Results for “computers orbits” — Page 87

NASA NTRS1992

Nonlinear feedback guidance law for aero-assisted orbit transfer maneuvers

Aero-assisted orbit transfer vehicles have the potential for significantly reducing the fuel requirements in certain classes of orbit transfer operations. Development of a nonlinear feedback guidance law for performing aero-assisted maneuvers that accomplish simultaneous change of all the orbital elements with least vehicle acceleration magnitude is discussed. The analysis is based on a sixth order nonlinear point-mass vehicle model with lift, bank angle, thrust and drag modulation as the control variables. The guidance law uses detailed vehicle aerodynamic and the atmosphere models in the feedback loop. Higher-order gravitational harmonics, planetary atmosphere rotation and ambient winds are included in the formulation. Due to modest computational requirements, the guidance law is implementable on-board an orbit transfer vehicle. The guidance performance is illustrated for three sets of boundary conditions.

Menon, P. K. A.↗

NASA NTRS2001

Computational Aerothermodynamics in Aeroassist Applications

Aeroassisted planetary entry uses atmospheric drag to decelerate spacecraft from super-orbital to orbital or suborbital velocities. Numerical simulation of flow fields surrounding these spacecraft during hypersonic atmospheric entry is required to define aerothermal loads. The severe compression in the shock layer in front of the vehicle and subsequent, rapid expansion into the wake are characterized by high temperature, thermo-chemical nonequilibrium processes. Implicit algorithms required for efficient, stable computation of the governing equations involving disparate time scales of convection, diffusion, chemical reactions, and thermal relaxation are discussed. Robust point-implicit strategies are utilized in the initialization phase; less robust but more efficient line-implicit strategies are applied in the endgame. Applications to ballutes (balloon-like decelerators) in the atmospheres of Venus, Mars, Titan, Saturn, and Neptune and a Mars Sample Return Orbiter (MSRO) are featured. Examples are discussed where time-accurate simulation is required to achieve a steady-state solution.

Gnoffo, Peter A.↗

DOE OSTI2019

Automatic Partition of Orbital Spaces Based on Singular Value Decomposition in the Context of Embedding Theories

Here, we present a simple approach for orbital space partitioning to be employed in the projection-based embedding theory developed by Goodpaster and co-workers [Manby et al. J. Chem. Theory Comput. 2012, 8, 2564]. Once the atoms are assigned to the desired subspaces, the molecular orbitals are projected onto the atomic orbitals centered on active atoms and then singular value decomposed. The right singular vectors are used to rotate the initial molecular orbitals, taking the largest gap in the singular values spectrum to define the most suitable partition of the occupied orbital space. This scheme is free from numerical parameters, contrary to the Mulliken charge threshold or the completeness criterion previously used. The performance of this new prescription is assessed in a test set of several distinct reactions, the deprotonation of decanoic acid, the Diels-Alder reaction of 1,3-butadiene and octadecanonaene, the torsional potential of a retinal derivative, and the critical points along the reaction coordinate of an instance of the Menshutkin S N2 reaction inside a carbon nanotube.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Short Circuiting the Controller – Missteps in Maintenance and Inspection of Process and Wiring in STS-93

