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At least 235 records · Page 13

A refined gravity model from Lageos /GEM-L2/

Lageos satellite laser ranging (SLR) data taken over a 2.5 yr period were employed to develop the Goddard Earth Model GEM-L2, a refined gravity field model. Additional data was gathered with 30 other satellites, resulting in spherical harmonics through degree and order 20, based on over 600,000 measurements. The Lageos data was accurate down to 10 cm, after which the GEM 9 data were used to make adjustments past order 7. The resolution of long wavelength activity, through degree and order 4, was made possible by the Lageos data. The GEM-L2 model features a 20 x 20 geopotential, tracking station coordinates (20), 5-day polar motion and A1-UT1 values, and a GM value of 398,600.607 cu km/sq sec. The accuracy of station positioning has been raised to within 6 cm total position globally and within 1.8 cm in baselines. It is concluded that SLR is useful for measuring tectonic plate motions and inter-plate deformations.

Lerch, F. J.↗

Development of a Numerical Model of Hypervelocity Impact into a Pressurized Composite Overwrapped Pressure Vessel

As the outlook for space exploration becomes more ambitious and spacecraft travel deeper into space than ever before, it is increasingly important that propulsion systems perform reliably within the space environment. The increased reliability compels designers to increase design margin at the expense of system mass, which contrasts with the need to limit vehicle mass to maximize payload. Such are the factors that motivate the integration of high specific strength composite materials in the construction of pressure vessels commonly referred to as composite overwrapped pressure vessels (COPV). The COPV consists of a metallic liner for the inner shell of the COPV that is stiff, negates fluid permeation and serves as the anchor for composite laminates or filaments, but the liner itself cannot contain the stresses from the pressurant it contains. The compo-site-fiber reinforced polymer (CFRP) is wound around the liner using a combination of hoop (circumferential) and helical orientations. Careful consideration of wrap orientation allows the composite to evenly bear structural loading and creates the COPV's characteristic high strength to weight ratio. As the CFRP overwrap carries most of the stresses induced by pressurization, damage to the overwrap can affect mission duration, mission success and potentially cause loss-of-vehicle/loss-of-crew. For this reason, it is critical to establish a fundamental understanding of the mechanisms involved in the failure of a stressed composite such as that of the COPV. One of the greatest external threats to the integrity of a spacecraft's COPV is an impact from the meteoroid and orbital debris environments (MMOD). These impacts, even from submillimeter particles, generate extremely high stress states in the CFRP that can damage numerous fibers. As a result of this possibility, initial assumptions in survivability analysis for some human-rated NASA space-craft have assumed that any alteration of the vessel due to impact is considered a catastrophic failure. This assumption is conservative and made due to lack of knowledge on the level of allow-able damage to the composite overwrap that can be sustained and still allow successful completion of the mission. To quantify the allowable damage level to the composite overwrap involves assessing stress redistribution following damage as well as evaluating possible time-dependent mechanisms involved in the COPV response to an impact event. Limited published work in this subject has shown that COPV can withstand at least some level of damage due to high energy impacts. These observations have been confirmed and expanded upon in recent experimental research performed