Mars Science Laboratory–Radiation Assessment Detector and particles (proton, alpha, and iron ions) with energies of 1 GeV/n. On-Line Tool for the Assessment of Radiation in Space (OLTARIS) is used for calculating the effective dose equivalent for the galactic cosmic ray spectra on the Mars surface. Martian regolith with Lithium Hydride (LiH) demonstrated greater efficiency in dose reduction. Based on the OLTARIS study, at 15 g/cm2 (10 g/cm2 Martian regolith with 5 g/cm2 chosen materials), these shields are even better than an aluminum shield of the same dimension.

A Study on Rocker-Bogie Mechanism for a Planetary Rover Prototype

Abstract: In light of the notable rocker-bogie mechanism, this paper shows an ideal plan of a rocker-bogie suspension framework so as to ensure high mobile steadiness as well as excellent versatility of a prototype rover vehicle while traversing through rough terrains. It is essentially a suspension arrangement utilized in mechanical automated vehicles utilized explicitly for space investigation. The rocker-bogie suspension-based rovers have been effectively presented for the Mars Pathfinder and Mars Exploration Rover (MER) and Mars Science Laboratory (MSL) missions led by zenith space investigation laboratories all through the world. The proposed suspension framework is presently the most supported structure for each space investigation organization. It is basically a mechanism which comprises of two arms with wheel mounted to each and the two arms are associated through a versatile joint. The current development in design has been studied as well as a different approach towards designing the basic structure of suspension has been done. It has been further verified using various static and dynamic load calculations, solid modeling computer aided design software and simulation software for analysis and testing

Sensitive and accurate determination of nitrogen in simulated Martian soil and environment with LIBS spectrum fusion and regression based on neural network

Nitrogen is a key element necessary for the emergence and development of life. It is one of the elements targeted by the landed missions on Mars in accordance with their scientific goal of investigation of habitability and search for traces of life. A gas chromatography mass spectrometer (GCMS) instrument on board the Mars Science Laboratory Curiosity rover has revealed the existence of oxidized nitrogen-bearing compounds on Martian surface with an equivalent nitrogen concentration up to 0.01 wt%. Although the detection with laser-induced breakdown spectroscopy (LIBS) also on board the Curiosity rover is desirable, the current performance of LIBS for nitrogen analysis does not show the capacity in terms of limit of detection (LOD) and accuracy. Research on a suitable method should therefore be first engaged in laboratory in order to guide further improvements of LIBS instrument on board Mars rover, as well as the data treatment method. Beyond the sensitivity issue, matrix effect also affects LIBS determination of nitrogen, especially due to its various chemical speciation in geological materials. Method research should answer thus double requirements of improving the sensitivity and reinforcing the robustness with respect to different nitrogen-bearing compounds. An experimental configuration of double detections with a narrow bandwidth Czerny-Tuner (CT) spectrometer and a broad bandwidth Echelle spectrometer, was implemented in this work, in such way that the first ensured a sensitive detection of emission lines from nitrogen and the second complemented with those from major elements in the sample. The fusion of the simultaneously acquired spectra took into account the emission characteristics of the both two types of elements, necessary for an effective and robust multivariate regression based on a neural network. In addition, for a better treatment of different chemical speciation of nitrogen in samples, generalized spectrum was used for training of regression models, after an unsupervised clustering having assigned a type label to each training spectrum. The trained model was tested by collections of independent test samples, resulting in a limit of detection (LOD) of 0.18 wt%, and a root mean square error of prediction (RMSEP) of 0.041 wt%, representing a step forward to nitrogen detection using LIBS on Mars.

Jack Dwayne Farmer April 18, 1947-February 22, 2023.

Jack Dwayne Farmer April 18, 1947-February 22, 2023.

Determination of Spatial Scale in Martian Landscape Images Acquired by the Curiosity Rover, and Viewing Image Scale and Target Chemistry Using the ASIC Website

AbstractIn this paper we describe a method to compute spatial scales for images acquired by NASA's Mars Curiosity rover (Mars Science Laboratory, MSL). The method is based on the assumption that the rover stands on an infinite plane that may have any orientation with respect to the local gravity vector. While not new, it is the first time that this method is systematically applied to Martian images acquired by a lander. A continuously run software pipeline processes the images acquired by the rover within a 20 m radius, adds approximate scalebars to the raw images, and generates, whenever possible, rectified (warped) versions of those images. The products of this software pipeline and the chemical compositions of relevant rover science targets from NASA's Planetary Data System archive, are made available to the public via the Approximate Scale for Images and Chemistry website, which has been developed in collaboration with the Planetary Data System Analyst's Notebook for the MSL mission. Hyperlinks connect the two resources.