The primary objective of the Space Transportation System mission 93 (STS-93) was to deploy the Chandra X-Ray Observatory. Chandra, the world's most powerful X-Ray telescope, allowed scientists from around the world to study some of the most distant and dynamic objects in the universe. Stripped of nearly 7,000 pounds of its own gear to make room for the payload, the orbiter assigned to this mission was Space Shuttle Columbia. Prior to STS-93, Columbia had flown 25 flights and was NASA's oldest and heaviest orbiter. On July 23, 1999, after two prior launch scrubs, Eileen Collins and her crew of four launched from Kennedy Space Center. About five seconds after launch, Mission Control at Johnson Space Center detected a voltage drop on one of Columbia's electrical buses. As a result of this power fluctuation, a primary and back-up Main Engine controller dropped offline. Given design redundancy, the two remaining controllers supported all three engines. If there had been any other AC bus issues, one engine of the three on the Orbiter would have shut down. The redundant set of digital computer units in each engine controller saved Columbia and her crew from a very risky contingency abort. Post-flight inspection revealed soot on a screw head and a hole in an adjacent Kapton insulated wire. The single strand of polyimide wire was located nearly half-way down the payload bay. The Shuttle Independent Assessment Team (SIAT) reported that the wire had rubbed and chaffed against a burred screw head. The burr was later determined to be the result of overtightening of the screw by a technician during a maintenance refurbishment. Alone, the burr may not have been problematic, but later, during another ground processing event, possibly years after, someone inadvertently stepped on the wiring harness. With the pressure and motion of unintended contact, some of the Kapton insulation rubbed off against the burred screw head. The SIAT suspected the wire damage was pre-existing and was caused 4 or 5 years prior to the flight. Finally, the intense vibrations during the launch sequence allowed contact between the exposed conductor and exposed metal area on the burred screw head, resulting in the arcing and shorting of the wire. Due to the quick turnaround times of Space Shuttle Orbiters, wiring issues caused from multiple maintenance events were often overlooked. Additionally, failing to incorporate thorough and early inclusion of human systems integration (HSI) applications as a crucial part of the decision process can result in these types of misshaps. In order to reduce human error associated with integrated manufacturing, maintenance, refurbishment and flight preparations, wire inspection criteria should be refined and standardized, visual inspection processes should be quantified, and technicians should be certified by specially trained instructors. This case, among many others, unveils why human error management and development of safety metrics is a vital piece in the development of complex systems, and why it should be supported aggressively and implemented program wide.

Human Systems Integration↗

DOE OSTI2022

Natural orbitals for the ab initio no-core configuration interaction approach

Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupation of low-lying orbitals, thus accelerating convergence in a configuration-interaction basis, while also possibly providing physical insight into the single-particle structure of the many-body wave function. We describe the implementation of natural orbitals in the NCCI framework and examine the nature of the natural orbitals thus obtained, the properties of the resulting many-body wave functions, and the convergence of observables. After taking 3 He as an illustrative testbed, we explore aspects of NCCI calculations with natural orbitals for the ground state of the p-shell neutron halo nucleus 6 He .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1999

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗

NASA NTRSDate not supplied

NASA's Small Spacecraft and Distributed Systems: Development and Demonstration of Technologies Enabling Swarms and New Spacecraft Platforms with AI and Edge Computing

