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NASA NTRSDate not supplied

Using Machine Learning to Infer Material Properties of Debris Fragments from X-ray Images in the DebriSat Project

The DebriSat project is a collaboration effort with the NASA Orbital Debris Program Office, the U.S. Space Force Space Systems Command Center, The Aerospace Corporation, and the University of Florida. To date, over 200,000 fragments from this ground-based, hypervelocity impact experiment have been collected, and processing is underway to determine their physical characteristics, such as material, shape, color, characteristic length, and average cross-sectional area. The x-ray process is primarily used to identify the location of the fragments and estimated size for extraction, so that these physical characteristics can be assessed. This paper proposes a machine learning-based approach to characterize materials from x-ray images of debris fragments embedded in soft-catch foam used in the DebriSat project. The novel methodology discussed in this paper will highlight the use of x-ray imagery data to characterize these fragments without extraction or a human-in-the-loop. Both supervised and unsupervised machine learning techniques are utilized with this approach to infer the physical parameters of the fragments embedded in the soft-catch foam panels used in the impact experiment based on x-ray images of the foam panels. Additionally, 3D reconstructions of the extracted fragments are created with images taken from two different angles using the structure from motion (SfM) method. The characteristic lengths and shape from the 3D reconstruction, alongside the physical characteristics of the debris, are used in the inference of the material type. To develop and test the approach, a dataset of x-ray images of debris fragments of varying sizes and materials is collected. Supervised learning methods such as convolutional neural networks (CNNs), support vector machines (SVM), decision trees, and random forest classifiers are used due to the high-dimensional feature spaces of the debris and nonlinear decision boundaries for material categorization. Given the limited pre-labeled data of embedded debris materials smaller than 10 mm, unsupervised machine learning techniques such as clustering algorithms and autoencoders are used, in addition to supervised learning methods. The clustering algorithms group similar fragments together based on their physical properties, and autoencoders reduce the dimensionality of the x ray images and extract relevant features. The performance of the proposed approach's is analyzed using a range of statistical methods, including confusion matrices, receiver operating characteristic curves, and precision-recall curves. The results are compared with those obtained using a baseline approach that relies on manual identification and classification of debris fragments. To evaluate the effectiveness of different machine learning methods, statistical tests such as t-tests, ANOVA, and cross-validation are performed, comparing the performance of CNNs, SVMs, clustering algorithms, and autoencoders. Additional analysis needs to be conducted to identify any sources of bias or variability that may affect the results, such as variations in imaging conditions or fragmentation patterns. Other topics explored are limitations, refinements, and the potential use of semi-supervised learning techniques, such as self-training to label unlabeled datasets and co-training using x-ray images taken from two different angles as two different models.

Saik Anam Siam↗
NASA NTRS2023

Using Machine Learning to Infer Material Properties of Debris Fragments from X-ray Images in the DebriSat Project

The DebriSat project is a collaboration effort with the NASA Orbital Debris Program Office, the U.S. Space Force Space Systems Command Center, The Aerospace Corporation, and the University of Florida. To date, over 200,000 fragments from this ground-based, hypervelocity impact experiment have been collected, and processing is underway to determine their physical characteristics, such as material, shape, color, characteristic length, and average cross-sectional area. The x-ray process is primarily used to identify the location of the fragments and estimated size for extraction, so that these physical characteristics can be assessed. This paper proposes a machine learning-based approach to characterize materials from x-ray images of debris fragments embedded in soft-catch foam used in the DebriSat project. The novel methodology discussed in this paper will highlight the use of x-ray imagery data to characterize these fragments without extraction or a human-in-the-loop. Both supervised and unsupervised machine learning techniques are utilized with this approach to infer the physical parameters of the fragments embedded in the soft-catch foam panels used in the impact experiment based on x-ray images of the foam panels. Additionally, 3D reconstructions of the extracted fragments are created with images taken from two different angles using the structure from motion (SfM) method. The characteristic lengths and shape from the 3D reconstruction, alongside the physical characteristics of the debris, are used in the inference of the material type. To develop and test the approach, a dataset of x-ray images of debris fragments of varying sizes and materials is collected. Supervised learning methods such as convolutional neural networks (CNNs), support vector machines (SVM), decision trees, and random forest classifiers are used due to the high-dimensional feature spaces of the debris and nonlinear decision boundaries for material categorization. Given the limited pre-labeled data of embedded debris materials smaller than 10 mm, unsupervised machine learning techniques such as clustering algorithms and autoencoders are used, in addition to supervised learning methods. The clustering algorithms group similar fragments together based on their physical properties, and autoencoders reduce the dimensionality of the x ray images and extract relevant features. The performance of the proposed approach's is analyzed using a range of statistical methods, including confusion matrices, receiver operating characteristic curves, and precision-recall curves. The results are compared with those obtained using a baseline approach that relies on manual identification and classification of debris fragments. To evaluate the effectiveness of different machine learning methods, statistical tests such as t-tests, ANOVA, and cross-validation are performed, comparing the performance of CNNs, SVMs, clustering algorithms, and autoencoders. Additional analysis needs to be conducted to identify any sources of bias or variability that may affect the results, such as variations in imaging conditions or fragmentation patterns. Other topics explored are limitations, refinements, and the potential use of semi-supervised learning techniques, such as self-training to label unlabeled datasets and co-training using x-ray images taken from two different angles as two different models.

