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At least 1,639 records · Page 91

A Comparison of Methods Used to Estimate the Height of Sand Dunes on Mars

The collection of morphometric data on small-scale landforms from other planetary bodies is difficult. We assess four methods that can be used to estimate the height of aeolian dunes on Mars. These are (1) stereography, (2) slip face length, (3) profiling photoclinometry, and (4) Mars Orbiter Laser Altimeter (MOLA). Results show that there is good agreement among the methods when conditions are ideal. However, limitations inherent to each method inhibited their accurate application to all sites. Collectively, these techniques provide data on a range of morphometric parameters, some of which were not previously available for dunes on Mars. They include dune height, width, length, surface area, volume, and longitudinal and transverse profiles. Thc utilization of these methods will facilitate a more accurate analysis of aeolian dunes on Mars and enable comparison with dunes on other planetary surfaces.

Bourke, M. C.↗

Definition phase of Grand Tour missions/radio science investigations study for outer planets missions

Scientific instrumentation for satellite communication and radio tracking systems in the outer planet exploration mission is discussed. Mission planning considers observations of planetary and satellite-masses, -atmospheres, -magnetic fields, -surfaces, -gravitational fields, solar wind composition, planetary radio emissions, and tests of general relativity in time delay and ray bending experiments.

Tyler, G. L.↗

Marshall Space Flight Center: Lunar Regolith Terrain (LRT)

Introduction: NASA is moving toward a new age of exploration and resource utilization of the lunar surface. Challenges related to exploration, resource utilization, and construction at the Lunar South Pole will require advanced technology and well-designed mission concepts and operations. NASA Marshall Space Flight Center (MSFC) has added new capabilities to support surface mobility and construction activities to meet industry, academia, and NASA research and development goals for lunar applications. The Lunar Regolith Terrain (LRT) field is a new, large-area, lunar regolith simulant planetary analog testing ground for users interested in surface mobility and lunar construction activities. The LRT complements NASA MSFC’s other lunar environment testing facilities such as the Lunar Surface Simulator (V20 dirty vacuum chamber), the Lunar Environment Testing System (LETS), among many others. Lunar Regolith Terrain (LTR) Description: The Lunar Regolith Terrain field is an outdoor planetary analog environment facility located on base at MSFC. The lunar regolith simulant is JSC-1A feedstock material (volcanic cinder sand sourced from Meriam Crater, Flagstaff, AZ). The field contains more than 500 tons of lunar regolith simulant confined within a 125 ft x 125 ft (38 m x 38 m) area. The field is placed ~ 50% over paved parking lot and ~ 50% over a natural ground. Currently, the depth of regolith ranges between ~ 5 in - ~ 4 ft (~ 13cm – 1.2m) but can be modified to suit user needs. The lunar regolith simulant that makes up the field has representative geotechnical, geochemical, and optical properties of lunar mare basalt. An area within the LRT of lunar highlands terrain simulant is planned. Additional Features of the LRT: The LRT was designed to allow rapid modification of the terrain’s topography obstacles in the field. The terrain can be reshaped to suit specific testing requirements that may require flat expanses, steep hills, or heavily cratered and rocky landscapes. Large rocky obstacles in Fig. 1 are artificial landscape boulders (faux-rocks) that can be easily placed by users or removed entirely. Areas of the field also contain buried fiducials, large sheets, bar stock, and pipes of various composition and dimensions to allow for possible ground penetrating radar and shallow seismic studies. Rapid modification capabilities will also allow for burial of additional user-specific materials to enable in-situ resource utilization detection (e.g., burial of hydrogen sources for neutron detection or other materials). The field is also equipped with on-site office space with an air-conditioned and heated trailer with 120/240V power and lighting. The site has Wi-Fi and Cellular signal coverage. Direct radio frequency communication with the Huntsville Operations Support Center (HOSC) is in development. Additional on-site workspace and secure equipment storage is available in adjacent buildings. Accessibility to the field is straightforward with on-site parking and access for delivery of instruments, payloads, and additional equipment. Community Availability: The LRTF provides an accessible planetary analog surface environment for surface mobility testing, autonomous roving operations, developing advanced navigation techniques and operations development. Interested parties can contact the abstract authors for additional details, tours, and scheduling.