NASA’s Small Spacecraft & Distributed Systems (SSDS) within the Research and Technology Mission Directorate (RTMD) expands U.S. capability to execute unique missions through targeted investment, rapid development, and flight demonstration of small spacecraft technologies applicable to exploration, science and the commercial space sector. SSDS strategically invests in technology development and on-orbit demonstrations executed across NASA, other government agencies, industry, and academia. The program’s University SmallSat Technology Partnerships initiative awards academic researchers with the opportunity to collaborate with NASA to mature innovative technology. Capabilities aligned with RTMD’s technology shortfalls and interests - power, processing, propulsion, sensors, communications, autonomous navigation, architectures, and advanced applications like artificial intelligence (AI), machine learning, and edge computing - are prioritized in SSDS investments. These investments enable distributed, autonomous, and cooperative small spacecraft systems that support swarm missions extending beyond low Earth orbit into cislunar and deep space. This paper highlights representative SSDS flight demonstrations that mature these capabilities to enable a future operational infrastructure needed to support sustained exploration of the Moon and beyond. SSDS’s investment strategy emphasizes rapid development and on-orbit demonstration to validate spacecraft technologies required for swarms and distributed mission architectures. The Starling swarm technology demonstration mission exemplifies this approach by advancing distributed spacecraft autonomy, cooperative operations, and space situational awareness. Extended flight testing and ongoing studies of next generation swarm configurations and on-orbit space traffic monitoring and management continue to inform future swarm designs. DiskSat’s four-spacecraft demonstration mission represents SSDS’s strategic vision to expand the design space for future small spacecraft through its commitment to advance novel platform concepts that can impact how science is performed on orbit. Continuing to invest in future platforms, the notional PY12 concept is a 12-spacecraft swarm hosting neuromorphic processors and is envisioned as an on-orbit testbed for AI, edge computing, and positioning, navigation and timing technologies. SSDS also invests in single-spacecraft technology demonstrations that underpin the success of future swarm missions and accelerate the availability of validated technologies across the small spacecraft ecosystem. Examples of such demonstrations include Pathfinder Technology Demonstrator-3 (PTD-3), which performed high-rate optical communications; PTD-R, which demonstrated a camera capable of simultaneous ultraviolet and short-wave infrared optical sensing; and CAPSTONE, the Cislunar Autonomous Positioning System Technology and Operations Navigation Experiment, which validated autonomous navigation in cislunar space. Collectively, SSDS-funded demonstrations advance capabilities across swarms and illustrate a coordinated investment strategy to mature high-impact technologies required for autonomous, distributed, and cooperative small spacecraft systems for low Earth orbit, cislunar, and deep space applications. Technology demonstrations strengthen SSDS partnerships with industry, academia, and other government agencies, and promote small spacecraft community adoption of capabilities required to close technical gaps for swarm missions.

Jan Stupl↗

NASA NTRSDate not supplied

NASA's Small Spacecraft and Distributed Systems: Development and Demonstration of Technologies Enabling Swarms and New Spacecraft Platforms with AI and Edge Computing

NASA’s Small Spacecraft & Distributed Systems (SSDS) within the Research and Technology Mission Directorate (RTMD) expands U.S. capability to execute unique missions through targeted investment, rapid development, and flight demonstration of small spacecraft technologies applicable to exploration, science and the commercial space sector. SSDS strategically invests in technology development and on-orbit demonstrations executed across NASA, other government agencies, industry, and academia. The program’s University SmallSat Technology Partnerships initiative awards academic researchers with the opportunity to collaborate with NASA to mature innovative technology. Capabilities aligned with RTMD’s technology shortfalls and interests - power, processing, propulsion, sensors, communications, autonomous navigation, architectures, and advanced applications like artificial intelligence (AI), machine learning, and edge computing - are prioritized in SSDS investments. These investments enable distributed, autonomous, and cooperative small spacecraft systems that support swarm missions extending beyond low Earth orbit into cislunar and deep space. This paper highlights representative SSDS flight demonstrations that mature these capabilities to enable a future operational infrastructure needed to support sustained exploration of the Moon and beyond. SSDS’s investment strategy emphasizes rapid development and on-orbit demonstration to validate spacecraft technologies required for swarms and distributed mission architectures. The Starling swarm technology demonstration mission exemplifies this approach by advancing distributed spacecraft autonomy, cooperative operations, and space situational awareness. Extended flight testing and ongoing studies of next generation swarm configurations and on-orbit space traffic monitoring and management continue to inform future swarm designs. DiskSat’s four-spacecraft demonstration mission represents SSDS’s strategic vision to expand the design space for future small spacecraft through its commitment to advance novel platform concepts that can impact how science is performed on orbit. Continuing to invest in future platforms, the notional PY12 concept is a 12-spacecraft swarm hosting neuromorphic processors and is envisioned as an on-orbit testbed for AI, edge computing, and positioning, navigation and timing technologies. SSDS also invests in single-spacecraft technology demonstrations that underpin the success of future swarm missions and accelerate the availability of validated technologies across the small spacecraft ecosystem. Examples of such demonstrations include Pathfinder Technology Demonstrator-3 (PTD-3), which performed high-rate optical communications; PTD-R, which demonstrated a camera capable of simultaneous ultraviolet and short-wave infrared optical sensing; and CAPSTONE, the Cislunar Autonomous Positioning System Technology and Operations Navigation Experiment, which validated autonomous navigation in cislunar space. Collectively, SSDS-funded demonstrations advance capabilities across swarms and illustrate a coordinated investment strategy to mature high-impact technologies required for autonomous, distributed, and cooperative small spacecraft systems for low Earth orbit, cislunar, and deep space applications. Technology demonstrations strengthen SSDS partnerships with industry, academia, and other government agencies, and promote small spacecraft community adoption of capabilities required to close technical gaps for swarm missions.