by NASA. This research has demonstrated that there is not only robustness in a COPV to compensate for CFRP damage, but has also identified two significant failure modes for pressurized COPV. The lowest threshold failure mode involves the perforation of the vessel, and the highest threshold failure mode is the catastrophic rupture. While both of these failure modes mean a loss of the COPV, system robustness affords some tolerance to the venting as opposed to the more catastrophic rupture. As a consequence, it is necessary to understand the conditions that result in the transition between these failure modes. The aforementioned experimental research has been performed in both the unpressurized and pressurized condition to identify the damage level that triggered the failure thresh-old. This COPV test program was sponsored by the NASA Engineering and Safety Center (NESC), and tests were performed at NASA White Sands Test Facility (WSTF). Planning and coordination were provided by NASA JSC Hypervelocity Impact Technology (HVIT) group, and the COPVs were provided by the ISS Program. Unpressurized testing has been conducted at the pressure of the vacuum test chamber, while, the pressurized testing has been conducted at 290 +/- 10 bar (4,200  100 psi) using nitrogen as the pressurizing gas, which corresponds to the design pressure for the target COPV. In this research, spherical aluminum projectiles with varying diameter has been chosen as the impactor. For the unpressurized COPV, the dependence of penetration up to the dependence of hole size in the liner has been obtained as a function of impact conditions. For the pressurized research, the dependence of penetration up to rupture has been obtained as a function of im-pact conditions. Two representative post-test photographs of the failed COPV's from a nor-mal impact into the COPV surface are shown in Fig. 1. These images display the dramatic difference between failure modes, venting (Fig. 1a) and rupture (Fig. 1b). For venting, liner perforation, severed composite fibers/tows and ply delamination are commonly observed damage characteristics of this COPV failure mode. In the case of rupture, the COPV typically experienced a separation of its domed regions and severe break-up of the cylindrical region. Fully understanding the transition from venting to rupture experimentally is costly and potentially unachievable for conditions that cannot be generated in the laboratory. These shortcomings have motivated the performance of three-dimensional numerical simulations to expand the existing experimental database. These simulations have been carried out with the nonlinear-structural-dynamics, analysis-tool, CTH. A typical pressure contour plot from an impact simulation of an entire COPV is shown in Fig. 2. To generate the COPV stress state without initiating a shock wave, the pressure in the simulated COPV is ramped up to the final pressure over a millisecond prior to impact of the projectile with nitrogen gas. Figure 2a shows the system in this initial condition. After one millisecond, a projectile is initiated into the simulation and impacts the COPV. Figure 2b shows the system after this impact. In the figure, the onset of venting is represented as the change in pressure (μbar), red to green, at the perforation site. Also seen in the figure is the eroded projectile that had passed into the COPV vessel with the generated shock wave in the pressurant propagating just ahead of the material. In this paper, pertinent experimental details and the development of the material constitutive models necessary for this work along with the efforts to validate their use are dis-cussed. The simulation results are presented and compared with the NASA experimental observations. While work is on-going from this effort, early observations pertinent to the failure threshold are presented.