Lunar Regolith↗

Marshall Space Flight Center: Lunar Regolith Terrain (LRT)

Introduction: NASA is moving toward a new age of exploration and resource utilization of the lunar surface. Challenges related to exploration, resource utilization, and construction at the Lunar South Pole will require advanced technology and well-designed mission concepts and operations. NASA Marshall Space Flight Center (MSFC) has added new capabilities to support surface mobility and construction activities to meet industry, academia, and NASA research and development goals for lunar applications. The Lunar Regolith Terrain (LRT) field is a new, large-area, lunar regolith simulant planetary analog testing ground for users interested in surface mobility and lunar construction activities. The LRT complements NASA MSFC’s other lunar environment testing facilities such as the Lunar Surface Simulator (V20 dirty vacuum chamber), the Lunar Environment Testing System (LETS), among many others. Lunar Regolith Terrain (LTR) Description: The Lunar Regolith Terrain field is an outdoor planetary analog environment facility located on base at MSFC. The lunar regolith simulant is JSC-1A feedstock material (volcanic cinder sand sourced from Meriam Crater, Flagstaff, AZ). The field contains more than 500 tons of lunar regolith simulant confined within a 125 ft x 125 ft (38 m x 38 m) area. The field is placed ~ 50% over paved parking lot and ~ 50% over a natural ground. Currently, the depth of regolith ranges between ~ 5 in - ~ 4 ft (~ 13cm – 1.2m) but can be modified to suit user needs. The lunar regolith simulant that makes up the field has representative geotechnical, geochemical, and optical properties of lunar mare basalt. An area within the LRT of lunar highlands terrain simulant is planned. Additional Features of the LRT: The LRT was designed to allow rapid modification of the terrain’s topography obstacles in the field. The terrain can be reshaped to suit specific testing requirements that may require flat expanses, steep hills, or heavily cratered and rocky landscapes. Large rocky obstacles in Fig. 1 are artificial landscape boulders (faux-rocks) that can be easily placed by users or removed entirely. Areas of the field also contain buried fiducials, large sheets, bar stock, and pipes of various composition and dimensions to allow for possible ground penetrating radar and shallow seismic studies. Rapid modification capabilities will also allow for burial of additional user-specific materials to enable in-situ resource utilization detection (e.g., burial of hydrogen sources for neutron detection or other materials). The field is also equipped with on-site office space with an air-conditioned and heated trailer with 120/240V power and lighting. The site has Wi-Fi and Cellular signal coverage. Direct radio frequency communication with the Huntsville Operations Support Center (HOSC) is in development. Additional on-site workspace and secure equipment storage is available in adjacent buildings. Accessibility to the field is straightforward with on-site parking and access for delivery of instruments, payloads, and additional equipment. Community Availability: The LRTF provides an accessible planetary analog surface environment for surface mobility testing, autonomous roving operations, developing advanced navigation techniques and operations development. Interested parties can contact the abstract authors for additional details, tours, and scheduling.

Lunar Regolith↗

Regional Moisture Budget and Land-Atmosphere Coupling Over the U.S. Southern Great Plains Inferred From the ARM Long-Term Observations

Ten–year warm–season (May–August) observations at the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) site are used to examine the large–scale atmospheric moisture budget and the strength of land–atmosphere coupling. Atmospheric moisture budget components, computed from the ARM variational analysis data, are compared between different wet/dry scenarios and convection regimes. Consistent with previous studies, large–scale moisture flux convergence dominates the SGP regional moisture budget on the daily time scale, but surface evaporation does play a more prominent role on late–afternoon deep convection days. Moreover, the relationship between moisture flux convergence and precipitation increases significantly from dry year to wet years. The land–atmosphere coupling strength is quantified for local convective events within the “Local L–A Coupling Process Chain” (Santanello et al., 2018, https://doi.org/10.1175/BAMS–D–17–0001.1). The impact of land surface on the evolution of planetary boundary layer is highly dependent on the vegetation leaf area index. A significantly larger surface sensible heat flux is found over the SGP forest region in midsummer, which is accompanied by a much higher planetary boundary layer development and a large increase in shallow cumulus cloud fraction. Here the significant relationship between afternoon precipitation and surface turbulent flux only exists in the northeast part of the ARM SGP site, which is mainly covered by grassland/pasture.