Saik Anam Siam↗
NASA NTRS2016

Average Cross-Sectional Area of DebriSat Fragments Using Volumetrically Constructed 3D Representations

Debris fragments from the hypervelocity impact testing of DebriSat are being collected and characterized for use in updating existing satellite breakup models. One of the key parameters utilized in these models is the ballistic coefficient of the fragment which is directly related to its area‐to‐mass ratio. However, since the attitude of fragments varies during their orbital lifetime, it is customary to use the average cross‐sectional area in the calculation of the area‐to‐mass ratio. The average cross‐sectional area is defined as the average of the projected surface areas perpendicular to the direction of motion and has been shown to be equal to one‐fourth of the total surface area of a convex object. Unfortunately, numerous fragments obtained from the DebriSat experiment show significant concavity (i.e., shadowing) and thus we have explored alternate methods for computing the average cross‐sectional area of the fragments. An imaging system based on the volumetric reconstruction of a 3D object from multiple 2D photographs of the object was developed for use in determining the size characteristic (i.e., characteristics length) of the DebriSat fragments. For each fragment, the imaging system generates N number of images from varied azimuth and elevation angles and processes them using a space‐carving algorithm to construct a 3D point cloud of the fragment. This paper describes two approaches for calculating the average cross‐sectional area of debris fragments based on the 3D imager. Approach A utilizes the constructed 3D object to generate equally distributed cross‐sectional area projections and then averages them to determine the average cross‐sectional area. Approach B utilizes a weighted average of the area of the 2D photographs to directly compute the average cross‐sectional area. A comparison of the accuracy and computational needs of each approach is described as well as preliminary results of an analysis to determine the "optimal" number of images needed for the 3D imager to accurately measure the average cross sectional area of objects with known dimensions.

Scruggs, T.↗
NASA NTRSDate not supplied

Using X-Ray Computed Tomography to Catalog Rock Fragments in Apollo Drive Tube 73002

