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High Altitude Long Endurance UAV Analysis Model Development and Application Study Comparing Solar Powered Airplane and Airship Station-Keeping Capabilities

There have been ongoing efforts in the Aeronautics Systems Analysis Branch at NASA Langley Research Center to develop a suite of integrated physics-based computational utilities suitable for modeling and analyzing extended-duration missions carried out using solar powered aircraft. From these efforts, SolFlyte has emerged as a state-of-the-art vehicle analysis and mission simulation tool capable of modeling both heavier-than-air (HTA) and lighter-than-air (LTA) vehicle concepts. This study compares solar powered airplane and airship station-keeping capability during a variety of high altitude missions, using SolFlyte as the primary analysis component. Three Unmanned Aerial Vehicle (UAV) concepts were designed for this study: an airplane (Operating Empty Weight (OEW) = 3285 kilograms, span = 127 meters, array area = 450 square meters), a small airship (OEW = 3790 kilograms, length = 115 meters, array area = 570 square meters), and a large airship (OEW = 6250 kilograms, length = 135 meters, array area = 1080 square meters). All the vehicles were sized for payload weight and power requirements of 454 kilograms and 5 kilowatts, respectively. Seven mission sites distributed throughout the United States were selected to provide a basis for assessing the vehicle energy budgets and site-persistent operational availability. Seasonal, 30-day duration missions were simulated at each of the sites during March, June, September, and December; one-year duration missions were simulated at three of the sites. Atmospheric conditions during the simulated missions were correlated to National Climatic Data Center (NCDC) historical data measurements at each mission site, at four flight levels. Unique features of the SolFlyte model are described, including methods for calculating recoverable and energy-optimal flight trajectories and the effects of shadows on solar energy collection. Results of this study indicate that: 1) the airplane concept attained longer periods of on-site capability than either airship concept, and 2) the airship concepts can attain higher levels of energy collection and storage than the airplane concept; however, attaining these energy benefits requires adverse design trades of reduced performance (small airship) or excessive solar array area (large airship).

Ozoroski, Thomas A.

Mariner 9 ultraviolet spectrometer experiment - Morning terminator observations of Mars

Mariner 9 ultraviolet morning terminator data indicate the presence of a high, optically thin scattering layer in the equatorial region of Mars extending to 50S. This is consistent with the afternoon terminator results, which showed the presence of a scattering layer for latitudes as far north as 50N. For both types of terminator observations, the magnitude of the reflectivity for large shadow heights and the apparent scale height of the signal are too large to be explained by a homogeneous atmosphere. The terminator observations poleward of 50S were modeled by a homogeneous atmosphere of molecular and particulate scatterers. As the lower atmosphere began to clear from the dust storm, a progressive change was noted in the magnitude of the terminator reflectivity which is attributed to a changing albedo for single scattering. The shape of the morning terminator reflectivity measured as a function of shadow height indicates larger apparent scale heights than were observed in the afternoon. The difference is attributed to an increase in thickness of the scattering layer during the night.

Ajello, J. M.

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earth's magnetosphere as a laboratory to study the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10 (sup -4) pascals (10 (sup -6) torr) and the surrounding temperature achieving -180 degrees Centigrade. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperature versus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDA/FLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 degrees Centigrade of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 degrees Centigrade and the heater power goal is to be within 5 percent of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Correlation

Thermal Testing and Model Correlation of the Magnetospheric Multiscale (MMS) Observatories