58 GEOSCIENCES↗

Morpheus: Advancing Technologies for Human Exploration

NASA's Morpheus Project has developed and tested a prototype planetary lander capable of vertical takeoff and landing. Designed to serve as a vertical testbed (VTB) for advanced spacecraft technologies, the vehicle provides a platform for bringing technologies from the laboratory into an integrated flight system at relatively low cost. This allows individual technologies to mature into capabilities that can be incorporated into human exploration missions. The Morpheus vehicle is propelled by a LOX/Methane engine and sized to carry a payload of 1100 lb to the lunar surface. In addition to VTB vehicles, the Project s major elements include ground support systems and an operations facility. Initial testing will demonstrate technologies used to perform autonomous hazard avoidance and precision landing on a lunar or other planetary surface. The Morpheus vehicle successfully performed a set of integrated vehicle test flights including hot-fire and tethered hover tests, leading up to un-tethered free-flights. The initial phase of this development and testing campaign is being conducted on-site at the Johnson Space Center (JSC), with the first fully integrated vehicle firing its engine less than one year after project initiation. Designed, developed, manufactured and operated in-house by engineers at JSC, the Morpheus Project represents an unprecedented departure from recent NASA programs that traditionally require longer, more expensive development lifecycles and testing at remote, dedicated testing facilities. Morpheus testing includes three major types of integrated tests. A hot-fire (HF) is a static vehicle test of the LOX/Methane propulsion system. Tether tests (TT) have the vehicle suspended above the ground using a crane, which allows testing of the propulsion and integrated Guidance, Navigation, and Control (GN&C) in hovering flight without the risk of a vehicle departure or crash. Morpheus free-flights (FF) test the complete Morpheus system without the additional safeguards provided during tether. A variety of free-flight trajectories are planned to incrementally build up to a fully functional Morpheus lander capable of flying planetary landing trajectories. In FY12, these tests will culminate with autonomous flights simulating a 1 km lunar approach trajectory, hazard avoidance maneuvers and precision landing in a prepared hazard field at the Kennedy Space Center (KSC). This paper describes Morpheus integrated testing campaign, infrastructure, and facilities, and the payloads being incorporated on the vehicle. The Project s fast pace, rapid prototyping, frequent testing, and lessons learned depart from traditional engineering development at JSC. The Morpheus team employs lean, agile development with a guiding belief that technologies offer promise, but capabilities offer solutions, achievable without astronomical costs and timelines.

Olansen, Jon B.↗

Combined backscatter Moessbauer spectrometer/x ray fluorescence analyzer (BaMS/XRF) for extraterrestrial surfaces

We have designed and tested a prototype combined backscatter Moessbauer spectrometer and x-ray fluorescence analyzer (BaMS/XRF). A space qualified instrument based on this design would be suitable for in-situ use on planetary missions to the surfaces of the Moon (Artemis and lunar outpost), Mars (MESUR), asteroids, or other solid solar system objects. The BaMS/XRF instrument is designed to be capable of concurrent sample analyses for the mineralogy of iron-bearing phases and elemental composition without the need for sample preparation.

Shelfer, T. D.↗

Asteroid Redirect Robotic Mission: Robotic Boulder Capture Option Overview

The National Aeronautics and Space Administration (NASA) is currently studying an option for the Asteroid Redirect Robotic Mission (ARRM) that would capture a multi-ton boulder (typically 2-4 meters in size) from the surface of a large (is approximately 100+ meter) Near-Earth Asteroid (NEA) and return it to cislunar space for subsequent human and robotic exploration. This alternative mission approach, designated the Robotic Boulder Capture Option (Option B), has been investigated to determine the mission feasibility and identify potential differences from the initial ARRM concept of capturing an entire small NEA (4-10 meters in size), which has been designated the Small Asteroid Capture Option (Option A). Compared to the initial ARRM concept, Option B allows for centimeter-level characterization over an entire large NEA, the certainty of target NEA composition type, the ability to select the boulder that is captured, numerous opportunities for mission enhancements to support science objectives, additional experience operating at a low-gravity planetary body including extended surface contact, and the ability to demonstrate future planetary defense strategies on a hazardous-size NEA. Option B can leverage precursor missions and existing Agency capabilities to help ensure mission success by targeting wellcharacterized asteroids and can accommodate uncertain programmatic schedules by tailoring the return mass.