Overview: The Apollo missions collected 382 kg of rock, regolith, and core samples from six locations on the nearside of the Moon. Approximately 84% by mass of the Apollo collection remains in pristine condition within the curation facility at Johnson Space Center (i.e., never allocated, continuously stored in dry-N2 purged cabinets, exposure history restricted to Teflon, stainless steel, and Al-metal). Although most Apollo samples have been well characterized, there are several types of samples that have remained wholly or largely unstudied since their return, and/or that have been cu-rated under special conditions, e.g., frozen samples, samples stored in He-purged environment, and previously unopened drive tubes. NASA solicited proposals for the Apollo Next Generation Sample Analysis Pro-gram (ANGSA), and 9 teams were selected to study a subset of the unopened and frozen samples [1]. The first sample opened as part of the ANGSA pro-gram was drive tube 73002. This was originally a ~30 cm long, 4 cm diameter drive tube collected on a land-slide deposit near Lara Crater at the Apollo 17 landing site. It was part of a ~60 cm long double drive tube collected, and the bottom half of the tube (73001) was sealed under vacuum on the Moon [2]. Prior to opening sample 73002, the sample was imaged with a high resolution X-ray Computed Tomography (XCT) scan of the entire tube [3], which provided invaluable information during the dissection process [4]. In addition to the pre-dissection XCT scans, individual >4 mm particles were separated from the 73002 regolith during processing and scanned at high resolution by XCT. Here we pre-sent the initial lithologic classification of 134 individual >4 mm rock fragments separated from the 73002 core during the dissection process. Methodology: Drive tube 73002 was manually dissected in 0.5 cm depth intervals in three passes (Fig. 1) [4,5]. Each interval from pass 1 and 2 was sieved to <1 mm and >1 mm size fractions, and >1 mm particles were further manually subdivided into 1-2, 2-4, 4-10, and >10 mm size fractions. Pass 3 was not sieved, but >10 mm clasts were separated manually. Each 4-10 mm and >10 mm fragment was individually weighed, triply bagged in Teflon, and scanned by XCT. There are 60 rock fragments in Pass 1, 64 rock fragments in Pass 2 (from the 4-10 mm and >10 mm size fractions), and 8 rock fragments from Pass 3 (>10 mm size fraction). Each individually bagged rock fragment was scanned using the 180 kV nano-focus transmission source on the Nikon XTH 320 XCT system at NASA Johnson Space Center [6]. Scanning conditions varied considerably for individual particles, in large part be-cause of the large variation in size (0.008-19.623 g). All scans fell within the following range of scan conditions: 2.8-20.6 um voxel size; 90-155 kV voltage; 18-39 uA current; 1891-3141 projections; and 902-2000 slices. Results and Discussion: The 132 rock fragments from sample 73002 fall into the following general cat-gories: agglutinates (n = 6); basalts (13); impact melts (5); impact melt breccias (IMB; 42); regolith breccias (62); and soil breccias (4); see Figure 2 for representative examples of each lithology. Within most of these broad lithologic groups are recognizable subgroups. For example, a significant portion of regolith breccia fragments contain some agglutinate-like glass (n = 9) or are dilithologic (7) because they contain a single large clast (~50% or more by volume). Subgroups can be based on similarities to previously identified lunar lithologies, such as high-Ti basalts (9) and VLT basalts (4; Fig. 3), or based on commonly seen features within the fragments, such as poikilitic ilmenite IMB (10), ilmenite-lath IMB (12), or vesicular IMB (11) “groups”. Particles in the same “group” are not necessarily intended to be genetically related, but rather identify particles that are similar and that follow-up studies can classify in more detail [7]. Conclusion: Identification of lithologies based on XCT is a powerful tool, but a more absolute classification will sometimes require additional textural information from thin sections (e.g., glassy-matrix regolith vs. impact-melt vs. granulitic breccia) or quantitative mineral compositions (e.g., basalt vs. monomict breccia).

R A Zeigler↗
NASA NTRSDate not supplied

Analysis of Darkened Fragments Resulting from Laboratory Hypervelocity Experiments

NASA’s Orbital Debris Program Office (ODPO) relies on measurements from optical, radar, and in situ measurements to facilitate the development of data-driven orbital debris environmental engineering models such as the NASA Orbital Debris Engineering Model (ORDEM). For optical measurements, the ODPO relies on ground-based optical telescopes to statistically assess objects in geosynchronous orbit and, in the future, low Earth orbit (LEO). The data collected include the detected object’s orbital parameters, time of observation, and optical magnitude. The latter parameter can be converted to a size using NASA’s optical Size Estimation Model (oSEM). It is well known that the observed magnitude of orbital debris can vary based on an object's material constituents, observational geometry, and the effects of space weathering. To assess these magnitude variations, the ODPO uses the Optical Measurement Center (OMC) at NASA Johnson Space Center to characterize a variety of materials and fragments from laboratory impact tests representative of fragments that constitute the orbital debris population. One experiment was DebriSat: a 56 kg spacecraft was built to incorporate structural elements of a modern LEO spacecraft and was subjected to a hypervelocity impact test at the U.S. Air Force’s Arnold Engineering Development Complex using test parameters that may be encountered in LEO. The DebriSat project has provided an abundance of information for assessing fragmentation debris in terms of material, color, shape, size, density, mass, and other derived parameters. Prior to the impact test, the ODPO collected spectral measurements on a subset of the materials used to construct DebriSat for a “ground-truth” of their optical properties. After the successful hypervelocity impact test, the DebriSat team observed a fine, dark dust coating all the fragments. Prior research has suggested that this came from ablated material deposited on the fragments during the impact test, causing a change in the reflective properties [1]. Given that this lower reflectivity on the DebriSat fragments will influence the laboratory-acquired magnitudes used to calculate size and inform potential updates to the oSEM, it is critical to assess if this darkening effect on the DebriSat fragments is a laboratory bias or something that could occur in on-orbit breakup events. This paper will provide a brief overview of the OMC and DebriSat experiment, focused on the optical characterization of a subset of materials using broadband photometric measurements and spectroscopic measurements. In addition, elemental analysis of various DebriSat fragments and the soft-catch foam used in the hypervelocity experiment compared with pristine foam will be examined to further evaluate the source of the dark material coating all fragments. Finally, the authors will present a twofold plan 1) for assessing potential biases in laboratory impact experiments that could affect laboratory optical characterization and 2) for mitigating biases when compared with ground-based optical telescopic measurements of the orbital debris environment.