Jan Stupl↗

DOE OSTI2016

Vibrational spectroscopic, structural and nonlinear optical activity studies on 2-amino-3-chloro-5-trifluoromethyl pyridine: A DFT approach

The conformational analysis was carried out for 2-amino-3-chloro-5-trifluoromethylpyridine using potential energy surface (PES) scan and the most stable optimized conformer was predicted. The theoretical vibrational frequencies were calculated for the optimized geometry using DFT/B3LYP cc-pVQZ basis set by Gaussian 09 Program. The vibrational frequencies were assigned on the basis of potential energy distribution calculation using VEDA 4.0 program package. The Mulliken atomic charge values were calculated. In the Frontier molecular orbitals analysis, the molecular reactivity, kinetic stability, intermolecular charge transfer studies and the calculation of ionization energy, electron affinity, global hardness, chemical potential, electrophilicity index and softness of the molecule were carried out. The nonlinear optical (NLO) activity was studied and the first order hyperpolarizability value was computed, which was 3.48 times greater than the urea. The natural bond orbital analysis was also performed to confirm the NLO activity of the molecule. Hence, the ACTP molecule is a promising candidate for NLO materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Binaries traveling through a gaseous medium: dynamical drag forces and internal torques

Using time-dependent linear theory, we investigate the morphology of the gravitational wake induced by a binary, whose center of mass moves at velocity V{sub cm} against a uniform background of gas. For simplicity, we assume that the components of the binary are on circular orbits about their common center of mass. The consequences of dynamical friction is twofold. First, gas dynamical friction may drag the center of mass of the binary and cause the binary to migrate. Second, drag forces also induce a braking torque, which causes the orbits of the components of the binary to shrink. We compute the drag forces acting on one component of the binary due to the gravitational interaction with its own wake. We show that the dynamical friction force responsible for decelerating the center of mass of the binary is smaller than it is in the point-mass case because of the loss of gravitational focusing. We show that the braking internal torque depends on the Mach numbers of each binary component about their center of mass, and also on the Mach number of the center of mass of the binary. In general, the internal torque decreases with increasing the velocity of the binary relative to the ambient gas cloud. However, this is not always the case. We also mention the relevance of our results to the period distribution of binaries.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1998

Monte Carlo Computational Modeling of the Energy Dependence of Atomic Oxygen Undercutting of Protected Polymers

A Monte Carlo computational model has been developed which simulates atomic oxygen attack of protected polymers at defect sites in the protective coatings. The parameters defining how atomic oxygen interacts with polymers and protective coatings as well as the scattering processes which occur have been optimized to replicate experimental results observed from protected polyimide Kapton on the Long Duration Exposure Facility (LDEF) mission. Computational prediction of atomic oxygen undercutting at defect sites in protective coatings for various arrival energies was investigated. The atomic oxygen undercutting energy dependence predictions enable one to predict mass loss that would occur in low Earth orbit, based on lower energy ground laboratory atomic oxygen beam systems. Results of computational model prediction of undercut cavity size as a function of energy and defect size will be presented to provide insight into expected in-space mass loss of protected polymers with protective coating defects based on lower energy ground laboratory testing.