Mazanek, Daniel D.↗

Online Rapid Analysis of Laser Heterodyne Radiometer (LHR) Data Using the Planetary Spectrum Generator (PSG)

One of the biggest challenges in developing scientific instruments is not just the build and testing of an instrument, but the method for processing the data and producing a consistent, well characterized data product that can be confidently used by the public and scientific community. Raw data products are frequently an array of numbers that are a read-out of voltages. The challenge is to convert these arrays into meaningful information as well as remove noise and interferences. Because this can be a tedious and time-consuming, the goal is to automate the process so that data ca be processed rapidly and be available in real-time for event monitoring. Here we present a rapid analysis method for Laser Heterodyne Radiometer (LHR) data that can be used to analyze data taken from a range of LHR observation modes (column, limb, etc.). This online tool uses the versatile Planetary Spectrum Generator (PSG) and allows LHR users to quickly analyze their own data using a NASA Goddard Space Flight Center (GSFC) monitored capability to ensure quality and reproducibility in the data products. Background: Development of a miniaturized LHR (mini-LHR) as a ground instrument for measuring carbon dioxide (CO 2 ) and methane (CH 4 ) in the atmospheric column started in 2009 with the commercial availability of distributive feedback lasers (DFB) in wavelengths that could measure absorption of gases in the near-IR. As new DFB lasers, detectors and hardware emerged at different wavelengths, additional gases were added to the capability. The mini-LHR was adapted into an occultation-viewing CubeSat with Lawrence Livermore National Laboratory (LLNL) for observing CO 2 , CH 4 , and H 2 O in the limb and was launched in 2019. Other versions of the LHR technology have been designed for observation of water vapor in the lunar exosphere as well as observations of trace gases in planetary atmospheres and plumes from icy moons. The PSG is an online tool developed at GSFC that can be used for synthesizing Earth and planetary spectra (atmospheres and surfaces) over a broad range of wavelengths (0.1 μm to 100 mm) for any observatory, orbiter or lander. Spectra are simulated by combining several state-of-the-art radiative transfer models, spectroscopic databases, planetary databases, as well as modern-era retrospective analysis for research and applications, version 2 (MERRA-2) data set which provides meteorological inputs such as modeled surface pressure for calculating dry-air columns.

Emily Wilson↗

Chemical differentiation of a convecting planetary interior: Consequences for a one-plate planet such as Venus

Chemically depleted mantle forming a buoyant, refractory layer at the top of the mantle can have important implications for the evolution of the interior and surface. On Venus, the large apparent depths of compensation for surface topographic features might be explained if surface topography were supported by variations in the thickness of a 100-200 km thick chemically buoyant mantle layer or by partial melting in the mantle at the base of such a layer. Long volcanic flows seen on the surface may be explained by deep melting that generates low-viscosity MgO-rich magmas. The presence of a shallow refractory mantle layer may also explain the lack of volcanism associated with rifting. As the depleted layer thickens and cools, it becomes denser than the convecting interior and the portion of it that is hot enough to flow can mix with the convecting mantle. Time dependence of the thickness of a depleted layer may create episodic resurfacing events as needed to explain the observed distribution of impact craters on the venusian surface. We consider a planetary structure consisting of a crust, depleted mantle layer, and a thermally and chemically well-mixed convecting mantle. The thermal evolution of the convecting spherical planetary interior is calculated using energy conservation: the time rate of change of thermal energy in the interior is equated to the difference in the rate of radioactive heat production and the rate of heat transfer across the thermal boundary layer. Heat transfer across the thermal boundary layer is parameterized using a standard Nusselt number-Rayleigh number relationship. The radioactive heat production decreases with time corresponding to decay times for the U, Th, and K. The planetary interior cools by the advection of hot mantle at temperature T interior into the thermal boundary layer where it cools conductively. The crust and depleted mantle layers do not convect in our model so that a linear conductive equilibrium temperature distribution is assumed. The rate of melt production is calculated as the product of the volume flux of mantle into the thermal boundary layer and the degree of melting that this mantle undergoes. The volume flux of mantle into the thermal boundary layer is simply the heat flux divided by amount of heat lost in cooling mantle to the average temperature in the thermal boundary layer. The degree of melting is calculated as the temperature difference above the solidus, divided by the latent heat of melting. A maximum degree of melting is prescribed corresponding to the maximum amount of basaltic melt that the mantle can initially generate. As the crust thickens, the pressure at the base of the crust becomes high enough and the temperature remains low enough for basalt to transform to dense eclogite.