International Conference on Envronmental Systems (ICES), Seattle WA NCTS 20964-15. The Magnetospheric Multiscale (MMS) mission is a Solar Terrestrial Probes mission comprising four identically instrumented spacecraft that will use Earths magnetosphere as a laboratory tostudy the microphysics of three fundamental plasma processes: magnetic reconnection, energetic particle acceleration, and turbulence. This paper presents the complete thermal balance (TB) test performed on the first of four observatories to go through thermal vacuum (TV) and the minibalance testing that was performed on the subsequent observatories to provide a comparison of all four. The TV and TB tests were conducted in a thermal vacuum chamber at the Naval Research Laboratory (NRL) in Washington, D.C. with the vacuum level higher than 1.3 x 10-4 Pa (10-6 torr)and the surrounding temperature achieving -180 C. Three TB test cases were performed that included hot operational science, cold operational science and a cold survival case. In addition to the three balance cases a two hour eclipse and a four hour eclipse simulation was performed during the TV test to provide additional transient data points that represent the orbit in eclipse (or Earth's shadow) The goal was to perform testing such that the flight orbital environments could be simulated as closely as possible. A thermal model correlation between the thermal analysis and the test results was completed. Over 400 1-Wire temperature sensors, 200 thermocouples and 125 flight thermistor temperature sensors recorded data during TV and TB testing. These temperatureversus time profiles and their agreements with the analytical results obtained using Thermal Desktop and SINDAFLUINT are discussed. The model correlation for the thermal mathematical model (TMM) is conducted based on the numerical analysis results and the test data. The philosophy of model correlation was to correlate the model to within 3 C of the test data using the standard deviation and mean deviation error calculation. Individual temperature error goal is to be within 5 C and the heater power goal is to be within 5 of test data. The results of the model correlation are discussed and the effect of some material and interface parameters on the temperature profiles are presented.

Thermal

Apron heights around stepped massifs in the Cydonia Mensae region: Do they record the local paleobathymetry of Oceanus Borealis?

The use of photoclinometry and shadow measurements to determine the basin volume without linking the measurements to a global datum is described. Since the boundary, or shoreline, of the basin cannot be tied to the datum and typically has no useful local relative height to measure, what is needed is a number of measurements of the height of the paleoshorelines distributed across the basin. Photoclinometric profiles are being compiled from Viking Orbiter images of the Cydonia Mensae region, which includes images with high sun elevations, necessary to avoid shadows, and images with low sun elevations, to enable the use of shadow measurements as an independent check, at high resolution (40 to 100 m/pixel). Both asymmetric and symmetric photoclinometric profile models are being used, and the results cross checked with one another to minimize errors. An apron-height map, potentially a paleobathymetric map of part of the margin of Oceanus Borealis, can be compiled from this data to determine whether variations in apron height are consistent with a lacustrine interpretation.

Parker, T. J.

SMART Ground-based Radiation Measurements during PRIDE

We deployed a suite of ground-based remote sensing instruments - SMART (Surface Measurements for Atmospheric Radiative Transfer), at the Roosevelt Road Naval Station in Puerto Rico during the Puerto Rico Dust Experiment (PRIDE). The instruments include several solar and infrared broadband radiometers, a sunphotometer, a shadow-band radiometer, a micro-pulse lidar, a total-sky imager, a microwave radiometer, and two solar spectrometers. These radiometers were set up on a mobile platform and a solar tracker. During 27 June - 23 July, about 25 days of data were acquired under partially cloudy sky conditions. The diurnal air temperature was fluctuating around 28.6 C to within a few degrees. Daytime average of solar irradiance reaching at the surface was ranged from about 400 W/sq m on a rainy day to about 640 W/sq m on a cloud-free day. The infrared irradiance at the surface during the measurement period was averaged about 408 W/sq m. The heights of boundary layer, dusts and clouds were captured by lidar images. Based on sunphotometer and shadow-band radiometer retrievals, the aerosol optical thickness varied from below 0.1 to over 0.6. Combining with radiative transfer modeling and other in-situ and remote sensing measurements, our ground-based measurements provide vital information on understanding the long-range transport of African dust into the Caribbean.