Banks, Bruce A.↗

NASA NTRS2018

Automatic Design of Missions to Small Bodies

The new JPL Small-Body Automatic Mission-Design System comprises two main elements: a database of pre-computed mission options to all known asteroids and comets, and an interactive web interface that can be used to design transfers to each small body. The system is kept current with the JPL Small Body orbit catalog, is publicly available, and can be accessed from the JPL Solar System Dynamics Group website. The missions computed by the automatic system are impulsive. However, a low-thrust v estimate is also provided. The database of pre-computed missions can be filtered to find potential targets with certain orbital and physical properties, and that meet specific mission-design constraints. In addition to describing the system in detail, this paper presents empirical analytic expressions to approximate the impulsive v requirements of missions to comets and to each family of asteroids, obtained by fitting statistical data. To show how the interactive interface works, we consider mission options to asteroid 99942 Apophis. We also include optimal mission opportunities to other selected small bodies.

Farnocchia, Davide↗

NASA NTRS1960

Early orbit determination scheme for the Juno space vehicle

The present status (1959-60) of the ABMA early orbit determination scheme for the Juno space vehicle is described. The design of the scheme was essentially influenced by three factors: its origin centered around postflight vehicle analysis, the flexibility required for accepting varied kinds of data, and the potential of highspeed computers concentrated in ABMA's Computation Laboratory. The scheme is outlined, the tracking stations participating are shortly described, and the physical layout and computational equipment are briefly mentioned. The evaluation techniques used for the various steps of the orbit determination are discussed in detail. Appendices describe briefly the principal coordinate systems used and characteristics of the digital computer programs.

Fletcher Kurtz↗

NASA NTRS1990

Reexamination of data from the asteroid/meteoroid detector

A reexamination of the results of the Pioneer 10 and 11 Asteroid Meteoroid Detector, or Sisyphus, was carried out in the light of a recently derived theory characterizing interplanetary matter and the Zodiacal Light (ZL). Sisyphus measured individual meteoroids from reflected sunlight and ZL between meteoroid events. The results were questioned because meteoroid orbits could not be calculated as intended and the ZL as computed from individual meteoroids did not agree with values determined from the ZL mode and from the other ZL sensor on the spacecraft. It is first shown that, independent of any explanation, the measurements are, with high probability, valid and strongly correlated with the ZL. The model which explains the strange behavior of the Sisyphus instrument also resolves the enigma why the three dust experiments on the Pioneer 10 and 11 spacecraft produced extreme disparate results for the distribution and orbits of meteoric particles and the ZL. The theory based primarily on these measurements requires a population in the inner solar system of cold meteoroid material composed mainly of volatile molecules. These meteoroids in orbits of high eccentricity are called cosmoids. They are impulsively disrupted from solar heating, resulting in order of magnitude increases in optical cross section. The dispersed particles, predominantly micron sized, scatter most of the ZL and supply the polarization. The sublimation time in sunlight for micron sized particles of volatile composition opposes the gravitational flux increase expected in approaching the sun. The other two Pioneer 10/11 dust experiments were: the Imaging Photopolarimeter for the ZL, and the Meteoroid Detection Experiment that measured penetration of 25 micron (Pioneer 10) and 50 micron (Pioneer 11) thick walls of pressurized gas cells.

Soberman, Robert K.↗

NASA NTRS1977

Calculations of the effects of angular momentum on the early evolution of Jupiter

Early phases in the evolutionary development of a rotating cloud of gas and dust are investigated to determine whether physically reasonable initial conditions are likely to produce a planet-satellite system with the values of specific orbital angular momentum currently observed for Jupiter and its inner satellites. Spherically symmetric computations of Jupiter's evolutionary history are reviewed, and transport of angular momentum is considered along with evolutionary sequences of individual differentially rotating models with decreasing values of equatorial radius. The problem of accounting for the present specific orbital angular momenta of Jupiter and its regular satellites is examined qualitatively, and a range of possible angular-momentum distributions in an initially tidally unstable cloud is assessed. The results show that particular physically plausible angular-momentum distributions, which could either be established as initial conditions or be caused by angular-momentum transport, will lead to favorable situations for the formation of a central planet and a surrounding rotating cloud with specific angular momentum comparable to that of the regular satellites.

