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Near-Term Options for a Nuclear Thermal Propulsion Flight Demonstrator

The Appropriations Bill passed by the US Congress in February 2019 instructed NASA to direct “not less than $100,000,000 for the development of nuclear thermal propulsion, of which not less than $70,000,000 shall be for the design of a flight demonstration by 2024 for which a multi-year plan is required by both the House and the Senate within 180 days of enactment of this agreement." As part of NASA’s response to this direction, the Advanced Concepts Office (ACO) at the Marshall Space Flight Center (MSFC) was tasked with leading a study to develop a nuclear thermal propulsion (NTP) flight demonstration (FD) concept and evaluate its feasibility with respect to the near-term schedule goal. During formulation for the NTP FD study, two perspectives emerged with regards to FD concept design. The first seeks to strictly observe the immediate near-term schedule goal, embracing a completely “off-the-shelf,” high-TRL approach to subsystem design and component selection. The downside to this approach is that the propulsion performance to be expected from such a design is significantly lower than what NTP promises for operational systems, and the value of the flight demo is potentially reduced due to a lack of traceability. The second approach advocates for an FD concept that shows increased traceability to the projected designs of operational systems, providing risk reduction for future NTP-enabled missions. This option comes at the cost of schedule and development risks, as it requires some new investments in nuclear reactor fuels and design. In order to understand the implications and differences between these two approaches, the ACO team elected to perform a concept design of each type, labeling the immediate near-term concept Flight Demo 1 (FD1), and the higher traceability concept Flight Demo 2 (FD2). This paper will present a summary of the mission profiles and system designs for both FD1 and FD2, identifying key drivers and challenges for each design.

Edwards, S. J.↗

Reliable Bonding of Composite Laminates Using Reflowable Epoxy Resins

Epoxy matrix composites assembled with adhesives maximize the performance of aerospace structures, but the possibility of forming weak bonds requires the installation of redundant fasteners, which add weight and manufacturing cost. Co-cured joints (e.g. unitized composite structures) are immune to weak bonds because the uncured resin undergoes diffusion and mixing through the joint. A means of co-curing complex structures may reduce the need for redundant fasteners in bondlines. To this end, NASA started the AERoBOND project to develop novel joining materials to enable a “secondary-co-cure” assembly process. Aerospace epoxy resin systems reformulated with offset stoichiometry prevented the resin from advancing beyond the gel point during a conventional autoclave cure cycle up to 180 °C. The offset resins were applied to the joining surfaces of laminate preforms as prepreg. Two surfaces with complimentary offset resins were joined using conventional secondary bonding techniques. Preliminary efforts have indicated that the resulting joint has no discernable interface and appears as a conventional co-cured laminate under optical magnification. This report will discuss the initial work performed regarding formulation of the epoxy resin system using calorimetry, rheology, and mechanical testing.

Palmieri, Frank L.↗

Coatings for CSP Lifetime

The feasibility and performance of tower-technology-based concentrated solar power (CSP) is highly dependent on the efficiency of the energy transformation from sun to heat at the receiver. The higher the solar absorptivity of the receiver coating, the higher the efficiency of the plant as a whole. BrightSource Energy (BSE) has developed a series of High-Performance Coating (HPC) systems in order to achieve high absorptivity over the plant lifetime (25-35 years). This requires stable coatings that are easily applicable on the large receiver surface and will maintain their optical properties under intense solar flux and thousands of heating and cooling cycles in desert conditions. Different coating formulations are required according to the differing plant conditions: receiver materials, operating conditions (temperatures, daily cycles, etc.), and environmental conditions. BSE also developed a coating for the next generation of CSP receivers, such as those being under DOE’s CSP Gen3 program, which will be operated with high temperature heat transfer fluids at temperatures of up to 800°C, which is significantly hotter than the operating temperature of current systems. Once the coating is formulated, the next challenge is evaluating its lifetime properties. BSE has found several independent failure modes that impact HPC absorptivity degradation: • Decrease in HPC optical properties due to oxidation in the receiver tubes surface below the HPC; • HPC film deterioration due to cycling of temperatures and humidity due to daily operation startup and shutdown as well as changing ambient conditions; • Mechanical degradation due to erosion by sand and wind. Existing test methods examine various aspects independently, but do not provide a combined accelerated lifetime result. Creating such a combined test suite, with a way to interpret the results to predict the coating’s projected lifetime, was the ultimate goal of this project. The project was divided into three major workstreams: lab testing (individual failure mode tests and combined failure mode tests); developing a theoretical model for aging; and validation of the test apparatus via on-sun testing in near real-world conditions at CIEMAT-PSA. Developing a test apparatus that accurately controlled the temperature while also introducing the desired solar flux proved more challenging than expected. While in the end we did succeed in creating a test apparatus that can control temperature, solar flux, and humidity, the results did not appear to accelerate the lifetime of the samples as desired. We suspect that to properly accelerate the samples we must also subject the samples to increased amounts of oxygen. Similarly, while we successfully created a combined model that is publicly available, we were unable to validate it sufficiently to feel comfortable recommending it as a general guideline.

