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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The application of satellite data to study the effects of latent heat release on cyclones

Generalized energetics were studied for nonlinear inviscid symmetric instability (SI). It was found that the linear theory fails to predict the stability in certain cases where the basic state is transitional between stability and instability. The initial growth of the SI perturbations can be fairly well approximated by linear theory, but the long time nonlinear evaluations will be bonded energetically if the SI region is finite. However, a further extension of the energetics to conditional symmetric instability (CSI) shows that the nonlinear evolution of circulation will energetically depend much more on the precipitation in a complicated way. By treating the latent heat as a source which is implicitly related to the motion field, the existence, uniqueness and stability of steady viscous (CSI) circulations are studied. Viscous CSI circulations are proved to be unique and asymptotically stable when the heat sources are weak and less sensitive to the motion perturbations. By considering the fact that moist updrafts are narrow and using eddy viscosity of 0(1,000 m squared/s) the stability criterion suggests that some frontal rainbands were probably dominated by the CSI mechanism even in their mature quasi-steady stage.

Clark, J. H. E.↗
NASA NTRS1986

Scientific investigations at a lunar base

Studies of lunar origin and history, astronomy, and applications of lunar environmental conditions to experiments in physics and chemistry are examined to gain some insight into their control over site selection and base characteristics. Lunar studies most likely will be distinguished by needs for surface mobility and laboratory support; astronomy will require initial construction and servicing by crews on a sporadic basis; physics and chemistry experiments will require complex facilities and the ability to support a research staff and supporting laboratory and fabrication shop facilities. Lunar bases dominated by lunar investigations will be sited relatively near important lunar geological features. Astronomical facilities may require access to the lunar limb or poles. Physics and chemistry facilities are probably not strongly tied to the specific base locations.

Duke, M. B.↗
NASA NTRS1996

Self-Consistent Simulation of the Brownian Stage of Dust Growth

It is a widely accepted view that in proto-planetary accretion disks the collision and following sticking of dust particles embedded in the gas eventually leads to the formation of planetesimals (coagulation). For the smallest dust grains, Brownian motion is assumed to be the dominant source of their relative velocities leading to collisions between these dust grains. As the dust grains grow they eventually couple to the turbulent motion of the gas which then drives the coagulation much more efficiently. Many numerical coagulation simulations have been carried out to calculate the fractal dimension of the aggregates, which determines the duration of the ineffective Brownian stage of growth. Predominantly on-lattice and off-lattice methods were used. However, both methods require simplification of the astrophysical conditions. The aggregates found by those methods had a fractal dimension of approximately 2 which is equivalent to a constant, mass-independent friction time. If this value were valid for the conditions in an accretion disk, this would mean that the coagulation process would finally 'freeze out' and the growth of a planetesimal would be impossible within the lifetime of an accretion disk. In order to investigate whether this fractal dimension is model independent, we simulate self-consistently the Brownian stage of the coagulation by an N-particle code. This method has the advantage that no further assumptions about homogeneity of the dust have to be made. In our model, the dust grains are considered as aggregates built up of spheres. The equation of motion of the dust grains is based on the probability density for the diffusive transport within the gas atmosphere. Because of the very low number density of the dust grains, only 2-body-collisions have to be considered. As the Brownian stage of growth is very inefficient, the system is to be simulated over long periods of time. In order to find close particle pairs of the system which are most likely to undergo a collision, we use a particle-in-cell (PIC) method for the early stages of the simulation where the system is still very homogeneous and a tree method later when the particles are more clustered.

Kempf, S.↗
NASA NTRS2008

Summertime Coincident Observations of Ice Water Path in the Visible/Near-IR, Radar, and Microwave Frequencies