Heather Cowardin↗
NASA NTRSDate not supplied

Analysis of Darkened Fragments Resulting from Laboratory Hypervelocity Experiments

NASA’s Orbital Debris Program Office (ODPO) relies on measurements from optical, radar, and in situ measurements to facilitate the development of data-driven orbital debris environmental engineering models such as the NASA Orbital Debris Engineering Model (ORDEM). For optical measurements, the ODPO relies on ground-based optical telescopes to statistically assess objects in geosynchronous orbit and, in the future, low Earth orbit (LEO). The data collected include the detected object’s orbital parameters, time of observation, and optical magnitude. The latter parameter can be converted to a size using NASA’s optical Size Estimation Model (oSEM). It is well known that the observed magnitude of orbital debris can vary based on an object's material constituents, observational geometry, and the effects of space weathering. To assess these magnitude variations, the ODPO uses the Optical Measurement Center (OMC) at NASA Johnson Space Center to characterize a variety of materials and fragments from laboratory impact tests representative of fragments that constitute the orbital debris population. One experiment was DebriSat: a 56 kg spacecraft was built to incorporate structural elements of a modern LEO spacecraft and was subjected to a hypervelocity impact test at the U.S. Air Force’s Arnold Engineering Development Complex using test parameters that may be encountered in LEO. The DebriSat project has provided an abundance of information for assessing fragmentation debris in terms of material, color, shape, size, density, mass, and other derived parameters. Prior to the impact test, the ODPO collected spectral measurements on a subset of the materials used to construct DebriSat for a “ground-truth” of their optical properties. After the successful hypervelocity impact test, the DebriSat team observed a fine, dark dust coating all the fragments. Prior research has suggested that this came from ablated material deposited on the fragments during the impact test, causing a change in the reflective properties [1]. Given that this lower reflectivity on the DebriSat fragments will influence the laboratory-acquired magnitudes used to calculate size and inform potential updates to the oSEM, it is critical to assess if this darkening effect on the DebriSat fragments is a laboratory bias or something that could occur in on-orbit breakup events. This presentation will provide a brief overview of the OMC and DebriSat experiment, focused on the optical characterization of a subset of materials using broadband photometric measurements and spectroscopic measurements. In addition, elemental analysis of various DebriSat fragments and the soft-catch foam used in the hypervelocity experiment compared with pristine foam will be examined to further evaluate the source of the dark material coating all fragments. Finally, the authors will present a twofold plan 1) for assessing potential biases in laboratory impact experiments that could affect laboratory optical characterization and 2) for mitigating biases when compared with ground-based optical telescopic measurements of the orbital debris environment.

Heather Cowardin↗
NASA NTRS1977

Blade fragment energy analysis

Two classes of fan blade fragments were considered in an analysis of blade fragment energy. The first, of relatively small size (.15 pound) and energy, tends to rebound from the fan and case when liberated in an FOD encounter. These small fragments have relatively low secondary damage potential and are less demanding in terms of protection. The larger fan blade fragments are ejected in a more direct release trajectory with higher energy and hence can represent a higher potential hazard. Simplified analytical methods were used to describe blade fragment energy transfer kinematics, establish fragment energy levels, evaluate damage potential and configure protection. The approach, methodology, and application are discussed as a possible building block for other applications. Development of effective local protection using Kevlar is also discussed. Analysis methods developed and applied to the rebound fragment problem and to the large direct release fragment problem are described.