Bodenheimer, P.↗

DOE OSTI2015

Building and testing correlations for the estimation of one‐electron reduction potentials of a diverse set of organic molecules

We describe and evaluate a method for computationally predicting reduction potentials of a diverse group of organic molecules by linearly correlating calculated lowest unoccupied molecular orbital energies with ground state reduction potentials measured in acetonitrile. The approach is shown to provide a unique combination of extreme computational simplicity and excellent accuracy across a diverse range of organic structures and a wide window of reduction potentials. A disparate set of molecules (74 compounds belonging to six distinct structural families, comprised of molecules containing C, H, N, O, F, Cl, and Br, with functional groups including esters, ketones, halides, nitriles, quinones, alkenes, arenes, heteroarenes, and pyridinium and higher benzologs, all containing conjugated pi systems, spanning a 3.5‐V range of reduction potentials) was used to build the correlations. This methodology was found to be computationally inexpensive compared with other approaches and to permit the useful prediction of reduction potentials of additional molecules of diverse structural types not included in the families used to determine the correlation parameters. The effects of varying the basis set used in the B3LYP electronic structure calculations and including solvent (compared with calculations in gas phase) were also examined. It was found that the inclusion of a continuum solvent model in the calculations was required for accurate results, particularly when including cationic species in the correlations (although when only neutral molecules were examined, reasonable results could even be obtained in vacuo ). Several of the best correlations were used to predict the reduction potentials of seven much larger and structurally diverse chromophores that were not included in the correlation data set. Strong correlations ( r 2 values > 0.99) with very good predictive abilities (root mean square deviation < 60 mV) were found. This extremely simple and computationally efficient entirely closed‐shell methodology is proven robust and useful for the design of new molecules capable of participating in redox processes, including electron transfer reactions. Copyright © 2015 John Wiley & Sons, Ltd.

Méndez‐Hernández, Dalvin D.↗

NASA NTRS1980

STS-1 mission contamination evaluation approach

The space transportation system 1 mission will be the first opportunity to assess the induced environment of the orbiter payload bay region. Two tools were developed to aid in this assessment. The shuttle payload contamination evaluation computer program was developed to provide an analytical tool for prediction of the induced molecular contamination environment of the space shuttle orbiter during its onorbit operations. An induced environment contamination monitor was constructed and tested to measure the space shuttle orbiter contamination environment inside the payload bay during ascent and descent and inside and outside the payload bay during the onorbit phase. Measurements are to be performed during the four orbital flight test series. Measurements planned for the first flight are described and predicted environmental data are discussed. The results indicate that the expected data are within the measurement range of the induced environment contamination monitor instruments evaluated, and therefore it is expected that useful contamination environmental data will be available after the first flight.

Jacobs, S.↗

NASA NTRS1983

A system for load isolation and precision pointing

A system capable of satisfying the accuracy and stability requirements dictated by Shuttle-borne payloads utilizing large optics has been under joint NASA/Sperry development. This device, denoted the Annular Suspension and Pointing System, employs a unique combination of conventional gimbals and magnetic bearing actuators, thereby providing for the complete isolation of the payload from its external environment, as well as for extremely accurate and stable pointing (equal to about 0.01 arcsec). This effort has been pursued through the fabrication and laboratory evaluation of engineering model hardware. Results from these tests have been instrumental in generating high fidelity computer simulations of this load isolation and precision pointing system, and in permitting confident predictions of the system's on-orbit performance. The applicability of this system to the Solar Optical Telescope mission has been examined using the computer simulation. The worst case pointing error predicted for this payload while subjected to vernier reaction control system thruster firings and crew motions aboard the Shuttle was approximately 0.006 arcsec.

Keckler, C. R.↗