Accurate representation of the physical and radiative properties of clouds in climate models continues to be a challenge. At present, both remote sensing observations and modeling of microphysical properties of clouds rely heavily on parameterizations or assumptions on particle size distribution (PSD) and cloud phase. In this study, we compare Ice Water Path (IWP), an important physical and radiative property that provides the amount of ice present in a cloud column, using measurements obtained via three different retrieval strategies. The datasets we use in this study include Visible/Near-IR IWP from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument flying aboard the Aqua satellite, Radar-only IWP from the CloudSat instrument operating at 94 GHz, and NOAA/NESDIS operational IWP from the 89 and 157 GHz channels of the Microwave Humidity Sounder (MHS) instrument flying aboard the NOAA-18 satellite. In the Visible/Near-IR, IWP is derived from observations of optical thickness and effective radius. CloudSat IWP is determined from measurements of cloud backscatter and assumed PSD. MHS IWP retrievals depend on scattering measurements at two different, non-water absorbing channels, 89 and 157 GHz. In order to compare IWP obtained from these different techniques and collected at different vertical and horizontal resolutions, we examine summertime cases in the tropics (30S - 30N) when all 3 satellites are within 4 minutes of each other (approximately 1500 km). All measurements are then gridded to a common 15 km x 15 km box determined by MHS. In a grid box comparison, we find CloudSat to report the highest IWP followed by MODIS, followed by MHS. In a statistical comparison, probability density distributions show MHS with the highest frequencies at IWP of 100-1000 g/m(exp 2) and CloudSat with the longest tail reporting IWP of several thousands g/m(exp 2). For IWP greater than 30 g/m(exp 2), MODIS is consistently higher than CloudSat, and it is higher at the lower IWPs but lower at the higher IWPs that overlap with MHS. Some of these differences can be attributed to the limitations of the measuring techniques themselves, but some can result from the assumptions made in the algorithms that generate the IWP product. We investigate this issue by creating categories based on various conditions such as cloud type, precipitation presence, underlying liquid water content, and surface type (land vs. ocean) and by comparing the performance of the IWP products under each condition.

Pittman, Jasna V.↗
NASA NTRS2009

Heating of the Solar Corona and its Loops

At several million degrees, the solar corona is more than two orders of magnitude hotter than the underlying solar surface. The reason for these extreme conditions has been a puzzle for decades and is considered one of the fundamental problems in astrophysics. Much of the coronal plasma is organized by the magnetic field into arch-like structures called loops. Recent observational and theoretical advances have led to great progress in understanding the nature of these loops. In particular, we now believe they are bundles of unresolved magnetic strands that are heated by storms of impulsive energy bursts called nanoflares. Turbulent convection at the solar surface shuffles the footpoints of the strands and causes them to become tangled. A nanoflare occurs when the magnetic stresses reach a critical threshold, probably by way of a mechanism called the secondary instability. I will describe our current state of knowledge concerning the corona, its loops, and how they are heated.

Klimchuk, James A.↗
NASA NTRS2010

Analysis of Flight Management System Predictions of Idle-Thrust Descents

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the predictor and its uncertainty models, descents from cruise to the meter fix were executed using vertical navigation in a B737-700 simulator and a B777-200 simulator, both with commercial FMSs. For both aircraft types, the FMS computed the intended descent path for a specified speed profile assuming idle thrust after top of descent (TOD), and then it controlled the avionics without human intervention. The test matrix varied aircraft weight, descent speed, and wind conditions. The first analysis in this paper determined the effect of the test matrix parameters on the FMS computation of TOD location, and it compared the results to those for the current ground predictor in the Efficient Descent Advisor (EDA). The second analysis was similar but considered the time to fly a specified distance to the meter fix. The effects of the test matrix variables together with the accuracy requirements for the predictor will determine the allowable error for the predictor inputs. For the B737, the EDA prediction of meter fix crossing time agreed well with the FMS; but its prediction of TOD location probably was not sufficiently accurate to enable idle-thrust descents in congested airspace, even though the FMS and EDA gave similar shapes for TOD location as a function of the test matrix variables. For the B777, the FMS and EDA gave different shapes for the TOD location function, and the EDA prediction of the TOD location is not accurate enough to fully enable the concept. Furthermore, the differences between the FMS and EDA predictions of meter fix crossing time for the B777 indicated that at least one of them was not sufficiently accurate.

Stell, Laurel↗
NASA NTRS1989

A simple, mass balance model of carbon flow in a controlled ecological life support system

Internal cycling of chemical elements is a fundamental aspect of a Controlled Ecological Life Support System (CELSS). Mathematical models are useful tools for evaluating fluxes and reservoirs of elements associated with potential CELSS configurations. A simple mass balance model of carbon flow in CELSS was developed based on data from the CELSS Breadboard project at Kennedy Space Center. All carbon reservoirs and fluxes were calculated based on steady state conditions and modelled using linear, donor-controlled transfer coefficients. The linear expression of photosynthetic flux was replaced with Michaelis-Menten kinetics based on dynamical analysis of the model which found that the latter produced more adequate model output. Sensitivity analysis of the model indicated that accurate determination of the maximum rate of gross primary production is critical to the development of an accurate model of carbon flow. Atmospheric carbon dioxide was particularly sensitive to changes in photosynthetic rate. The small reservoir of CO2 relative to large CO2 fluxes increases the potential for volatility in CO2 concentration. Feedback control mechanisms regulating CO2 concentration will probably be necessary in a CELSS to reduce this system instability.