Garcia, M. A.↗

Self-pressurization of a spherical liquid hydrogen storage tank in a microgravity environment

Thermal stratification and self-pressurization of partially filled liquid hydrogen (LH2) storage tanks under microgravity condition is studied theoretically. A spherical tank is subjected to a uniform and constant wall heat flux. It is assumed that a vapor bubble is located in the tank center such that the liquid-vapor interface and tank wall form two concentric spheres. This vapor bubble represents an idealized configuration of a wetting fluid in microgravity conditions. Dimensionless mass and energy conservation equations for both vapor and liquid regions are numerically solved. Coordinate transformation is used to capture the interface location which changes due to liquid thermal expansion, vapor compression, and mass transfer at liquid-vapor interface. The effects of tank size, liquid fill level, and wall heat flux on the pressure rise and thermal stratification are studied. Liquid thermal expansion tends to cause vapor condensation and wall heat flux tends to cause liquid evaporation at the interface. The combined effects determine the direction of mass transfer at the interface. Liquid superheat increases with increasing wall heat flux and liquid fill level and approaches an asymptotic value.

Lin, C. S.↗

Self-pressurization of a spherical liquid hydrogen storage tank in a microgravity environment

Thermal stratification and self-pressurization of partially filled liquid hydrogen (LH2) storage tanks under microgravity condition is studied theoretically. A spherical tank is subjected to a uniform and constant wall heat flux. It is assumed that a vapor bubble is located in the tank center such that the liquid-vapor interface and tank wall form two concentric spheres. This vapor bubble represents an idealized configuration of a wetting fluid in microgravity conditions. Dimensionless mass and energy conservation equations for both vapor and liquid regions are numerically solved. Coordinate transformation is used to capture the interface location which changes due to liquid thermal expansion, vapor compression, and mass transfer at liquid-vapor interface. The effects of tank size, liquid fill level, and wall heat flux on the pressure rise and thermal stratification are studied. Liquid thermal expansion tends to cause vapor condensation and wall heat flux tends to cause liquid evaporation at the interface. The combined effects determine the direction of mass transfer at the interface. Liquid superheat increases with increasing wall heat flux and liquid fill level and approaches an asymptotic value.

Lin, C. S.↗

Solwnd: A 3D Compressible MHD Code for Solar Wind Studies. Version 1.0: Cartesian Coordinates

Solwnd 1.0 is a three-dimensional compressible MHD code written in Fortran for studying the solar wind. Time-dependent boundary conditions are available. The computational algorithm is based on Flux Corrected Transport and the code is based on the existing code of Zalesak and Spicer. The flow considered is that of shear flow with incoming flow that perturbs this base flow. Several test cases corresponding to pressure balanced magnetic structures with velocity shear flow and various inflows including Alfven waves are presented. Version 1.0 of solwnd considers a rectangular Cartesian geometry. Future versions of solwnd will consider a spherical geometry. Some discussions of this issue is presented.

Deane, Anil E.↗

Algorithm for Rapid Searching Among Star-Catalog Entries

An algorithm searches a star catalog to identify guide stars within the field of view of a telescope or camera. The algorithm is fast: the number of computations needed to perform the search is approximately proportional to the logarithm of the number of stars in the catalog. The algorithm requires the prior organization of the star catalog into a hierarchy utilizing independent spherical coverings (see figure), such that each successively higher level contains fewer elements. In the lowest and most numerous level of the hierarchy, the elements are individual stars in the star catalog. The next higher level contains a spherical covering (a constellation of n points on a sphere that minimizes the maximum distance of any point on the sphere from the closest one of the n points), the next higher level contains a smaller spherical covering, and so forth, ending at the highest level, which contains one element representing the point of entry into the search structure. With necessary exceptions at the lowest and highest levels, each element at each level is labeled in terms of the element to which it is linked in the next higher level and the first element to which it is linked in the next lower level. Each element is also labeled in terms of (1) its coordinates on the celestial sphere and (2) the largest angular distance to any element in any lower level in the hierarchy. The elements at all levels of the hierarchy are numbered on a single list, such that the elements of each constellation at each level are numbered consecutively. The algorithm is recursive. The input required to start the algorithm comprises the coordinates of a point on the celestial sphere. Attention is then focused on individual elements of the hierarchy, starting from the topmost one, as follows: The angle between the input point and the element under consideration is calculated. If the calculated angle is larger than the sum of (1) the predetermined angle to the most distant element plus (2) the half field of view of the telescope, then no stars will be within the field of view and this recursive part of the algorithm is terminated.

Liebe, Carl Christian↗

Synchronized Position Hold, Engage, Reorient, Experimental Satellites

Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES) are bowling-ball sized spherical satellites. They will be used inside the space station to test a set of well-defined instructions for spacecraft performing autonomous rendezvous and docking maneuvers. Three free-flying spheres will fly within the cabin of the station, performing flight formations. Each satellite is self-contained with power, propulsion, computers and navigation equipment. The results are important for satellite servicing, vehicle assembly and formation flying spacecraft configurations. SPHERES is a testbed for formation flying by satellites, the theories and calculations that coordinate the motion of multiple bodies maneuvering in microgravity. To achieve this inside the ISS cabin, bowling-ball-sized spheres perform various maneuvers (or protocols), with one to three spheres operating simultaneously . The Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES) experiment will test relative attitude control and station-keeping between satellites, re-targeting and image plane filling maneuvers, collision avoidance and fuel balancing algorithms, and an array of geometry estimators used in various missions. SPHERES consists of three self-contained satellites, which are 18 sided polyhedrons that are 0.2 meter in diameter and weigh 3.5 kilograms. Each satellite contains an internal propulsion system, power, avionics, software, communications, and metrology subsystems. The propulsion system uses CO2, which is expelled through the thrusters. SPHERES satellites are powered by AA batteries. The metrology subsystem provides real-time position and attitude information. To simulate ground station-keeping, a laptop will be used to transmit navigational data and formation flying algorithms. Once these data are uploaded, the satellites will perform autonomously and hold the formation until a new command is given.