Parmentier, E. M.↗

Manipulator control for rover planetary exploration

An anticipated goal of Mars surface exploration missions will be to survey and sample surface rock formations which appear scientifically interesting. In such a mission, a planetary rover would navigate close to a selected sampling site and the remote operator would use a manipulator mounted on the rover to perform a sampling operation. Techniques for accomplishing the necessary manipulation for the sampling components of such a mission have been developed and are presented. We discuss the implementation of a system for controlling a seven (7) degree of freedom Puma manipulator, equipped with a special rock gripper mounted on a planetary rover prototype, intended for the purpose of performing the sampling operation. Control is achieved by remote teleoperation. This paper discusses the real-time force control and supervisory control aspects of the rover manipulation system. Integration of the Puma manipulator with the existing distributed computer architecture is also discussed. The work described is a contribution toward achieving the coordinated manipulation and mobility necessary for a Mars sample acquisition and return scenario.

Cameron, Jonathan M.↗

An Overview of Surface Heat Microbial Reduction as a Viable Microbial Reduction Modality for Spacecraft Surfaces

In accordance with NASA Planetary Protection (PP) policy requirements, flight project hardware may be required to undergo microbial reduction processes to prevent the forward contamination of target planetary bodies with Earth organisms. Heat microbial reduction (HMR) is the most commonly employed modality used at JPL for reducing the microbial bioburden on flight hardware. In 2013, longstanding HMR specifications were abandoned, and revised specifications were developed which integrated the latest findings on bacterial spore heat resistivity. Revised decimal reduction values (D-values) for time-temperature lethality curves (110 °C to 200 °C) were developed to account for “hardy” bacterial spores that exhibit greater heat resistance than previously understood. Presented here is a comparative analysis of the revised NASA HMR specifications against empirical data compiled from recent JPL studies, and peer-reviewed, published literature. Bacillus sp. strain ATCC 29669 displayed high heat resistance, and this strain’s 4-log heat lethality curve was comparable to the revised 4-log specification. Spores of Bacillus atrophaeus ATCC 9372 displayed less heat resistance, and exhibited D-values which were less than the revised 3-log microbial reduction specifications. Extrapolations indicate that the current 6-log reduction credit applied to 350 °C for 1 hr. and 500 °C for 0.5 sec. is highly conservative. Projections indicate that a 10- to 18-log reduction of both hardy and non-hardy spores may be achievable at bakeouts of 350 °C for 1 hr. The findings reported here indicate the revised NASA HMR specifications from 110 °C to 200 °C are appropriate for achieving 4-log and 6-log reductions with hardy spore populations; however, for non-hardy spore populations, or for temperatures above 200 °C, the specifications are exceedingly conservative.

Shirey, Brian T.↗

Nasa Exploration Atmosphere Tests 3 & 4: Development and Validation of Planetary Extravehicular Activity Prebreathe Protocols for Alternate Atmospheres and Suit Pressures

INTRODUCTION: Space suits operate at low pressures to optimize astronauts’ performance. The drop in pressure from the habitat environment to the suit carries a risk of decompression sickness (DCS), which is mitigated by a 95% O2 prebreathe protocol. Prebreathe protocols for the lunar surface have a significantly higher risk compared to International Space Station microgravity Extravehicular Activities (EVA). In previous studies, we validated a prebreathe protocol from a 56.5 kPa 34% O2 cabin to a 29.6 kPa EVA pressure; however, the enriched oxygen cabin environment poses a flammability risk that requires significant changes to material design and selections. Here, we report outcomes for prebreathe protocols from a sub-30% O2 cabin and associated changes necessary to control DCS risk critical to upcoming lunar missions. METHODS: Fourteen volunteers completed 11-day hypobaric chamber studies with an “alternate exploration atmosphere” of 66.2kPa, 28.5% O2. Subjects acclimated for 48 hrs and then participated in five 6-hour simulated EVAs at 29.6 or 35.6kPa, 95% O2. Prior to EVA, subjects underwent a 20, 90, or 150-minute prebreathe. The EVA simulation was designed to be representative of future planetary EVAs, proportionate to the subject’s VO2max. Decompression stress was monitored by real-time doppler and echocardiograph alternating every 15 min, as well as clinical monitoring for DCS signs/symptoms. Venous gas emboli (VGE) and DCS outcomes were verified against NASA-STD-3001 acceptance criteria. RESULTS AND DISCUSSION: Venous gas emboli (VGE) were identified during all EVAs. A neurological DCS case was identified in the 90-min/29.6kPa prebreathe, terminating further testing of this protocol. No DCS cases were identified in the 150 min/29.6kPa protocol. The 20 min/36.5kPa protocol was rejected due to a Type II DCS case. All DCS symptoms resolved with treatment, with no sequelae post initial treatment of DCS. These various test points highlighted to the significant benefit of elevated suit pressure to shorten prebreathe protocols, but also the difficulty in assessing and managing DCS during sustained EVA operations in remote planetary surfaces.