Boron adsorption in clay minerals: Implications for martian groundwater chemistry and boron on Mars

Boron has been detected on Mars in calcium-sulfate veins found within clay mineral rich rocks on Mars by the Mars Science Laboratory (MSL) Curiosity rover using Laser Induced Breakdown Spectroscopy (LIBS) analysis. Borates play a vital role in stabilizing ribose on Earth and has been suggested as a key requirement for life. Borate ions readily adsorb to phyllosilicate clay minerals. The discovery of boron on Mars in proximity to phyllosilicate-bearing bedrock may have strong implications for potential past prebiotic conditions on Mars. In this study we generated a suite of clay minerals with adsorbed borate, including both typical terrestrial clay minerals (montmorillonite) and Mars-analog clay minerals (nontronite, saponite, griffithite), to understand controls on borate adsorption and to analyze with LIBS to compare with MSL data. Clay minerals were subjected to mineralogical and chemical analysis before and after adsorption. Adsorption analysis revealed that the Mars analog clay minerals adsorbed less boron than terrestrial counterparts, but within comparable amounts to those detected on Mars and in meteorites. Post-adsorption analysis by X-ray diffraction (XRD) revealed slight changes in the interlayer spacing of many of the clay minerals. Based on the adsorption analysis of the Mars-analog clay minerals, phyllosilicate-bearing bedrock in Gale crater may contain up to 90-110 ppm B. A series of borate-enriched samples were created for analysis of LIBS spectra from ChemCam on the Curiosity rover and SuperCam on the Perseverance Rover. The results of this study may provide insight into martian groundwater geochemistry processes and the mobility of a key molecule connected with life.

Space radiation quality factor for Galactic Cosmic Rays and typical space mission scenarios using a microdosimetric approach

Space radiation exposure from omnipresent Galactic Cosmic Rays (GCRs) in interplanetary space poses a serious carcinogenic risk to astronauts due to the—limited or absent—protective effect of the Earth’s magnetosphere and, in particular, the terrestrial atmosphere. The radiation risk is directly influenced by the quality of the radiation, i.e., its pattern of energy deposition at the micron/DNA scale. For stochastic biological effects, radiation quality is described by the quality factor, Q, which can be defined as a function of Linear Energy Transfer (LET) or the microdosimetric lineal energy (y). In the present work, the average Q of GCR for different mission scenarios was calculated using a modified version of the microdosimetric Theory of Dual Radiation Action (TDRA). NASA’s OLTARIS platform was utilized to generate the radiation environment behind different aluminum shielding (0–30 g/cm2) for a typical mission scenario in low-earth orbit (LEO) and in deep space. The microdosimetric lineal energy spectra of ions (Zge 1) in 1 μm liquid water spheres were calculated by a generalized analytical model which considers energy-loss fluctuations and δ-ray transport inside the irradiated medium. The present TDRA-based Q-values for the LEO and deep space missions were found to differ by up to 10% and 14% from the corresponding ICRP-based Q-values and up to 3% and 6% from NASA’s Q-model. In addition, they were found to be in good agreement with the Q-values measured in the International Space Station (ISS) and by the Mars Science Laboratory (MSL) Radiation Assessment Detector (RAD) which represent, respectively, a LEO and deep space orbit.

Two-temperature ablative material response model with application to Stardust and MSL atmospheric entries

Ablative material response codes currently in use consider local thermal equilibrium between the solid phases and the pyrolysis gases. For typical entry conditions, this hypothesis may be justified by the fact that the thermal Peclet number within the pores is small, which is a necessary condition for thermal equilibrium in non-reactive materials. However, the validity of this analysis may fall under some circumstances. The thermal Peclet number may become large due to high pyrolysis gas velocities. Additional physical phenomena not accounted for in the Peclet analysis may become non-negligible, such as the change of enthalpy due to chemical reactions. The objective of this study is two-fold. First, a detailed two temperature material response model for porous reactive materials is presented. This model has been implemented and made available in the Porous material Analysis Toolbox based on OpenFOAM (PATO). Second, the model is applied to the Theoretical Ablative Composite for Open Testing (TACOT) in a wide range of conditions to assess the true range of validity of the thermal equilibrium hypothesis. Simulations are carried out on the Stardust and Mars Science Laboratory (MSL) atmospheric entries. The main design variables have been monitored and compared between the two models: temperature evolution and species concentration within the material, pyrolysis gas blowing rate, extension of the pyrolysis zone, and wall recession due to ablation. Results show that under chemical equilibrium conditions, no significant deviation in the monitored quantities are observed, while under chemical non-equilibrium conditions there is a large impact on the species concentration.

The Zenith‐Angle Dependence of the Downward Radiation Dose Rate on the Martian Surface: Modeling Versus MSL/RAD Measurement

AbstractThe Radiation Assessment Detector (RAD) on board the Mars Science Laboratory's Curiosity rover has been monitoring the surface radiation environment on Mars for just over 10 years. It has been found by Wimmer‐Schweingruber et al. (2015, https://doi.org/10.1002/2015gl066664) that within the narrow view cone of RAD, the directionality of the radiation field is close to but not completely isotropic. In order to better understand the directionality of the surface radiation over a wide range of zenith angles (θ), we perform a three‐dimensional Geant4 Monte Carlo simulation to derive the θ‐dependence of the surface dose rate. The results show that galactic cosmic ray protons, coming in at θ ∼ 74° make the greatest contribution to the surface dose. For helium ions, this angle is at around 46°. This is a consequence of the increasing column depth at larger zenith angles and the complex interplay of the destruction of primary and the creation of secondary particles as the primary cosmic ray interacts with the Martian atmosphere. We also compared the simulated results with the RAD measurements and found a reasonable agreement. Our results are important for future human exploration of Mars, for instance, to estimate the effectiveness of radiation shielding of a given geometry or for optimizing the radiation shielding design of a Martian habitat.