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246 records · Page 14

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

McKinley, David P.↗

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 (Goddard Earth Model, 36x36 spherical harmonic field) were employed toward application of this technique for gravity field parameters. Also, GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized here. The method employs subset solutions of the data associated with the complete solution and uses an algorithm to adjust the data weights by requiring the differences of parameters between solutions to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting as compared to the nominal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, F. J.↗

BATSE Observations of the Large-Scale Isotropy of Gamma-Ray Bursts

We use dipole and quadrupole statistics to test the large-scale isotropy of the first 1005 gamma-ray bursts observed by the Burst and Transient Source Experiment (BATSE). In addition to the entire sample of 1005 gamma-ray bursts, many subsets are examined. We use a variety of dipole and quadrupole statistics to search for Galactic and other predicted anisotropies and for anisotropies in a coordinate-system independent manner. We find the gamma-ray burst locations to be consistent with isotropy, e.g., for the total sample the observed Galactic dipole moment (cos theta) differs from the value predicted for isotropy by 0.9 sigma and the observed Galactic quadrupole moment (sin(exp 2) b - 1/3) by 0.3 sigma. We estimate for various models the anisotropies that could have been detected. If one-half of the locations were within 86 deg of the Galactic center, or within 28 deg of the Galactic plane, the ensuing dipole or quadrupole moment would have typically been detected at the 99% confidence level. We compare the observations with the dipole and quadrupole moments of various Galactic models. Several Galactic gamma-ray bursts models have moments within 2 sigma of the observations; most of the Galactic models proposed to date are no longer in acceptable agreement with the data. Although a spherical dark matter halo distribution could be consistent with the data, the required core radius is larger than the core radius of the dark matter halo used to explain the Galaxy's rotation curve. Gamma-ray bursts are much more isotropic than any observed Galactic population, strongly favoring but not requiring an origin at cosmological distances.

Briggs, Michael S.↗

Novel white light-emitting CdSe:Mn 2+ synthesized by photo-assisted chemical bath deposition

Nowadays, white light-emitting materials have attracted extensive research due to their potential applications in lighting devices and displaying images. Several semiconductor nanoparticles have been explored to achieve efficient white light emission. In this work, we report on novel white light-emitting CdSe:Mn 2+ thin films synthesized by photo-assisted chemical bath deposition. The effect of varying the Mn 2+ ion concentrations on the thin film structure, morphology, and optical properties was investigated. X-ray powder diffraction results indicated that all the films annealed at 250 degrees C possessed a cubic structure, with crystallite sizes in the range of 1-130 nm. Scanning electron microscopy demonstrated spherical nanoparticles with no significant changes with varying Mn 2+ doping concentrations. Energy dispersive X-ray spectroscopy confirmed the presence of the anticipated elements. The atomic force microscope revealed that the surface roughness has decreased with an increase in Mn 2+ ion concentrations but decreased for 0.7 %Mn 2+ . The UV-Vis absorption spectra showed absorption edges around 600-650 nm. Photoluminescence emission spectra excited at 3.8 eV (325 nm) showed emission bands at around 1.75 eV (709 nm), and 1.88 eV (659 nm), which were attributed to the band-to-band emission, and 4 T 1 ( 4 G)-> 6 A 1 ( 6 S) transitions of Mn 2+ ions, respectively, while emission bands at 2.35 eV (528 nm), and prominent at 3.17 eV (391 nm) were due to the glass substrate. The temperature-dependent luminescence showed a decrease in relative emission intensity with the increase in the operating temperature. The chromaticity colour coordinates showed white light-emitting thin films. These present findings open a new door to developing white light using CdSe thin films.

36 MATERIALS SCIENCE↗

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical modeling of flame-balls in fuel-air mixtures

At low gravity, when buoyancy effects are small, flame-balls can be generated. These are stationary spherical structures whose existence appears to require a near-limit mixture, a small Lewis number and heat losses from radiation. It is our goal to combine computational modeling with existing experimental and theoretical studies (NASA) of these structures so that an improved understanding of flammability limits and near-limit phenomena will occur. The question of flammability limits is of fundamental importance and has long been examined. It is of great practical importance to predict, from first principles, a limit mixture strength that agrees with experimental values for the configuration at hand. Flame-balls provide an excellent configuration in which convective losses can be eliminated and the resulting stable solutions are produced from a diffusive, reactive and radiative balance. Although analytical modeling provides convincing evidence that the key physical ingredients of flame-balls have been identified, quantitative confirmation can only come from detailed numerical simulations. Our goal is to predict theoretically the mass fractions of the species and the temperature as functions of the independent coordinate r.

Smooke, Mitchell D.↗

The 3-D world modeling with updating capability based on combinatorial geometry

A 3-D world modeling technique using range data is discribed. Range data quantify the distances from the sensor focal plane to the object surface, i.e., the 3-D coordinates of discrete points on the object surface are known. The approach proposed herein for 3-D world modeling is based on the Combinatorial Geometry (CG) method which is widely used in Monte Carlo particle transport calculations. First, each measured point on the object surface is surrounded by a small sphere with a radius determined by the range to that point. Then, the 3-D shapes of the visible surfaces are obtained by taking the (Boolean) union of all the spheres. The result is an unambiguous representation of the object's boundary surfaces. The pre-learned partial knowledge of the environment can be also represented using the CG Method with a relatively small amount of data. Using the CG type of representation, distances in desired directions to boundary surfaces of various objects are efficiently calculated. This feature is particularly useful for continuously verifying the world model against the data provided by a range finder, and for integrating range data from successive locations of the robot during motion. The efficiency of the proposed approach is illustrated by simulations of a spherical robot in a 3-D room in the presence of moving obstacles and inadequate prelearned partial knowledge of the environment.