14 SOLAR ENERGY↗

TAT-C: A Trade-Space Analysis Tool for Constellations

Under a changing technological and economic environment, there is growing interest in implementing future NASA Earth Science missions as Distributed Spacecraft Missions (DSM). The objective of our project is to provide a framework that facilitates DSM Pre-Phase A investigations and optimizes DSM designs with respect to a-priori Science goals. In this first version of our Trade-space Analysis Tool for Constellations (TAT-C), we are investigating questions such as: Which type of constellations should be chosen? How many spacecraft should be included in the constellation? Which design has the best costrisk value? This paper describes the overall architecture of TAT-C including: a User Interface (UI) interacting with multiple users - scientists, missions designers or program managers; an Executive Driver gathering requirements from UI and formulating Trade-space Search Requests for the Trade-space Search Iterator, which in collaboration with the Orbit Coverage, Reduction Metrics, and Cost Risk modules generates multiple potential architectures and their associated characteristics. UI will include Graphical, Command Line and Application Programmer Interfaces to respond to the demands of various levels of users expertise. Science inputs are grouped into various mission concepts, satellite specifications, and payload specifications, while science outputs are grouped into several types of metrics - spatial, temporal, angular and radiometric. Orbit Coverage leverages the use of the Goddard Mission Analysis Tool (GMAT) to compute coverage and ancillary data that are passed to Reduction Metrics. Then, for each architecture design, Cost Risk will provide estimates of the cost and life cycle cost as well as technical and cost risk of the proposed mission. Additionally, the Knowledge Base module is a centralized store of structured data readable by humans and machines. It will support both TAT-C analysis when composing new mission concepts from existing model inputs, and TAT-C exploration when discovering new mission concepts by querying previous results.

Science Data Processing↗

Directed Acyclic Graph Guidance Documentation

For over a decade, the National Aeronautics and Space Administration (NASA) has tracked and configuration-managed approximately 30 risks to astronaut health and performance that occur before, during and after spaceflight. The Human System Risk Board (HSRB), a Health and Medical Technical Authority (HMTA) Board at NASA Johnson Space Center, is the entity responsible for identifying, assessing, analyzing, and monitoring the official understanding of the risk or risk posture for each of the Human System Risks and determining – based on evaluation of the available evidence – when that risk posture changes. The ultimate purpose of tracking and researching these risks is to find ways to reduce the risk that astronaut crews face during spaceflight. Historically, research, development and operations relevant to one risk have been conducted in isolation from other risks; these individual risk ‘silos’ enabled initial characterization of each specific risk. In spaceflight however, the impact of exposure to risk for astronaut crews is cumulative, and not independent of exposures or other risks, as all the adverse effects of the spaceflight environment begin at launch, continue throughout the duration of the mission and in some cases across the lifetime of the crews. In January of 2020, the HSRB at NASA embarked on a pilot project designed to assess the potential value of causal diagramming as a tool to facilitate understanding these cumulative and interdependent effects as applied within Human System Risk management. This process uses directed acyclic graphs as a means of formalizing a shared mental model of the causal flow of risk among Risk Board stakeholders. Initially this model was to improve communication among those stakeholders, but the potential value exceeds communication alone. Formalization of the process for creating these causal diagrams will enable the creation of a composite risk network that is vetted by members of the NASA community and configuration managed. The causal diagrams are formulated as directed acyclic graphs (DAGs) to function as a type of knowledge graph for reference for the board and its stakeholders. This document outlines the pilot process, the standardized approaches, and guidance for risk custodian teams when creating and updating DAGs as a part of the NASA Human System Risk Management process.