Oconnor, M. A., Jr.↗
NASA NTRS1978

Fragmentation of molecular clouds

Fragmentation is generally considered to be the initial process that a molecular cloud must undergo before stars can form. Yet its role in determining the final mass spectrum remains obscure. It appears that gravitational fragmentation, considered as a unique process, is unsatisfactory. Both fragmentation and complementary physical processes are, therefore, discussed. One of the principle aims of the discussion is to indicate how stars of solar mass (and more generally, how the initial mass spectrum of stars) can form. Attention is given to the evidence for fragmentation, opacity-limited fragmentation, magnetic flux-limited fragmentation, fragmentation induced by molecule formation and excitation, protostellar heat input, fragment coalescence, accretion, binary formation, and probabilistic theories.

Silk, J.↗
NASA NTRS1978

Chemistry and petrology of Luna 24 lithic fragments and less than 250-micron soils - Constraints on the origin of VLT mare basalts

Results are reported on a combined INAA-petrologic study of 17 small (0.2-1.5 mg) Luna 24 lithic and mineral fragments and INAA study of 5 bulk soils and mineral separates from gabbro 24170. Lithic and mineral fragments are classified into VLT mare basalts (ferrobasalt and metabasalts), low-Ti, variolitic mare basalt, gabbros, melt rock and soil breccia. Data indicate 5 possible magma types, represented by: (1) VLT ferrobasalt and gabbro fragments, with low-TiO2 (about 1%), slightly bow-shaped REE pattern, and low REE concentrations (5-10X chondritic); (2) a ferrobasalt (Laul et al., 1978) and metabasalt fragments with major and trace element contents similar to (1), but positive Eu anomalies; (3) one gabbro fragment with distinctive pyroxene compositional trend (increasing Ti with nearly constant Fe/Fe + Mg) and highest REE contents of any Luna 24 mare basaltic sample, (4) a gabbro fragment with considerably less V and Cr2O3 than ferrobasalt and metabasalt fragments; and (5) variolitic basalt fragment with higher Ti2(2.3%) than other Luna 24 basalts and pyroxene that has increasing then decreasing Ti with increasing Fe/Fe + Mg. Trace element data place constraints on the nature of the source region and possible parent magmas for the Luna 24 VLT ferrobasalt.

Ma, M.-S.↗
NASA NTRS1983

Impact and explosion crater ejecta, fragment size, and velocity

A model was developed for the mass distribution of fragments that are ejected at a given velocity for impact and explosion craters. The model is semi-empirical in nature and is derived from (1) numerical calculations of cratering and the resultant mass versus ejection velocity, (2) observed ejecta blanket particle size distributions, (3) an empirical relationship between maximum ejecta fragment size and crater diameter and an assumption on the functional form for the distribution of fragements ejected at a given velocity. This model implies that for planetary impacts into competent rock, the distribution of fragments ejected at a given velocity are nearly monodisperse, e.g., 20% of the mass of the ejecta at a given velocity contain fragments having a mass less than 0.1 times a mass of the largest fragment moving at that velocity. Using this model, the largest fragment that can be ejected from asteroids, the moon, Mars, and Earth is calculated as a function of crater diameter. In addition, the internal energy of ejecta versus ejecta velocity is found. The internal energy of fragments having velocities exceeding the escape velocity of the moon will exceed the energy required for incipient melting for solid silicates and thus, constrains the maximum ejected solid fragment size.

Okeefe, J. D.↗
NASA NTRS1992

Gross-fragmentation of meteoroids and bulk density of Geminids from photographic fireball records

The explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid moving in any actual atmosphere was published several years ago. The solution yields the theoretical relation of l, the distance flown by the meteoroid in its trajectory, as a function of time, t, assuming that the height, h, is a known function of l. The photographic records of meteors and fireballs are coded by time marks, using a rotating shutter or a similar device to break the moving image. Time is, thus, the independent variable and for each time mark on a meteoroid trajector, the observed distance along the trajectory, l sub obs, as well as the double- or multiple- station photographs of the same meteoroid. Applying this solution to all available Prairie Network (PN) fireball-records, we recognized that the majority of them gave good solutions with standard deviations somewhat bigger than the intrinsic geometrical precision of the data. We also noticed that, on an average, previous methods of evaluation of the meteoroid velocities (interpolation polynomials, numerical differenciation of the observed l sub obs) used up to only several tens of percent of the intrinsic precision of the PN observational data. When residuals of these solutions, i.e. l sub obs - l sub com, were represented as a function of time for about 75 percent of solutions. The remaining 25 percent of residuals showed systematic changes with time exceeding one standard deviation. We tried to explain these systematic time course of residuals by using different meteoroids first computed theoretically and then analyzed by the same model as the natural PN fireballs were. The conclusion of these model computations is that systematic time changes of residuals in the nonfragmenting model exceeding one standard of deviation are caused by sudden gross fragmentation at one or more trajectory points. Thus, we generalized the explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid by allowing for one or more points, where sudden gross fragmentation can occur. Using this generalized solution, the distances along the meteoroid trajectory can be computed for any choice of input parameters and compared with the observed distances flown by the meteoroid. For the most precise and long fireball trajectories, the least-squares solution can, thus, yield the initial velocities, the ablation coefficients, the dynamical masses, the positions of gross-fragmentation points, and the terminal mass. At a gross-fragmentation point, the ratio of the main mass to all the remaining fragments can be compared with the dynamic mass determined from our gross-fragmentation model and, thus, the meteoroid bulk density can be evaluated. We applied the gross-fragmentation model to sever PN fireballs showing time changes of residuals, and we recognized that, in all these cases, the new computed bulk densities of meteoroids resulted higher in comparison with the meteoroid densities determined with the non-gross-fragmentation model. Other aspects of the study are discussed.