Miller, David W.↗

Plans for the Meter Class Autonomous Telescope and Potential Coordinated Measurements with Kwajalein Radars

The National Aeronautics and Space Administration's (NASA) Orbital Debris Program Office is teaming with the US Air Force Research Laboratory's (AFRL) Maui Optical Site to deploy a moderate field-of-view, 1.3 m aperture, optical telescope for orbital debris applications. The telescope will be located on the island of Legan in the Kwajalein Atoll and is scheduled for completion in the Spring of 2011. The telescope is intended to sample both low inclination/high eccentricity orbits and near geosynchronous orbits. The telescope will have a 1 deg diagonal field-of-view on a 4K x 4K CCD. The telescope is expected to be able to detect 10-cm diameter debris at geosynchronous altitudes (5 sec exposure assuming a spherical specular phase function w/ albedo =0.13). Once operational, the telescope has the potential of conducting simultaneous observations with radars operated by the US Army at Kwajalein Atoll (USAKA) and located on the island of Roi-Namur, approximately 55 km to the north of Legan. Four radars, representing 6 frequency bands, are available for use: ALTAIR (ARPA-Long Range Tracking and Instrumentation Radar) operating at VHF & UHF, TRADEX (Target Resolution and Discrimination Experiment) operating at L-band and S-band, ALCOR (ARPA-Lincoln C-band Observables Radar) operating at S-band, and MMW (Millimeter Wave) Radar operating at Ka-band. Also potentially available is the X-band GBRP (Ground Based Radar-Prototype located 25 km to the southeast of Legan on the main island of Kwajalein.

Stansberry, Gene↗

Computing supernova collapse to neutron stars and black holes

We present a new numerical code for spherical hydrodynamics in general relativity. The code can handle gravitational collapse to a neutron star or to a black hole without the appearance of singularities. Moreover, the variables and equations in the code are very similar to those appearing in traditional Lagrangian supernova codes. Any such existing code can thus be easily adapted to treat collapse where the final fate is uncertain and may be either a neutron star or a black hole. The code is based on the formulation of Hernandez & Misner, in which retarded time is used as coordinate. This prevents the computational grid from penetrating inside any black hole that may form. We present the equations and a complete finite difference scheme for the adiabatic evolution of a fluid that obeys a gamma-law equation of state. We summarize the results of several testbed calculations performed to check our code. We also give the transformation of the analytic Oppenheimer-Snyder solution for homogeneous dust collapse to our coordinate system.

Baumgarte, Thomas W.↗

A computer program for mapping satellite-borne narrow-beam antenna footprints on earth

A computer program has been developed that computes the locus of intersection of a quadric cone and a sphere. The outputs of the program are a list of the longitude and latitude coordinates of the locus of intersection and a plot of the locus. It was written primarily to define the area of the earth covered by a narrow beam antenna carried on a synchronous satellite in circular, near equatorial orbits. The program was written for use with a CalComp 570/563 off-line plotting system and uses the standard CalComp subroutines supplied with the system. The plot is drawn using linear longitude and latitude scales and nonlinear scales such as Mercator scales cannot be used. It should be noted that this program assumes the earth to be spherical rather than oblate is it actually is. However, by assuming a spherical earth, maximum error distances of about 11.5 nautical miles are introduced. For many purposes, this error can be ignored.