Risk↗

Low order dynamical models for mixing layers

The goal of this project was to investigate the feasibility of developing useful low order dynamical systems to allow one to determine cheaply the effect of various initial conditions on the evolution of mixing layers. A mathematically rigorous approach for a time evolving base flow as found in a mixing layer seems to be the singular value decomposition of the linear operator transforming some initial perturbations into the solution at a given later time. Unfortunately, this is very costly, if at all feasible, and only deals with the linear evolution of a disturbance. A different approach based on weakly nonlinear analysis was attempted, but numerous difficulties were encountered. Several formulations were proposed which may be ill-posed. The reasons for this possible failure of the attempted approach is related to the fundamental limitations of weakly nonlinear analysis. The clarification of these issues is attempted in this report.

Riahi, D. N.↗

An Update on GPM and TRMM Data Services at NASA GES DISC

The Goddard Earth Sciences (GES) Data and Information Services Center (DISC) is home to data archives of the NASA-JAXA Global Precipitation Measurement (GPM), the Tropical Rainfall Measuring Mission (TRMM), and other NASA missions and projects. To maximize the use of NASA data products in scientific research and applications as well as for societal benefits, we provide data and information services that make datasets easy to find and use through simplification of data access for users at all levels around the world. Over the years, user-friendly data services have been developed at GES DISC, including data subsetting, format conversion, online visualization and analysis (i.e. Giovanni), user support system, etc. We routinely analyze questions, feedback, and use cases from users and algorithm developers around the world as well as best practices and new technology to improve existing services and formulate new data services. Interaction between users and algorithm developers is an important process for identifying issues in products, collecting user requirements, and improving product quality and usability. Staff members regularly communicate with algorithm developers with user questions and concerns through conferences and workshops. We publish peer-reviewed papers and articles in major Earth science journals and book chapters to describe NASA global and regional precipitation datasets and services with examples. News articles about GPM and TRMM datasets associated with significant events are regularly posted in the GES DISC Web portal and social media. We also actively participate in training activities. In this presentation, we present our latest activities about GPM and TRMM data services, data/service metrics, and future plans at GES DISC.

Liu, Z.↗

Development of Numerical Extended Hydrodynamics for Transition-Regime Non-Equilibrium Flows Encountered in Semiconductor Manufacturing Processes

Six months of funding was received for the proposed three year research program (funding for the period from March 1, 1997 to August 31, 1997). Although the official starting date for the project was March 1, 1997, no funding for the project was received until July 1997. In the funded research period, considerable progress was made on Phase I of the proposed research program. The initial research efforts concentrated on applying the 10-, 20-, and 35-moment Gaussian-based closures to a series of standard two-dimensional non-reacting single species test flow problems, such as the flat plate, couette, channel, and rearward facing step flows, and to some other two-dimensional flows having geometries similar to those encountered in chemical-vapor deposition (CVD) reactors. Eigensystem analyses for these systems for the case of two spatial dimensions was carried out and efficient formulations of approximate Riemann solvers have been formulated using these eigenstructures. Formulations to include rotational non-equilibrium effects into the moment closure models for the treatment of polyatomic gases were explored, as the original formulations of the closure models were developed strictly for gases composed of monatomic molecules. The development of a software library and computer code for solving relaxing hyperbolic systems in two spatial dimensions of the type arising from the closure models was also initiated. The software makes use of high-resolution upwind finite-volumes schemes, multi-stage point implicit time stepping, and automatic adaptive mesh refinement (AMR) to solve the governing conservation equations for the moment closures. The initial phase of the code development was completed and a numerical investigation of the solutions of the 10-moment closure model for the simple two-dimensional test cases mentioned above was initiated. Predictions of the 10-moment model were compared to available theoretical solutions and the results of direct-simulation Monte Carlo (DSMC) calculations. The first results of this study were presented at a meeting last year.

Groth, Clinton P. T.↗

Time-series learning of latent-space dynamics for reduced-order model closure

In this work, we study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation. Our formulation is devised in a nonintrusive manner with an equation-free evolution of dynamics in a reduced space with the latter being obtained through a proper orthogonal decomposition. In addition, we leverage the sequential nature of learning for both LSTMs and NODEs to demonstrate their capability for closure in systems that are not completely resolved in the reduced space. We assess our hypothesis for two advection-dominated problems given by the viscous Burgers equation. We observe that both LSTMs and NODEs are able to reproduce the effects of the absent scales for our test cases more effectively than does intrusive dynamics evolution through a Galerkin projection. This result empirically suggests that time-series learning techniques implicitly leverage a memory kernel for coarse-grained system closure as is suggested through the Mori–Zwanzig formalism.