Ceplecha, Zdenek↗
NASA NTRS1993

Alkali-granitoids as fragments within the ordinary chondrite Adzhi-Bogdo: Evidence for highly fractionated, alkali-granitic liquids on asteroids

Adzhi-Bogdo is an ordinary chondrite regolith breccia (LL3-6) that fell October 30, 1949 in Gobi Altay, Mongolia. The rock consists of submm- to cm-sized fragments embedded in a fine-grained elastic matrix. The breccia contains various types of clasts, some of which must be of foreign heritage. Based on chemical compositions of olivine some components have to be classified as L-type. Components of the breccia include chondrules, impact melts (some are K-rich, similar to those found in other LL-chondrites, highly recrystalized rock fragments ('granulites'), pyroxene-rich fragments with achondritic textures, and alkali-granitoidal fragments that mainly consist of K-feldspar and quartz or tridymite. Probably, this is the first report on granitoids from asteroids. It can be ruled out that these fragments represent huge rock assemblages of the parent body like granites do on Earth. Therefore, to avoid misunderstandings, these rocks will be designated as granitoids. In one thin section four granitoids were observed. The main phases within these clasts are K-feldspar and SiO2-phases. Minor phases include albite, Cl-apatite, whitlockite, ilmenite, zircon, Ca-poor pyroxene, and an unidentified Na,Ti-bearing silicate. Based on chemical composition and on optical properties quartz appears to be the SiO2-phase in two fragments, whereas tridymite seems to occur in the other two. The calculated formula of the unknown Na,Ti-rich silicate is very close to (Na,Ca)2.7(Fe,Mg)6(Ti)1.3(Si)7(O)24. Quartz and K-feldspar can reach sizes of up to 700 microns. Thus, the fragments can be described as coarse-grained (by chondritic standards). This is especially the case considering that quartz and K-feldspar are very rare minerals in ordinary chondrites. Representative analyses of minerals from some granitoidal clasts are given. Based on the mineral compositions and the modal abundances the bulk compositions were calculated. Besides these granitoidal rocks, pyroxene-rich fragments occur that show exsolution textures that are similar to those found in eucrites.

Bischoff, A.↗
NASA NTRS2003

Fragmentation under the Scaling Symmetry and Turbulent Cascade with Intermittency

Fragmentation plays an important role in a variety of physical, chemical, and geological processes. Examples include atomization in sprays, crushing of rocks, explosion and impact of solids, polymer degradation, etc. Although each individual action of fragmentation is a complex process, the number of these elementary actions is large. It is natural to abstract a simple 'effective' scenario of fragmentation and to represent its essential features. One of the models is the fragmentation under the scaling symmetry: each breakup action reduces the typical length of fragments, r (right arrow) alpha r, by an independent random multiplier alpha (0 < alpha < 1), which is governed by the fragmentation intensity spectrum q(alpha), integral(sup 1)(sub 0) q(alpha)d alpha = 1. This scenario has been proposed by Kolmogorov (1941), when he considered the breakup of solid carbon particle. Describing the breakup as a random discrete process, Kolmogorov stated that at latest times, such a process leads to the log-normal distribution. In Gorokhovski & Saveliev, the fragmentation under the scaling symmetry has been reviewed as a continuous evolution process with new features established. The objective of this paper is twofold. First, the paper synthesizes and completes theoretical part of Gorokhovski & Saveliev. Second, the paper shows a new application of the fragmentation theory under the scale invariance. This application concerns the turbulent cascade with intermittency. We formulate here a model describing the evolution of the velocity increment distribution along the progressively decreasing length scale. The model shows that when the turbulent length scale gets smaller, the velocity increment distribution has central growing peak and develops stretched tails. The intermittency in turbulence is manifested in the same way: large fluctuations of velocity provoke highest strain in narrow (dissipative) regions of flow.