Stagl, T. W.↗

Experimental Study of Nonane and Nonane/Hexanol Fuel Droplet Combustion in Microgravity

In this presentation we review experiments carried out on nonane droplets, and a nonane/hexanol droplet, burning in microgravity to promote spherical symmetry. The nonane/hexanol combination was selected for the following reasons: 1) the spherically symmetric burning history of nonane and nonane/hexanol mixtures has not been previously studied; 2) measurements of the burning history of pure nonane droplets in air extend the existing data base of spherical droplet flames of soot-producing fuels which are useful for testing detailed chemical kinetic models of the spherically symmetric droplet burning process; 3) nonane and hexanol have almost identical boiling points so heterogeneous nucleation on a support fiber is unlikely; 4) hexanol does not have a strong propensity for water vapor absorption; 5) hexanol produces less soot than nonane so that mixtures of nonane and hexanol should show an effect of composition on soot formation. The far-field gas was atmospheric pressure air at room temperature. The evolution of droplet diameter was measured using high speed cine photography of spark-ignited droplets within a confined volume in a drop tower. The importance of soot formation during droplet combustion is derived from the fact that soot is the basic component of the particulate emission process that occurs in spray combustion. The complexity of soot formation motivates a one-dimensional transport condition which is advantageous for modeling. Recent numerical studies of droplet combustion have assumed spherical symmetry when incorporating such aspects as detailed chemistry and radiation, though soot formation itself has not yet been included in any droplet combustion modeling effort. If radiation is not important as would be the case for'small' droplets (i.e., droplets with initial diameters less than about ]mm), soot formation can lead to a nonlinear burning process and a time-varying burning rate, (non-linear burning of a non-sooting fuel like methanol is due to water vapor absorption on the droplet. The classical quasi-steady droplet burning theory predicts a linear evolution of droplet diameter in scaled coordinates for any fuel type.

Avedisian, C. T.↗

Magnetic Mapping in the Inner Magnetosphere using Kamodo

Many models require specialized access and interpolation schemes to effectively extract and interpolate their outputs. In particular, the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATSRUS) component of the Space Weather Modeling Framework (SWMF) requires Kamodo to take advantage of its block-based adaptive grid structure, and the Lyon-Fedder Mobarry magnetosphere model (or its successor GAMERA) needs a scheme that appreciates the distorted spherical arrangement of grid vertices on a non-orthogonal grid. With the flythrough layer developed by Ringuette et al. (SH42E-2337), the underlying model readers have been adapted to use multiple time steps in a single Python session to perform 4- dimensional interpolations in time and space. Kamodo now utilizes lazy interpolation that loads data only when needed. We present the successful integration of SWMF/BATSRUS magnetosphere access and interpolation into the new 4D Kamodo framework utilizing an external library of C code. Through function composition, Kamodo facilitates the calculation of derived quantities and the transformation of positions and vectors into different coordinate systems. This work is a significant step towards performing field line tracing in Kamodo with SWMF magnetosphere outputs.

Lutz Rastaetter↗

US-UK fusion energy collaborations in the digital space

The US and UK share the vision for fusion as a vital part of the clean energy future. This vision is reflected in the respective national plans in the form of the Bold Decadal Vision for Commercial Fusion (BDV) in the US and the Spherical Tokamak for Energy Production (STEP) program in the UK. Digital tools such as simulation and control frameworks, design tools, AI/ML, high performance computing (HPC), and virtual reality (VR) will play an important role in developing, diagnosing, operating, and further improving burning-plasma-class fusion power plants. Therefore, a collaborative approach, involving both the public and private sectors, to developing these digital tools can accelerate the path to fusion energy commercialization. In this report we discuss previous and ongoing collaborations and opportunities to expand these collaborations into new areas. We conclude this report with near term actions and a vision of the collaboration to the Joint Coordinating Committee.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Relativistic jet models for the BL Lacertae object Mrk 421 during three epochs of observation

Coordinated observation of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984, and March 1984 are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model. In general, the models reproduce the data well. Many of the observed differences during the three epochs can be attributed to variations in the opening angle of the jet and in the angle that the jet makes to the line of sight. The jet models obtained here are compared with the homogeneous, spherically symmetric, synchrotron self-Compton models for this source. The models are also compared with the relativistic jet models obtained for other active galactic nuclei.