97 MATHEMATICS AND COMPUTING↗

Compact, Engineered, 2-Micron Coherent Doppler Wind Lidar Prototype: A New NASA Instrument Incubator Program Project

A new project, selected in 2005 by NASA s Science Mission Directorate (SMD) under the Instrument Incubator Program (IIP), will be described. The 3-year effort is intended to design, fabricate, and demonstrate a packaged, rugged, compact, space-qualifiable coherent Doppler wind lidar (DWL) transceiver capable of future validation in an aircraft and/or Unmanned Aerial Vehicle (UAV). The packaged DWL will utilize the numerous advances in pulsed, solid-state, 2-micron laser technology at NASA s Langley Research Center (LaRC) in such areas as crystal composition, architecture, efficiency, cooling techniques, pulse energy, and beam quality. The extensive experience of Raytheon Space and Airborne Systems (RSAS) in coherent lidar systems, in spacebased sensors, and in packaging rugged lidar systems will be applied to this project. The packaged transceiver will be as close to an envisioned space-based DWL system as the resources and technology readiness allow. We will attempt to facilitate a future upgrade to a coherent lidar system capable of simultaneous wind and CO2 concentration profile measurements. Since aerosol and dust concentration is also available from the lidar signal, the potential for a triple measurement lidar system is attractive for both Earth and Mars remote sensing. A key follow on step after the IIP will be to add a telescope, scanner, and software for aircraft validation. This IIP should also put us in a position to begin a parallel formulation study in the 2006-2007 timeframe for a space-based DWL demonstration mission early next decade.

Kavaya, Michael J.↗

The cosmic X-ray background-IRAS galaxy correlation and the local X-ray volume emissivity

We have cross-correlated the galaxies from the IRAS 2 Jy redshift survey sample and the 0.7 Jy projected sample with the all-sky cosmic X-ray background (CXB) map obtained from the High Energy Astronomy Observatory (HEAO) 1 A-2 experiment. We have detected a significant correlation signal between surface density of IRAS galaxies and the X-ray background intensity, with W(sub xg) = (mean value of ((delta I)(delta N)))/(mean value of I)(mean value of N)) of several times 10(exp -3). While this correlation signal has a significant implication for the contribution of the local universe to the hard (E greater than 2 keV) X-ray background, its interpretation is model-dependent. We have developed a formulation to model the cross-correlation between CXB surface brightness and galaxy counts. This includes the effects of source clustering and the X-ray-far-infrared luminosity correlation. Using an X-ray flux-limited sample of active galactic nuclei (AGNs), which has IRAS 60 micrometer measurements, we have estimated the contribution of the AGN component to the observed CXB-IRAS galaxy count correlations in order to see whether there is an excess component, i.e., contribution from low X-ray luminosity sources. We have applied both the analytical approach and Monte Carlo simulations for the estimations. Our estimate of the local X-ray volume emissivity in the 2-10 keV band is rho(sub x) approximately = (4.3 +/- 1.2) x 10(exp 38) h(sub 50) ergs/s/cu Mpc, consistent with the value expected from the luminosity function of AGNs alone. This sets a limit to the local volume emissivity from lower luminosity sources (e.g., star-forming galaxies, low-ionization nuclear emission-line regions (LINERs)) to rho(sub x) less than or approximately = 2 x 10(exp 38) h(sub 50) ergs/s/cu Mpc.

Miyaji, Takamitsu↗

The Application of Lean Thinking Principles and Kaizen Practices for the Successful Development and Implementation of the Ares I-X Flight Test Rocket and Mission