Gorokhovski, M.↗
NASA NTRS2008

Characterization of the Catalog Fengyun-1C Fragments and Their Long-term Effect on the LEO Environment

The intentional breakup of Fengyun-1C on 11 January 2007 created the most severe orbital debris cloud in history. More than 2500 large fragments were identified and tracked by the U.S. Space Surveillance Network by the end of the year. The altitude where the event occurred was probably the worst location for a major breakup in the low Earth orbit (LEO) region, since it was already highly populated with operational satellites and debris generated from previous breakups. The addition of so many fragments not only poses a realistic threat to operational satellites in the region, but also increases the instability (i.e., collision cascade effect) of the debris population there. Preliminary analysis of the large Fengyun-1C fragments indicates that their size and area-to-mass ratio (A/M) distributions are very different from those of other known events. About half of the fragments appear to be composed of light-weight materials and more than 100 of them have A/M values exceeding 1 square meter per kilogram, consistent with thermal blanket pieces. In addition, the orbital elements of the fragments suggest nontrivial velocity gain by the fragment cloud during the impact. These important characteristics were incorporated into a numerical simulation to assess the long-term impact of the Fengyun-1C fragments to the LEO debris environment. The main objectives of the simulation were to evaluate (1) the collision probabilities between the Fengyun-1C fragments and the rest of the catalog population and (2) the collision activities and population growth in the region in the next 100 years.

Liou, J.-C.↗
NASA NTRS2013

Observations of Titan IIIC Transtage Fragmentation Debris

The fragmentation of a Titan IIIC Transtage (1968-081) on 21 February 1992 is one of only two known break-ups in or near geosynchronous orbit. The original rocket body and 24 pieces of debris are currently being tracked by the U. S. Space Surveillance Network (SSN). The rocket body (SSN# 3432) and several of the original fragments (SSN# 25000, 25001, 30000, and 33511) were observed in survey mode during 2004-2010 using the 0.6-m Michigan Orbital DEbris Survey Telescope (MODEST) in Chile using a broad R filter. This paper presents a size distribution for all calibrated magnitude data acquired on MODEST. Size distribution plots are also shown using historical models for small fragmentation debris (down to 10 cm) thought to be associated with the Titan Transtage break-up. In November 2010, visible broadband photometry (Johnson/Kron-Cousins BVRI) was acquired with the 0.9-m Small and Moderate Aperture Research Telescope System (SMARTS) at the Cerro Tololo Inter-American Observatory (CTIO) in Chile on several Titan fragments (SSN 25001, 33509, and 33510) and the parent rocket body (SSN 3432). Color index data are used to determine the fragment brightness distribution and how the data compares to spacecraft materials measured in the laboratory using similar photometric measurement techniques. In order to better characterize the break-up fragments, spectral measurements were acquired on three Titan fragments (one fragment observed over two different time periods) using the 6.5-m Magellan telescopes at Las Campanas Observatory in Chile. The telescopic spectra of SSN 25000 (May 2012 and January 2013), SSN 38690, and SSN 38699 are compared with laboratory acquired spectra of materials (e.g., aluminum and various paints) to determine the surface material.

Cowardin, Heather↗
NASA NTRS2014

A Monte Carlo Approach to Modeling the Breakup of the Space Launch System EM-1 Core Stage with an Integrated Blast and Fragment Catalogue