Tsay, Si-Chee

Near Real Time Prospecting for Lunar Volatiles: Demonstrating RESOLVE Science in the Field

The Regolith and Environment Science and Oxygen & Lunar Volatile Extraction (RESOLVE) project aims to demonstrate the utility of "in situ resource utilization". In situ resource utilization (ISRU) is a way to rebalance the economics of spaceflight by reducing or eliminating materials that must be brought up from Earth and placed on the surface of the Moon for human use. RESOLVE is developing a rover-borne payload that (1) can locate near subsurface volatiles, (2) excavate and analyze samples of the volatile-bearing regolith, and (3) demonstrate the form, extractability and usefulness of the materials. Such investigations are important not only for ISRU but are also critically important for understanding the scientific nature of these intriguing lunar polar volatile deposits. Temperature models and orbital data suggest near surface volatile concentrations may exist at briefly lit lunar polar locations outside persistently shadowed regions. A lunar rover could be remotely operated at some of these locations for the 4-7 days of expected sunlight at relatively low cost. In July 2012 the RESOLVE project conducted a full-scale field demonstration. In particular, the ability to perform the real-time measurement analysis necessary to search for volatiles and the ability to combine the various measurement techniques to meet the mission measurement and science goals. With help from the Pacific International Space Center for Exploration Systems (PISCES), a lunar rover prototype (provided by the Canadian Space Agency) was equipped with prospecting instruments (neutron spectrometer and near-infrared spectrometer), subsurface access and sampling tools, including both an auger and coring drill (provided by CSA) and subsurface sample analysis instrumentation, including a sample oven system, the Oxygen and Volatile Extraction Node (OVEN), and Gas Chromatograph / Mass Spectrometer system, the Lunar Advanced Volatile Analysis (LAVA) system. Given the relatively short time period this lunar mission is being designed to, prospecting needs to occur in near real-time. The two prospecting instruments are the neutron and NIR spectrometers. In the field demo a small radioactive source was provided the neutron flux. The NIR spectrometer, which includes its own light source, looks at surface reflectance for signatures of bound H20/0H and general mineralogy. Once a "hot spot" was found by the prospecting instruments, the drill could either auger or core. The auger drill worked to a depth of 50 cm and is monitored with a drill camera and the NIR spectrometer. As cuttings are brought up the NIR spectra is monitored. If a particular location is considered of high -interest then the decision to core could be made. The coring drill (a push-tube) allowed a meter sample to be acquired processed by the OVEN/LAVA sys-tem. This presentation will provide details as how these instruments worked together and how and if the planned measurements and science was obtained.

Elphic, Richard

Prospecting for Polar Volatiles: Results from the Resolve Field

Both the Moon and Mercury evidently host ice and other volatile compounds in cold traps at the planets poles. Determining the form, spatial distribution, and abundance of these volatiles at the lunar poles can help us understand how and when they were delivered and emplaced. This bears directly on the delivery of water and prebiotic compounds to the inner planets over the solar system s history, and also informs plans for utilizing the volatiles as resources for sustained human exploration as well as the commercial development of space. Temperature models and orbital data suggest near-surface volatile concentrations may exist at polar locations not strictly in permanent shadow. Remote operation of a robotic lunar rover mission for the 7-10 days of available sunlight would permit key questions to be answered. But such a short, quick-tempo mission has unique challenges and requires a new concept of operations. Both science and rover operations decisionmaking must be done in real time, requiring immediate situational awareness, data analysis, and decision support tools.

Elphic, Richard C.