On October 28, 2009 the Ares I-X flight test rocket launched from Kennedy Space Center and flew its suborbital trajectory as designed. The mission was successfully completed as data from the test, and associated development activities were analyzed, transferred to stakeholders, and well documented. Positive lessons learned from Ares I-X were that the application of lean thinking principles and kaizen practices are effective in streamlining development activities. Ares I-X, like other historical rocket development projects, was hampered by technical, cost, and schedule challenges and if not addressed boldly could have resulted in cancellation of the test. The mission management team conducted nine major meetings, referred to as lean events, across its elements to assess plans, procedures, processes, requirements, controls, culture, organization, use of resources, and anything that could be changed to optimize schedule or reduce risk. The preeminent aspect of the lean events was the focus on value added activities and the removal or at least reduction in non-value activities. Trained Lean Six Sigma facilitators assisted the Ares I-X developers in conducting the lean events. They indirectly helped formulate the mission s own unique methodology for assessing schedule. A core team was selected to lead the events and report to the mission manager. Each activity leveraged specialized participants to analyze the subject matter and its related processes and then recommended alternatives and solutions. Stakeholders were the event champions. They empowered and encouraged the team to succeed. The keys to success were thorough preparation, honest dialog, small groups, adherence to the Ares I-X ground rules, and accountability through disciplined reporting and tracking of actions. This lean event formula was game-changing as demonstrated by the success of Ares I-X. It is highly recommended as a management tool to help develop other complex systems efficiently. The key benefits for Ares I-X were obtaining unambiguous schedule margin, defining enabling options for risk reduction, and most importantly a stronger more unified team.

Askins, B. R.↗

Additive Manufacturing (AM) for Propulsion Component and System Applications

NASA MSFC is developing several areas of additive manufacturing (AM) for propulsion component and system applications. These developments include new AM process and material development, large-scale AM pathfinder component fabrication and hot-fire testing, AM-centric design methodology, modeling and simulation, post-processing advancements, and new design applications of AM in aerospace. Some specific areas NASA has focused is the development and commercial infusion of AM supply chain for materials such as copper-alloy GRCop (Cu-Cr-Nb), Hydrogen-resistant alloys (NASA HR-1, JBK-75), refractory-based alloys (C-103, W, Mo, new formulations), and bimetallic and multi-metallic AM processes. Additional efforts have been focused on large scale AM demonstrating complex thin-wall structures up to 60” diameter using directed energy deposition. Material characterization, properties and component hot-fire testing has been completed using many of these newly developed AM alloys/processes. NASA has also focused on improvements to post-processing including powder removal, surface enhancements, and support removal to further realize cost and schedule benefits to the overall supply chain. These developments are part of the NASA Rapid Analysis and Manufacturing Propulsion Technology (RAMPT), Low Cost Upper Stage Propulsion (LCUSP) and Long Life Additive Manufacturing (LLAMA) projects, in addition to internal IRAD, and external collaborations.

Additive Manufacturing↗

Metal hydride composition-derived parameters as machine learning features for material design and H 2 storage

Though hydrogen is a promising energy carrier for a green future, many challenges persist. One is the difficulty in engineering storage solutions, with metal hydrides being a leading contender among solid-state strategies. To facilitate efficient searching of candidate materials, ridge regression, simple decision trees, random forest ensembles, and gradient boosting ensembles were employed to predict the energy of formation, with the random forest ensemble resulting in the lowest test set error. First, two public databases, Materials Project and HydPark, were searched for metal hydrides. Feature engineering was performed before the models were developed, resulting in electronegativity, density, atomic density, d-character, f-character, band gap, hydrogen weight fraction, magnetization, temperature, and pressure being retained. The models were then benchmarked by the lowest test error before a random forest ensemble was used to populate entries missing energy of formation. Furthermore, all were then scored by hydrogen storage capacity and energy of formation suitability. Readily available features including several derived from only the chemical formula which were found to be highly predictive. and so are promising for high-throughput screening of arbitrary novel hydride formulations and blends for thermodynamic feasibility.

25 ENERGY STORAGE↗

The Application of Lean Thinking Principles and Kaizen Practices for the Successful Development and Implementation of the Ares I-X Flight Test Rocket and Mission