Garland, Jay L.↗
NASA NTRS1994

An X-ray and optical study of the supernova remnant W44

We report the results of a 8000 s observation of the supernova remnant W44 using the ROSAT Position Sensitive Proportional Counter (PSPC). The image shows the same centrally peaked morphology observed by the Einstein IPC and contrasts with the shell-like radio morphology. The eastern limb shows a lack of X-ray emission within the radio shell, probably due to the interaction between the Supernova Remnants (SNR) and a molecular cloud. No counterpart to the pulsar 1853 + 01 in W44 has been detected, with L(sub X) less than 1.3 x 10(exp 32) ergs/s in the 0.2 to 2.4 keV band. The spectral analysis of the central part of W44, combining EXOSAT ME and Einstein SSS data, shows that the shocked plasma has not reached ionization equilibrium. The best nonequilibrium fit to PSPC, ME, and SSS spectra gives Eta = 10(exp 51) ergs cm(exp -6), T(sub s) = 10(exp 7) K with T(sub e) = T(sub i), suggesting conditions are approaching ionization equilibrium. There is no evidence of enhanced abundances of Mg, Si, S, or Fe. The variation of temperature and column density was obtained region by region using the PSPC and Einstein IPC. The temperature is largely uniform over the remnant, but strong column density variations are found to be consistent with molecular clouds in the line of sight. An evaporation model with a two-phase interstellar medium structure of clumps and interclump gas (White & Long 1991) can explain the X-ray centrally peaked morphology of W44. The clumps remaining behind a SN shock provide a reservoir of material, and evaporat e to increase the density of X-ray emitting gas in the interior of a SNR. The uniform temperature distribution of W44 strongly supports the predictions of this model. In addition, mosaiced H alpha and (S II) images of W44, taken using the prime focus universal extragalactic instrument (PFUEI) camera on the Palomar 60 sec telescope, reveal the first discovery of optical filaments (both H alpha and (S II)) in the northwestern and southeastern portion of the remnant, within the X-ray emitting region. The optical filaments and the X-ray image showing locally brighter emission and clumps along the filaments suggest both are produced by the interaction between the supernova shock front and regions of enhanced ambient density.

Rho, Jeongee↗
NASA NTRS2003

Carbon-Nitrogen-Oxygen Line Radiation and the X-ray Bowen Fluorescence Mechanism in Optically Thick, Highly Ionized Media

Radiative transfer effects due to overlapping X-ray lines in a high-temperature, optically thick, highly ionized medium are investigated. One particular example, in which the O VIII Lyalpha doublet (2(sup 2) P(sub 1/2,3/2)-1(sup 2) S(sub 1/2) coincides in frequency with the N VII Lyzeta lines (7(sup 2) P(sub 1/2,3/2)-1(sup 2) S(sub 1/2) is studied in detail to illustrate the effects on the properties of the emergent line spectrum. We solve the radiative transfer equation to study the energy transport of resonance-line radiation in a static, infinite, plane-parallel geometry, which is used to compute the destruction/escape probabilities for each of the lines for various total optical thicknesses of the medium, as well as destruction probabilities by sources of underlying photoelectric opacity. It is found that a large fraction of the O vIII Lyalpha line radiation can be destroyed by N VII, which can result in a reversal of the O VIII Lyalpha/N VII Lyalpha line intensity ratio similar to what may be seen under nonsolar abundances. Photoelectric absorption by ionized carbon and nitrogen can also subsequently increase the emission-line intensities of these ions. We show that line ratios, which are directly proportional to the abundance ratios in optically thin plasmas, are not good indicators of the true CNO abundances. Conversely, global spectral modeling that assumes optically thin conditions may yield incorrect abundance estimates when compared with observations, especially if the optical depth is large. Other potentially important overlapping lines and continua in the X-ray band are also identified, and their possible relevance to recent high-resolution spectroscopic observations with Chandra and XMM-Newton are briefly discussed.