Real-Time Science Operations to Support a Lunar Polar Volatiles Rover Mission

Future human exploration of the Moon will likely rely on in situ resource utilization (ISRU) to enable long duration lunar missions. Prior to utilizing ISRU on the Moon, the natural resources (in this case lunar volatiles) must be identified and characterized, and ISRU demonstrated on the lunar surface. To enable future uses of ISRU, NASA and the CSA are developing a lunar rover payload that can (1) locate near subsurface volatiles, (2) excavate and analyze samples of the volatile-bearing regolith, and (3) demonstrate the form, extractability and usefulness of the materials. Such investigations are important both for ISRU purposes and for understanding the scientific nature of these intriguing lunar volatile deposits. Temperature models and orbital data suggest near surface volatile concentrations may exist at briefly lit lunar polar locations outside persistently shadowed regions. A lunar rover could be remotely operated at some of these locations for the approx. 2-14 days of expected sunlight at relatively low cost. Due to the limited operational time available, both science and rover operations decisions must be made in real time, requiring immediate situational awareness, data analysis, and decision support tools. Given these constraints, such a mission requires a new concept of operations. In this paper we outline the results and lessons learned from an analog field campaign in July 2012 which tested operations for a lunar polar rover concept. A rover was operated in the analog environment of Hawaii by an off-site Flight Control Center, a rover navigation center in Canada, a Science Backroom at NASA Ames Research Center in California, and support teams at NASA Johnson Space Center in Texas and NASA Kennedy Space Center in Florida. We find that this type of mission requires highly efficient, real time, remotely operated rover operations to enable low cost, scientifically relevant exploration of the distribution and nature of lunar polar volatiles. The field demonstration illustrated the need for science operations personnel in constant communications with the flight mission operators and the Science Backroom to provide immediate and continual science support and validation throughout the mission. Specific data analysis tools are also required to enable immediate data monitoring, visualization, and decision making. The field campaign demonstrated that this novel methodology of real-time science operations is possible and applicable to providing important new insights regarding lunar polar volatiles for both science and exploration.

Moon; Volatiles; Rover; Missions

SPACE-Gateway: Modeling the Electrical Performance of the Gateway Power & Propulsion Element (PPE) Solar Arrays

The System Power Analysis for Capability Evaluation (SPACE) computer model was originally developed in 1988 at NASA Glenn Research Center to model the International Space Station (ISS) electrical power system (EPS). Since then, SPACE development has continued with the rise of new NASA human spaceflight missions. Today, SPACE’s uniquely complex and robust solar array model is being leveraged to model the solar arrays on the Gateway Power & Propulsion Element (PPE) for NASA's Artemis Program. This presentation will discuss the model’s integrated features, including its solar cell current-voltage (IV) curve, degradation, temperature, and on-orbit shadowing components. The presentation will also discuss recent SPACE advancements to meet the needs of NASA's latest spaceflight missions.

SPACE

Implementation of a Parameterized Interacting Multiple Model Filter on an FPGA for Satellite Communications

In a communications channel, the space environment between a spacecraft and an Earth ground station can potentially cause the loss of a data link or at least degrade its performance due to atmospheric effects, shadowing, multipath, or other impairments. In adaptive and coded modulation, the signal power level at the receiver can be used in order to choose a modulation-coding technique that maximizes throughput while meeting bit error rate (BER) and other performance requirements. It is the goal of this research to implement a generalized interacting multiple model (IMM) filter based on Kalman filters for improved received power estimation on software-dened radio (SDR) technology for satellite communications applications. The IMM filter has been implemented in Verilog consisting of a customizable bank of Kalman filters for choosing between performance and resource utilization. Each Kalman filter can be implemented using either solely a Schur complement module (for high area efficiency) or with Schur complement, matrix multiplication, and matrix addition modules (for high performance). These modules were simulated and synthesized for the Virtex II platform on the JPL Radio Experimenter Development System (EDS) at NASA Glenn Research Center. The results for simulation, synthesis, and hardware testing are presented.

cognitive radio

Validation of Rendered Natural and Artificial Lighting Environments in Real Time Lunar South Pole Simulations