On October 28, 2009 the Ares I-X flight test rocket launched from Kennedy Space Center and flew its suborbital trajectory as designed. The mission was successfully completed as data from the test, and associated development activities were analyzed, transferred to stakeholders, and well documented. A positive lesson learned from Ares I-X was that the application of lean thinking principles and kaizen practices was very effective in streamlining development activities. Ares I-X, like other historical rocket development projects, was hampered by technical, cost, and schedule challenges and if not addressed boldly could have resulted in cancellation of the test. The mission management team conducted nine major meetings, referred to as lean events, across its elements to assess plans, procedures, processes, requirements, controls, culture, organization, use of resources, and anything that could be changed to optimize schedule or reduce risk. The preeminent aspect of the lean events was the focus on value added activities and the removal or at least reduction in non-value added activities. Trained Lean Six Sigma facilitators assisted the Ares I-X developers in conducting the lean events. They indirectly helped formulate the mission s own unique methodology for assessing schedule. A core team was selected to lead the events and report to the mission manager. Each activity leveraged specialized participants to analyze the subject matter and its related processes and then recommended alternatives and solutions. Stakeholders were the event champions. They empowered and encouraged the team to succeed. The keys to success were thorough preparation, honest dialog, small groups, adherence to the Ares I-X ground rules, and accountability through disciplined reporting and tracking of actions. This lean event formula was game-changing as demonstrated by Ares I-X. It is highly recommended as a management tool to help develop other complex systems efficiently. The key benefits for Ares I-X were obtaining unambiguous schedule margin, defining enabling options for risk reduction, and most importantly a stronger more unified team.

Askins, B. R.↗

Configuration and Assessment of the GISS ModelE2 Contributions to the CMIP5 Archive

We present a description of the ModelE2 version of the Goddard Institute for Space Studies (GISS) General Circulation Model (GCM) and the configurations used in the simulations performed for the Coupled Model Intercomparison Project Phase 5 (CMIP5). We use six variations related to the treatment of the atmospheric composition, the calculation of aerosol indirect effects, and ocean model component. Specifically, we test the difference between atmospheric models that have noninteractive composition, where radiatively important aerosols and ozone are prescribed from precomputed decadal averages, and interactive versions where atmospheric chemistry and aerosols are calculated given decadally varying emissions. The impact of the first aerosol indirect effect on clouds is either specified using a simple tuning, or parameterized using a cloud microphysics scheme. We also use two dynamic ocean components: the Russell and HYbrid Coordinate Ocean Model (HYCOM) which differ significantly in their basic formulations and grid. Results are presented for the climatological means over the satellite era (1980-2004) taken from transient simulations starting from the preindustrial (1850) driven by estimates of appropriate forcings over the 20th Century. Differences in base climate and variability related to the choice of ocean model are large, indicating an important structural uncertainty. The impact of interactive atmospheric composition on the climatology is relatively small except in regions such as the lower stratosphere, where ozone plays an important role, and the tropics, where aerosol changes affect the hydrological cycle and cloud cover. While key improvements over previous versions of the model are evident, these are not uniform across all metrics.

ocean model↗

Critical research and advanced technology (CRT) support project

A critical technology base for utility and industrial gas turbines by planning the use of coal-derived fuels was studied. Development tasks were included in the following areas: (1) Combustion - investigate the combustion of coal-derived fuels and methods to minimize the conversion of fuel-bound nitrogen to NOx; (2) materials - understand and minimize hot corrosion; (3) system studies - integrate and focus the technological efforts. A literature survey of coal-derived fuels was completed and a NOx emissions model was developed. Flametube tests of a two-stage (rich-lean) combustor defined optimum equivalence ratios for minimizing NOx emissions. Sector combustor tests demonstrated variable air control to optimize equivalence ratios over a wide load range and steam cooling of the primary zone liner. The catalytic combustion of coal-derived fuels was demonstrated. The combustion of coal-derived gases is very promising. A hot-corrosion life prediction model was formulated and verified with laboratory testing of doped fuels. Fuel additives to control sulfur corrosion were studied. The intermittent application of barium proved effective. Advanced thermal barrier coatings were developed and tested. Coating failure modes were identified and new material formulations and fabrication parameters were specified. System studies in support of the thermal barrier coating development were accomplished.

Furman, E. R.↗

Orbital debris environment for spacecraft in low earth orbit

Modeling and measurement results used in formulating an environment model that can be used for the engineering design of spacecraft are reviewed. Earth-based and space-based sensors are analyzed and it is noted that the effects of satellite breakups can be modeled to predict a uncatalogued population, if the nature of the breakup is understood. It is observed that the telescopic data indicate that the current model is too low for sizes slightly larger than 10 cm, and may be too low for sizes between 2 cm and 10 cm, while there is an uncertainty in the current development, especially for sizes smaller than 10 cm, and at altitudes different from 500 km. Projections for the catastrophic collision rate for different growth conditions are made, emphasizing that the rate of growth of fragments will be twice the rate of intact objects.

Kessler, Donald J.↗