Sako, Masao↗
NASA NTRS2012

An Initial Examination for Verifying Separation Algorithms by Simulation

An open question in algorithms for aircraft is what can be validated by simulation where the simulation shows that the probability of undesirable events is below some given level at some confidence level. The problem is including enough realism to be convincing while retaining enough efficiency to run the large number of trials needed for high confidence. The paper first proposes a goal based on the number of flights per year in several regions. The paper examines the probabilistic interpretation of this goal and computes the number of trials needed to establish it at an equivalent confidence level. Since any simulation is likely to consider the algorithms for only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. This paper is an initial effort, and as such, it considers separation maneuvers, which are elementary but include numerous aspects of aircraft behavior. The scenario includes decisions under uncertainty since the position of each aircraft is only known to the other by broadcasting where GPS believes each aircraft to be (ADS-B). Each aircraft operates under feedback control with perturbations. It is shown that a scenario three or four orders of magnitude more complex is feasible. The question of what can be validated by simulation remains open, but there is reason to be optimistic.

White, Allan L.↗
NASA NTRS1993

Dynamic of Langmuir and Ion-Sound Waves in Type 3 Solar Radio Sources

The evolution of Langmuir and ion-sound waves in type 3 sources is investigated, incorporating linear growth, linear damping, and nonlinear electrostatic decay. Improved estimates are obtained for the wavenumber range of growing waves and the nonlinear coupling coefficient for the decay process. The resulting prediction for the electrostatic decay threshold is consistent with the observed high-field cutoff in the Langmuir field distribution. It is shown that the conditions in the solar wind do not allow a steady state to be attained; rather, bursty linear and nonlinear interactions take place, consistent with the highly inhomogeneous and impulsive waves actually observed. Nonlinear growth is found to be fast enough to saturate the growth of the parent Langmuir waves in the available interaction time. The resulting levels of product Langmuir and ion-sound waves are estimated theoretically and shown to be consistent with in situ ISEE 3 observations of type 3 events at 1 AU. Nonlinear interactions slave the growth and decay of product sound waves to that of the product Langmuir waves. The resulting probability distribution of ion-sound field strengths is predicted to have a flat tail extending to a high-field cutoff. This prediction is consistent with statistics derived here from ISEE 3 observations. Agreement is also found between the frequencies of the observed waves and predictions for the product S waves. The competing processes of nonlinear wave collapse and quasilinear relaxation are discussed, and it is concluded that neither is responsible for the saturation of Langmuir growth. When wave and beam inhomogeneities are accounted for, arguments from quasi-linear relaxation yield an upper bound on the Langmuir fields that is too high to be relevant. Nor are the criteria for direct wave collapse of the beam-driven waves met, consistent with earlier simulation results that imply that this process is not responsible for saturation of the beam instability. Indeed, even if the highest observed Langmuir fields are assumed to he part of a long-wavelength 'condensate' produced via electrostatic decay, they still fall short of the relevant requirements for wave collapse. The most stringent requirement for collapse is that collapsing wave packets not be disrupted by ambient density fluctuations in the solar wind. Fields of several mV m(exp -1) extending over several hundred km would be needed to satisfy this requirement; at 1 AU such fields are rare at best.

Robinson, P. A.↗
NASA NTRS2001

Transient Reliability Analysis Capability Developed for CARES/Life

The CARES/Life software developed at the NASA Glenn Research Center provides a general-purpose design tool that predicts the probability of the failure of a ceramic component as a function of its time in service. This award-winning software has been widely used by U.S. industry to establish the reliability and life of a brittle material (e.g., ceramic, intermetallic, and graphite) structures in a wide variety of 21st century applications.Present capabilities of the NASA CARES/Life code include probabilistic life prediction of ceramic components subjected to fast fracture, slow crack growth (stress corrosion), and cyclic fatigue failure modes. Currently, this code can compute the time-dependent reliability of ceramic structures subjected to simple time-dependent loading. For example, in slow crack growth failure conditions CARES/Life can handle sustained and linearly increasing time-dependent loads, whereas in cyclic fatigue applications various types of repetitive constant-amplitude loads can be accounted for. However, in real applications applied loads are rarely that simple but vary with time in more complex ways such as engine startup, shutdown, and dynamic and vibrational loads. In addition, when a given component is subjected to transient environmental and or thermal conditions, the material properties also vary with time. A methodology has now been developed to allow the CARES/Life computer code to perform reliability analysis of ceramic components undergoing transient thermal and mechanical loading. This means that CARES/Life will be able to analyze finite element models of ceramic components that simulate dynamic engine operating conditions. The methodology developed is generalized to account for material property variation (on strength distribution and fatigue) as a function of temperature. This allows CARES/Life to analyze components undergoing rapid temperature change in other words, components undergoing thermal shock. In addition, the capability has been developed to perform reliability analysis for components that undergo proof testing involving transient loads. This methodology was developed for environmentally assisted crack growth (crack growth as a function of time and loading), but it will be extended to account for cyclic fatigue (crack growth as a function of load cycles) as well.