decompression sickness↗

Mapping Planetary Volcanic Deposits: Identifying Vents and Distinguishing between Effects of Eruption Conditions and Local Storage and Release on Flow Field Morphology

Terrestrial geologic mapping techniques are regularly used for "photogeologic" mapping of other planets, but these approaches are complicated by the diverse type, areal coverage, and spatial resolution of available data sets. When available, spatially-limited in-situ human and/or robotic surface observations can sometimes introduce a level of detail that is difficult to integrate with regional or global interpretations. To assess best practices for utilizing observations acquired from orbit and on the surface, our team conducted a comparative study of geologic mapping and interpretation techniques. We compared maps generated for the same area in the San Francisco Volcanic Field (SFVF) in northern Arizona using 1) data collected for reconnaissance before and during the 2010 Desert Research And Technology Studies campaign, and 2) during a traditional, terrestrial field geology study. The operations, related results, and direct mapping comparisons are discussed in companion LPSC abstracts. Here we present new geologic interpretations for a volcanic cone and related lava flows as derived from all approaches involved in this study. Mapping results indicate a need for caution when interpreting past eruption conditions on other planetary surfaces from orbital data alone.

Bleacher, J. E.↗

Mapping Planetary Volcanic Deposits: Identifying Vents and Distingushing between Effects of Eruption Conditions and Local Lava Storage and Release on Flow Field Morphology

Terrestrial geologic mapping techniques are regularly used for "photogeologic" mapping of other planets, but these approaches are complicated by the diverse type, areal coverage, and spatial resolution of available data sets. When available, spatially-limited in-situ human and/or robotic surface observations can sometimes introduce a level of detail that is difficult to integrate with regional or global interpretations. To assess best practices for utilizing observations acquired from orbit and on the surface, our team conducted a comparative study of geologic mapping and interpretation techniques. We compared maps generated for the same area in the San Francisco Volcanic Field (SFVF) in northern Arizona using 1) data collected for reconnaissance before and during the 2010 Desert Research And Technology Studies campaign, and 2) during a traditional, terrestrial field geology study. The operations, related results, and direct mapping comparisons are discussed in companion LPSC abstracts [1-3]. Here we present new geologic interpretations for a volcanic cone and related lava flows as derived from all approaches involved in this study. Mapping results indicate a need for caution when interpreting past eruption conditions on other planetary surfaces from orbital data alone.

Bleacher, J. E.↗

The effects of Venus' thermal structure on buoyant magma ascent

The recent Magellan images have revealed a broad spatial distribution of surface volcanism on Venus. Previous work in modeling the ascent of magma on both Venus and Earth has indicated that the planetary thermal structure significantly influences the magmatic cooling rates and thus the amount of magma that can be transported to the surface before solidification. In order to understand which aspects of the thermal structure have the greatest influence on the cooling of ascending magma, we have constructed magma cooling curves for both plutonic and crack buoyant ascent mechanisms, and evaluated the curves for variations in the planetary mantle temperature, thermal gradient curvature with depth, surface temperature gradient, and surface temperature. The planetary thermal structure is modeled as T/T(sub 0) = 1-tau(1-Z/Z(sub 0)(exp n), where T is the temperature, T(sub 0) is the source depth temperature, tau = 1-(T(sub s)/T(sub 0)) where T(sub s) is the planetary surface temperature, Z is the depth, Z(sub 0) is the source depth, and n is a constant that controls thermal gradient curvature with depth. The equation is used both for mathematical convenience and flexibility, as well as its fit to the thermal gradients predicted by the cooling half-space models. We assume a constant velocity buoyant ascent, body-averaged magma temperatures and properties, an initially crystal-free magma, and the same liquidus and solidus for both Venus and Earth.

Sakimoto, S. E. H.↗