Mufson, S. L.↗

The effects of gravity darkening on the ultraviolet continuum polarization produced by circumstellar disks

We investigate the effects of gravity darkening on the UV continuum polarization produced by an axisymmetric disk that surrounds a rapidly rotating star. Although the model is a single scattering approximation, we do include the effects of attenuation (electron scattering plus hydrogen bound-free absorption) by the disk, using an approach similar to that of Sobolev (1963). Because of the gravity darkening of the star and the attenuation within the disk, the radiation field is not axially symmetric about the radius vector. This implies that the polarization source functions are no longer provided by the finite disk depolarization factors of Cassinelli, Nordsieck, & Murison (1987), which are functions of the intensity moments in a spherically symmetric atmosphere. We reformulate the polarization source functions using generalized intensity moment tensors (J, H(sub i), K(sub ij)) that are valid for an arbitrary radiation field and envelope geometry. We find that the polarization source functions are simplest when using intensity moments in the observer's reference frame. On the other hand, the intensity moments are most easily evaluated in the stellar reference frame. Using the rotation transformation properties of the generalized intensity moments, we relate the observer's moments to those evaluated in the stellar reference frame. Our procedure for determining the polarization source functions thus merely involves choosing a set of Euler angles for the coordinate rotations, and then evaluating the associated rotation matrix. The geometrical complications of polarization transfer are thus reduced to obtaining a coordinate rotation matrix.

Bjorkman, J. E.↗

Processing of laser formed SiC powder

Superior SiC characteristics can be achieved through the use of ideal constituent powders and careful post-synthesis processing steps. High purity SiC powders of approx. 1000 A uniform diameter, nonagglomerated and spherical were produced. This required major revision of the particle formation and growth model from one based on classical nucleation and growth to one based on collision and coalescence of Si particles followed by their carburization. Dispersions based on pure organic solvents as well as steric stabilization were investigated. Although stable dispersions were formed by both, subsequent part fabrication emphasized the pure solvents since fewer problems with drying and residuals of the high purity particles were anticipated. Test parts were made by the colloidal pressing technique; both liquid filtration and consolidation (rearrangement) stages were modeled. Green densities corresponding to a random close packed structure (approx. 63%) were achieved; this highly perfect structure has a high, uniform coordination number (greater than 11) approaching the quality of an ordered structure without introducing domain boundary effects. After drying, parts were densified at temperatures ranging from 1800 to 2100 C. Optimum densification temperatures will probably be in the 1900 to 2000 C range based on these preliminary results which showed that 2050 C samples had experienced substantial grain growth. Although overfired, the 2050 C samples exhibited excellent mechanical properties. Biaxial tensile strengths up to 714 MPa and Vickers hardness values of 2430 kg/sq mm 2 were both more typical of hot pressed than sintered SiC. Both result from the absence of large defects and the confinement of residual porosity (less than 2.5%) to small diameter, uniformly distributed pores.

Haggerty, J. S.↗

An evolving relativistic jet model for the BL Lacertae object Markarian 421

Coordinated observations of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984 and March 1984, are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model described by Hutter and Mufson. The studies show that it is difficult to describe the data by a single jet whose properties vary as a function of time in a self-consistent manner unless the flat spectrum, hard X-ray tail present in January 1984 is due to an additional short-lived component of emission. These jet models are compared with homogeneous, spherically symmetric, synchrotron self-Compton models for this source.

Mufson, S. L.↗

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.↗