Nemeth, Noel N.↗
NASA NTRS2007

Improved High-Voltage Gas Isolator for Ion Thruster

A report describes an improved high-voltage isolator for preventing electrical discharge along the flow path of a propellant gas being fed from a supply at a spacecraft chassis electrical potential to an ion thruster at a potential as high as multiple kilovolts. The isolator must survive launch vibration and must remain electrically nonconductive for thousands of hours under conditions that, in the absence of proper design, would cause formation of electrically conductive sputtered metal, carbon, and/or decomposed hydrocarbons on its surfaces. The isolator includes an alumina cylinder containing a spiral channel filled with a porous medium made from alumina microbeads fired together with an alumina slurry. Connections to gas-transport tubes are made at both ends of the alumina cylinder by means of metal caps containing fine-mesh screens to prevent passage of loose alumina particles. The outer surface of the alumina cylinder is convoluted to lengthen the electrical path between the metal caps and to afford shadow shielding to minimize the probability of formation of a continuous deposit that would electrically connect the ends. A flanged cylindrical metal cap that surrounds the alumina cylinder without touching one of the ends provides additional shadow shielding.

Banks, Bruce↗
NASA NTRS1990

Numerical simulations of the rebound shock model for solar spicules

Using time-dependent numerical simulations, the proposed rebound shock mechanism for spicules has been examined. At temperatures above a critical value, T(c), the radiation is characteristic of the conditions in the optically thin corona and near optically thin transition region. When T less than T(c), the atmosphere has a radiative cooling time, tau(rad) characteristic of chromosphere. The spicule is initiated with a quasi-impulsive force in the low chromosphere, which drives a train of upward propagating rebound shocks along the rigid magnetic flux tube. These shocks then move the transition region upward. The material below the displaced transition region has temperatures and densities similar to those of spicules when T(c) = 20,000 K or more and tau(rad) = 500 s or more, but not when T(c) = 10,000 K, and probably not when tau(rad) = 100 s. For all the cases where the cross sectional area diverges rapidly with height, the upward velocity of the transition region is less than that of spicules. Moreover, the maximum height is less than that of average spicules. Taller, higher velocity spicules result when the magnetic field cross sectional area is constant. In all cases, the rebound shock mechanism produces substantial motions and temperature and density variations in chromospheric and transition region material. It is suggested that this may be a partial explanation for the continuous dynamic state of the lower solar atmosphere.

Sterling, Alphonse C.↗
NASA NTRS1994

Shock recovery analogs and the origin of mesosiderites

The origin of mesosiderites, which consist of approximately equal-weight proportions of Fe-Ni metal and silicates (gabbros, basalts, orthopyroxenites, dunites), remains an interesting and complex problem in meteoritics. There is general agreement that multiple impact events were probably involved in the formation of these brecciated stony-iron meteorites, but given the heterogeneity of mesosiderites, additional processes have been invoked to explain the unique and intricate textural and compositional makeup of mesosiderites. We conducted a series of shock recovery experiments to test the impact event(s) scenario. The results indicated significant similarities between the shocked analogs and many mesosiderites. We have compared our analogs with a suite of thin sections of Barea mesosiderite. I have conducted a series of flash heating experiments in which equal-weight proportions of gabbro and stainless steel (SS304) powders were compressed into small charges and heated under reducing conditions for short times. These experiments were used to bracket localized, peak postshock temperatures in our analog shots and to compare the mixing relations between the silicate and metal. The shock recovery experiments used porous metal-silicate powder starting mixtures, therefore our experiments are most analogous to an impact scenario where the target is an asteroidal regolith surface composed of a loose mixture of Fe-Ni metal and heterogeneous silicates. Analog experiments may really describe a secondary impact process similar to the late-stage, localized impact melting event. This leaves one of the crucial questions about mesosiderite genesis unanswered, namely what is the source of the Fe-Ni metal that is so intimately distributed in these meteorites?