NASA’s Artemis campaign is making heavy use of simulation to help return humans to the lunar surface by the end of the decade. There are several aspects of the lunar surface and its environment which must be accurately modeled before these simulations can be relied upon to influence decisions being made under these programs. Digital Lunar Exploration Sites, a paper submitted to the 2022 IEEE Aerospace Conference, outlined the process used to generate the lunar surface in a digital environment. This paper will expand upon this topic and delve into the steps being taken by the NASA Exploration Systems Simulations (NExSyS) team at NASA’s Johnson Space Center (JSC) to properly verify and validate these simulations, with a focus on the visual aspects of the environment. Natural lighting validation relies in part on the wealth of data generated during the Apollo program. Many images taken by Apollo astronauts on the lunar surface have been replicated in the simulated environments to gain confidence in the accuracy of terrain and lighting models. However, because the environment the Artemis astronauts will experience at the Lunar South Pole (LSP) is dissimilar from the near-equatorial Apollo sites, other validation techniques must be applied. At the LSP, the sun crests only about three degrees above the horizon and when combined with the lack of a lunar atmosphere, lighting in this region is often very different than what a human would experience on Earth. Solar illumination, earthshine, human eye response, solar blooming, lunar regolith optical properties, and shadows cast by rocks and crater walls will play a significant role in an astronaut’s ability to safely conduct an Extra-Vehicular Activity (EVA) or perform a traverse with a lunar rover. Approaches for validation of these aspects of the rendered LSP environment are considered in this paper. In addition to natural lighting, approaches for the validation of artificial lighting models at the LSP are discussed. The JSC Lighting Lab has been studying the illumination profile of the Exploration Infomatics Subsystem (xINFO) lighting on the Exploration EVA Mobility Unit (xEMU). How these lights interact with the solar illumination and the shadows being cast on the lunar surface is of particular interest, so the validity of models representing these lights in a human-in-the-loop virtual reality environment becomes very important. This paper also touches on some of the simulation performance considerations when a Human in the Loop (HITL) is present, which drives the need for real time rendering of the environment. Natural and artificial lighting will play a crucial role to decisions being made when planning and executing missions at the Lunar South Pole (LSP) and it is vitally important to understand the LSP environment before we return.

Lunar

Approaches for Validation of Lighting Environments in Realtime Lunar South Pole Simulations

NASA’s Artemis campaign is making heavy use of simulation to help return humans to the lunar surface by the end of the decade. There are several aspects of the lunar surface and its environment which must be accurately modeled before these simulations can be relied upon to influence decisions being made under these programs. Digital Lunar Exploration Sites, a paper submitted to the 2022 IEEE Aerospace Conference, outlined the process used to generate the lunar surface in a digital environment. This paper will expand upon this topic and delve into the steps being taken by the NASA Exploration Systems Simulations (NExSyS) team at NASA’s Johnson Space Center (JSC) to properly verify and validate these simulations, with a focus on the visual aspects of the environment. Natural lighting validation relies in part on the wealth of data generated during the Apollo program. Many images taken by Apollo astronauts on the lunar surface have been replicated in the simulated environments to gain confidence in the accuracy of terrain and lighting models. However, because the environment the Artemis astronauts will experience at the Lunar South Pole (LSP) is dissimilar from the near-equatorial Apollo sites, other validation techniques must be applied. At the LSP, the sun crests only about 1.5 degrees above the horizon and when combined with the lack of a lunar atmosphere, lighting in this region is often very different than what a human would experience on Earth. Solar illumination, earthshine, human eye response, solar blooming, lunar regolith optical properties, and shadows cast by rocks and crater walls will play a significant role in an astronaut’s ability to safely conduct an Extra-Vehicular Activity (EVA) or perform a traverse with a lunar rover. Approaches for validation of these aspects of the rendered LSP environment are considered in this paper. In addition to natural lighting, approaches for the validation of artificial lighting models at the LSP are discussed. The JSC Lighting Lab has been studying the illumination profile of the Exploration Informatics Subsystem (xINFO) lighting on the Exploration EVA Mobility Unit (xEMU). How these lights interact with the solar illumination and the shadows being cast on the lunar surface is of particular interest, so the validity of models representing these lights in a human-in-the-loop virtual reality environment becomes very important. This paper also touches on some of the simulation performance considerations when a Human in the Loop (HITL) is present, which drives the need for realtime rendering of the environment. Natural and artificial lighting will play a crucial role to decisions being made when planning and executing missions at the Lunar South Pole (LSP) and it is vitally important to understand the LSP environment before we return.