Goldstein, M.↗

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Roberts, G. O.↗

Effects of negative triangularity on microinstabilities in a low-recycling lithium-wall spherical tokamak

In this work, we present a linear gyrokinetic study of the impact of negative triangularity (NT) on microinstabilities in the Lithium Tokamak eXperiment-β (LTX-β), a low-recycling spherical tokamak with liquid lithium plasma-facing components that produce flat electron-temperature profiles [Elliott et al., IEEE Trans. Plasma Sci. 48, 1382 (2020)]. While NT is widely recognized as a stabilizing mechanism and often associated with improved confinement in conventional tokamaks, this study reveals that its effect is not universally stabilizing in the parameter regime of LTX-β and is shown to be highly sensitive to local equilibria. Using local linear simulations with the GS2 code [Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)] at ρ=0.3, 0.5, and 0.8 for two representative discharges (#103955 and #109355), and employing the Miller equilibrium model to isolate shaping effects, we find that NT can transition from stabilizing to destabilizing depending on magnetic shear, safety factor, and electron-temperature gradient. In shot #103955, NT reduces growth rates across radii, with strongest stabilization at the edge, whereas in shot #109355, it is stabilizing in the core but destabilizing at mid-radius and edge under experimental conditions. Parametric scans show that flattening the electron-temperature profile, increasing magnetic shear, and reducing the safety factor recover NT stabilization. These results demonstrate that NT stabilization is tunable rather than intrinsic and requires coordinated control of magnetic geometry and gradient drive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗

Toward Realistic Dynamics of Rotating Orbital Debris, and Implications for Lightcurve Interpretation

Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation state has a large component of initial angular velocity directed along the intermediate axis of inertia, leading to large angular reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study. However, effects of internal friction and solar radiation are likely to cause significant modification of rotation states within a time as short as a few orbital periods. In order to examine the rotational dynamics of debris objects under the influences of these effects, a set of seven first-order coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are a four-dimensional extension of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation in terms of spherical harmonics, and terms representing effects of a prescribed rate of internal friction. Numerical integrations of these equations of motion are being performed, and results will be presented. Initial tests show that internal friction without solar radiation torque leads to rotation about the maximum principal axis of inertia, as required, and solar radiation torque is expected to lead to spin-up of objects. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction is expected to lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the same on phase angle. At a given phase angle, databases are generated which contain reflected intensities for comprehensive sets of equally-likely orientations, represented as unit quaternions. When projected onto three dimensions (S2) and color-coded by intensity, the set is depicted as points within a solid, semi-transparent unit sphere, within which all possible reflected intensities for an object at a given phase angle may be inspected simultaneously. Rotational sequences are represented by trajectories through the sphere. Databases are generated for each of a set of phase angles separately, forming a comprehensive dataset of reflected intensities spanning all object orientations and solar phase angles. Symmetries in the problem suggest that preferred rotation states are likely, defined relative to the object-sun direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem.

Ojakangas, Gregory W.↗

Greenhouse Gas Concentration Data Recovery Algorithm for a Low Cost, Laser Heterodyne Radiometer

The goal of a coordinated effort between groups at GWU and NASA GSFC is the development of a low-cost, global, surface instrument network that continuously monitors three key carbon cycle gases in the atmospheric column: carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), as well as oxygen (O2) for atmospheric pressure profiles. The network will implement a low-cost, miniaturized, laser heterodyne radiometer (mini-LHR) that has recently been developed at NASA Goddard Space Flight Center. This mini-LHR is designed to operate in tandem with the passive aerosol sensor currently used in AERONET (a well established network of more than 450 ground aerosol monitoring instruments worldwide), and could be rapidly deployed into this established global network. Laser heterodyne radiometry is a well-established technique for detecting weak signals that was adapted from radio receiver technology. Here, a weak light signal, that has undergone absorption by atmospheric components, is mixed with light from a distributed feedback (DFB) telecommunications laser on a single-mode optical fiber. The RF component of the signal is detected on a fast photoreceiver. Scanning the laser through an absorption feature in the infrared, results in a scanned heterodyne signal io the RF. Deconvolution of this signal through the retrieval algorithm allows for the extraction of altitude contributions to the column signal. The retrieval algorithm is based on a spectral simulation program, SpecSyn, developed at GWU for high-resolution infrared spectroscopies. Variations io pressure, temperature, composition, and refractive index through the atmosphere; that are all functions of latitude, longitude, time of day, altitude, etc.; are modeled using algorithms developed in the MODTRAN program developed in part by the US Air Force Research Laboratory. In these calculations the atmosphere is modeled as a series of spherically symmetric shells with boundaries specified at defined altitudes. Temperature, pressure, and species mixing ratios are defined at these boundaries. Between the boundaries, temperature is assumed to vary linearly with altitude while pressure (and thus gas density) vary exponentially. The observed spectrum at the LHR instrument will be the integration of the contributions along this light path. For any absorption measurement the signal at a particular spectral frequency is a linear combination of spectral line contributions from several species. For each species that might absorb in a spectral region, we have pre-calculated its contribution as a function of temperature and pressure. The integrated path absorption spectrum can then by calculated using the initial sun angle (from location, date, and time) and assumptions about pressure and temperature profiles from an atmospheric model. The modeled spectrum is iterated to match the experimental observation using standard multilinear regression techniques. In addition to the layer concentrations, the numerical technique also provides uncertainty estimates for these quantities as well as dependencies on assumptions inherent in the atmospheric models.

Miller, J. Houston↗