Rowan, L. R.↗
NASA NTRS1993

The response of the high-latitude dayside ionosphere to an abrupt northward transition in the IMF

We examine the response of the high-latitude ionosphere in the prenoon sector to a northward turning of the IMF. The event was observed in the 11-13 UT interval on June 1, 1987, in the course of a multiday SUNDIAL campaign. The transition in the IMF was observed by the IMP-8 satellite which was located upstream of the earth at a distance of 36 Re. The ionospheric response in the 70-80 deg invariant latitude interval was monitored by two radars. The preexisting plasma convection observed by the radars exhibited large velocities (500-1000 m/s) and stable longterm trends, consistent with the inertial rotation of the convection pattern expected of the conditions then prevailing, B(z) less than 0, B(y) greater than 0. The plasma flow rapidly abated in response to the IMF transition. The electron density measurements made by radar in the meridional plane showed that the ionosphere had been rich in structure with the active deposition of ionization by particle precipitation. Subsequently it resembled an inactive, unstructured mid-latitude configuration. There was a dramatic decrease in the amount of backscatter observed by the HF radar. We analyze the times of transition in the various data sets and show that the ionosphere began to show the effects of the IMF transition about 2 min after its probable arrival at the magnetopause boundary.

Ruohoniemi, J. M.↗
NASA NTRS2008

Investigation of Flow Instabilities in the Inlet Ducts of DP-1C VTOL Aircraft

An investigation of flow instabilities in the inlet ducts of a two-engine vertical takeoff and landing aircraft DP-1C is described in this report. Recent tests revealed that the engines stall during run ups while the aircraft is operating on the ground. These pop stalls occurred at relatively low power levels, sometimes as low as 60 percent of the engine full speed. Inability to run the engines up to the full speed level is attributed to in-ground effects associated with hot gas ingestion. Such pop stalls were never experienced when the aircraft was tested on a elevated grid platform, which ensured that the aircraft was operating in out-of-the-ground-effect conditions. Based on available information on problems experienced with other vertical takeoff and landing aircraft designs, it was assumed that the engine stalls were caused by partial ingestion of hot gases streaming forward from the main exit nozzle under the aircraft inlets, which are very close to the ground. It was also suggested that the nose wheel undercarriage, located between the inlets, may generate vortices or an unstable wake causing intense mixing of hot exit gases with incoming inlet flow, which would enhance the hot gas ingestion. After running a short three-day series of tests with fully instrumented engine inlets, it is now believed the most probable reason for engine pop stalls are random ingestions of a vortex generated between the two streams moving in opposite directions: outbound hot gas stream from the main nozzle close to the ground and inbound inlet flow above. Originally, the vortex is in a horizontal plane. However, at a certain velocity ratio of these two streams, the vortex attaches either to the ground or the aircraft surface at one end and the other end is swallowed by one of the aircraft inlets. Once the vortex enters the inlet duct, a puff of hot air can be sucked through the vortex core into the engine, which causes a serious inlet flow field distortion followed by an engine stall. Once the engine stalls, the outflow from the inlet pushes the vortex away and the engine resumes normal operation. This hypothesis needs to be verified experimentally; e.g., by extensive smoke flow visualization ahead of the aircraft inlets.

Lepicovsky, Jan↗
NASA NTRS2008

Statistical Issues for Uncontrolled Reentry Hazards

A number of statistical tools have been developed over the years for assessing the risk of reentering objects to human populations. These tools make use of the characteristics (e.g., mass, shape, size) of debris that are predicted by aerothermal models to survive reentry. The statistical tools use this information to compute the probability that one or more of the surviving debris might hit a person on the ground and cause one or more casualties. The statistical portion of the analysis relies on a number of assumptions about how the debris footprint and the human population are distributed in latitude and longitude, and how to use that information to arrive at realistic risk numbers. This inevitably involves assumptions that simplify the problem and make it tractable, but it is often difficult to test the accuracy and applicability of these assumptions. This paper looks at a number of these theoretical assumptions, examining the mathematical basis for the hazard calculations, and outlining the conditions under which the simplifying assumptions hold. In addition, this paper will also outline some new tools for assessing ground hazard risk in useful ways. Also, this study is able to make use of a database of known uncontrolled reentry locations measured by the United States Department of Defense. By using data from objects that were in orbit more than 30 days before reentry, sufficient time is allowed for the orbital parameters to be randomized in the way the models are designed to compute. The predicted ground footprint distributions of these objects are based on the theory that their orbits behave basically like simple Kepler orbits. However, there are a number of factors - including the effects of gravitational harmonics, the effects of the Earth's equatorial bulge on the atmosphere, and the rotation of the Earth and atmosphere - that could cause them to diverge from simple Kepler orbit behavior and change the ground footprints. The measured latitude and longitude distributions of these objects provide data that can be directly compared with the predicted distributions, providing a fundamental empirical test of the model assumptions.

Matney, Mark↗