Lunar

The reflection for dense plant canopies from the one-angle radiative transfer equation

An essential component of remote sensing of vegetation canopies from satellites is fundamental understanding. Since passive remote is driven by photons, the modeling of photon interactions with vegetation is a basic building block in that understanding. Several such photon transport models have been developed during the past two decades and continue to be developed. Different approaches have been followed including monte carlo, radiosity methods, geometric shadowing, and radiative transfer. In general, each approach has application for canopies with specific attributes. This presentation concerns the application of radiative transfer to dense vegetation canopies in which the soil does not participate. The approach taken here is novel in that a consistent theory for photon transport for non-rotationally invariant leaf scattering is developed in a canopy with a general leaf angle distribution (LAD). The theory is limited to the one-angle approximation (azimuthally averaged radiance) and is based on Chandrasekhar's analytical theory. While such a model is admittedly only approximate, it does fulfill a unique function in our search for understanding. In particular, the model is simple in its construct yet contains the essential features of canopy architecture that are mainly responsible for observed responses. Thus, this model will not only be a predictive tool but also an educational one. The mathematical setting is the radiative transfer equation in a dense (semiinfinite) canopy. The leaf scattering phase function is assumed to be Lambertian with different reflectance and transmittance. In addition, abaxial and adaxial differentiation is allowed which effectively destroys optical reciprocity. The analytical solution for the canopy BRDF is obtained by manipulation of the integral transport equation (a la Chandrasekhar) for a general LAD. With discretization of the. leaf angle, the resulting set of integral equations are solved iteratively including an acceleration procedure when the single scatter albedo is near one (in the NIR). Results will be compared to the LARS soybean canopy radiances as well as to broadleaf results from a recent Ames experiment.

Ganapol, B. D.

Measurement of kaon directed flow in Au+Au collisions in the high baryon density region

Rapidity-odd directed flow v 1 measurements are presented for $K^±$ and $K^0_S$ in Au + Au collisions for $\sqrt{s_{NN}}$ from 3.0 to 3.9 GeV with the STAR experiment. For comparison, v 1 of π ± , protons, and Λ from the same collisions are also discussed. The mid-rapidity v 1 slope dv 1 /dy| y=0 for protons and Λ is positive in these collisions. On the other hand, v 1 slope of kaons exhibits a strong dependence: negative at p T < 0.6 GeV/c and positive at higher p T . A similar p T dependence is also evident for the v 1 slope of charged pions. Compared to the spectator-removed calculations in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0–3.9 GeV, the JAM model demonstrates a pronounced shift of the v 1 slopes of mesons towards the negative direction. It suggests that the shadowing effect of the spectators plays an important role in the observed kaon anti-flow at low p T in the high baryon density region of non-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Employing static excitation control and tie line reactance to stabilize wind turbine generators

An analytical representation of a wind turbine generator is presented which employs blade pitch angle feedback control. A mathematical model was formulated. With the functioning MOD-0 wind turbine serving as a practical case study, results of computer simulations of the model as applied to the problem of dynamic stability at rated load are also presented. The effect of the tower shadow was included in the input to the system. Different configurations of the drive train, and optimal values of the tie line reactance were used in the simulations. Computer results revealed that a static excitation control system coupled with optimal values of the tie line reactance would effectively reduce oscillations of the power output, without the use of a slip clutch.

Hwang, H. H.

Solar insolation model

Computer program SOLINS helps engineers with relatively complex task of choosing best orientation of fixed flat-plate solar collectors for local conditions. Program models average hourly solar insolation on fixed but arbitrarily-oriented surface. Consideration is given to problems of array spacing, shadowing, and use of augmentation reflectors to increase insolation at collector surface.

Smith, J. H.

Airburst origin of dark shadows on Venus

The Magellan images showed presence of radar-dark shadowlike disks surrounding small impact craters on the Venusian surface, which are also found without craters. This paper examines the hypothesis of Phillips et al. (1991) that the dark shadows formed where shock waves from airbursting impactors met the ground, pulverizing decimeter-scale surface features. A simple analytic model is used successfully to simulate the catastrophic disruption and the deceleration of impactors in a thick atmosphere to reproduce observed Venusian cratering statistics and generate radar-dark disks by the impact of atmospheric shock waves on the surface.

Zahnle, Kevin J.