The Liquid Propellant Fragment Overpressure Acceleration Model (L-FOAM) is a tool developed by Bangham Engineering Incorporated (BEi) that produces a representative debris cloud from an exploding liquid-propellant launch vehicle. Here it is applied to the Core Stage (CS) of the National Aeronautics and Space Administration (NASA) Space Launch System (SLS launch vehicle). A combination of Probability Density Functions (PDF) based on empirical data from rocket accidents and applicable tests, as well as SLS specific geometry are combined in a MATLAB script to create unique fragment catalogues each time L-FOAM is run-tailored for a Monte Carlo approach for risk analysis. By accelerating the debris catalogue with the BEi blast model for liquid hydrogen / liquid oxygen explosions, the result is a fully integrated code that models the destruction of the CS at a given point in its trajectory and generates hundreds of individual fragment catalogues with initial imparted velocities. The BEi blast model provides the blast size (radius) and strength (overpressure) as probabilities based on empirical data and anchored with analytical work. The coupling of the L-FOAM catalogue with the BEi blast model is validated with a simulation of the Project PYRO S-IV destruct test. When running a Monte Carlo simulation, L-FOAM can accelerate all catalogues with the same blast (mean blast, 2 σ blast, etc.), or vary the blast size and strength based on their respective probabilities. L-FOAM then propagates these fragments until impact with the earth. Results from L-FOAM include a description of each fragment (dimensions, weight, ballistic coefficient, type and initial location on the rocket), imparted velocity from the blast, and impact data depending on user desired application. LFOAM application is for both near-field (fragment impact to escaping crew capsule) and far-field (fragment ground impact footprint) safety considerations. The user is thus able to use statistics from a Monte Carlo set of L-FOAM catalogues to quantify risk for a multitude of potential CS destruct scenarios. Examples include the effect of warning time on the survivability of an escaping crew capsule or the maximum fragment velocities generated by the ignition of leaking propellants in internal cavities.

Richardson, Erin↗
NASA NTRS2016

A Fragment-Cloud Model for Breakup of Asteroids with Varied Internal Structures

As an asteroid descends toward Earth, it deposits energy in the atmosphere through aerodynamic drag and ablation. Asteroid impact risk assessments rely on energy deposition estimates to predict blast overpressures and ground damage that may result from an airburst, such as the one that occurred over Chelyabinsk, Russia in 2013. The rates and altitudes at which energy is deposited along the entry trajectory depend upon how the bolide fragments, which in turn depends upon its internal structure and composition. In this work, we have developed an analytic asteroid fragmentation model to assess the atmospheric energy deposition of asteroids with a range of structures and compositions. The modeling approach combines successive fragmentation of larger independent pieces with aggregate debris clouds released with each fragmentation event. The model can vary the number and masses of fragments produced, the amount of mass released as debris clouds, the size-strength scaling used to increase the robustness of smaller fragments, and other parameters. The initial asteroid body can be seeded with a distribution of independent fragment sizes amid a remaining debris mass to represent loose rubble pile conglomerations, can be given an outer regolith later, or can be defined as a coherent or fractured monolith. This approach enables the model to represent a range of breakup behaviors and reproduce detailed energy deposition features such as multiple flares due to successive burst events, high-altitude regolith blow-off, or initial disruption of rubble piles followed by more energetic breakup of the constituent boulders. These capabilities provide a means to investigate sensitivities of ground damage to potential variations in asteroid structure.

Asteroid↗
NASA NTRS2016

Meteorite Falls and the Fragmentation of Meteorites

In order to understand the fragmentation of objects entering the atmosphere and why some produce more fragments than others, I have searched the Meteoritical Society database for meteorites greater than 20 kilograms that fell in the USA, China, and India. I also studied the video and film records of 21 fireballs that produced meteorites. A spreadsheet was prepared that noted smell, fireball, explosion, whistling, rumbling, the number of fragments, light, and impact sounds. Falls with large numbers of fragments were examined to look for common traits. These were: the Norton County aubrite, explosion and a flare greater than 100 fragments; the Forest City H5 chondrite explosion, a flare, a dust trail, 505 specimens; the Richardton H5 chondrite explosion and light, 71 specimens; the Juancheng H5 chondrite explosion, a rumbling, a flare, a dust trail,1000 specimens; the Tagish Lake C2 chondrite explosion, flare, dust trail, 500 specimens. I conclude that fragmentation is governed by the following: (1) Bigger meteors undergo more stress which results in more specimens; (2) Harder meteorites also require more force to break them up which will cause greater fragmentation; (3) Force and pressure are directly proportional during falls. General observations made were; (1) Meteorites produce fireballs sooner due to high friction; (2) Meteors tend to explode as well because of high stress; (3) Softer meteorites tend to cause dust trails; (4) Some falls produce light as they fall at high velocity. I am grateful to NASA Ames for this opportunity and Derek Sears, Katie Bryson, and Dan Ostrowski for discussions.

fragmentations↗