Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Shape constraints”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A global/local analysis method for treating details in structural design

A method for analyzing global/local behavior of plate and shell structures is described. In this approach, a detailed finite element model of the local region is incorporated within a coarser global finite element model. The local model need not be nodally compatible (i.e., need not have a one-to-one nodal correspondence) with the global model at their common boundary; therefore, the two models may be constructed independently. The nodal incompatibility of the models is accounted for by introducing appropriate constraint conditions into the potential energy in a hybrid variational formulation. The primary advantage of this method is that the need for transition modeling between global and local models is eliminated. Eliminating transition modeling has two benefits. First, modeling efforts are reduced since tedious and complex transitioning need not be performed. Second, errors due to the mesh distortion, often unavoidable in mesh transitioning, are minimized by avoiding distorted elements beyond what is needed to represent the geometry of the component. The method is applied reduced to a plate loaded in tension and transverse bending. The plate has a central hole, and various hole sixes and shapes are studied. The method is also applied to a composite laminated fuselage panel with a crack emanating from a window in the panel. While this method is applied herein to global/local problems, it is also applicable to the coupled analysis of independently modeled components as well as adaptive refinement.

Aminpour, Mohammad A.↗
NASA NTRS1995

Space Science for the 21st Century: The Space Science Enterprise Strategic Plan

Throughout its history, the U.S. Space Science technologies program has been enormously productive. Its accomplishments have rewritten the textbooks. But now, the economic environment has changed dramatically. The Nation's scientific and technological goals are being reexamined and redefined.And the social contract between the scientific community and the Federal Government is being rewritten. There is an expectation that the American public should receive more direct benefits from its investment in science and technology. This Strategic Plan reflects this new paradigm. It presents a carefully selected set of new scientific initiatives that build on past accomplishments to continue NASA's excellence in Space Science. At the same time, it responds to fiscal constraints by defining a new approach to planning, developing, and operating Space Science missions. In particular, investments in new technologies will permit major scientific advances to be made with smaller, more focused, and less costly missions. With the introduction of advanced technologies, smaller does not have to mean less capable. The focus on new technologies also provides and opportunity for the Space Science program to enhance its direct contribution to the country's economic base. At the same time, the program can build on public interest to strengthen its contributions to education and scientific literacy. With this plan we are taking the first steps toward shaping the Space Science program of the 21st century. In doing so, we face major challenges. It will be a very different program than might have been envisioned even a few years ago. But it will be a program that remains at the forefront of science, technology, and education. We intend to continue rewriting the textbooks.

Source record↗
NASA NTRS2020

Test-Analysis Modal Correlation of Rocket Engine Structures in Liquid Hydrogen - Phase II

Many structures in a launch vehicle operate in liquid hydrogen, from the hydrogen fuel tanks through the ducts and valves and into the turbopumps. Calculating the structural dynamic response of these structures is critical for successful qualification, but accurate knowledge of the natural frequencies is based entirely on numerical or analytical predictions since testing in operating conditions is problematic. A comprehensive test/analysis program has therefore been performed at NASA/MSFC to enable accurate prediction of the modal characteristics of the Space Launch System’s (SLS) RS-25 Low Pressure Fuel Turbopump Inducer including the effects of fluid-added mass, mechanical property change at cryogenic temperatures, operation within tight tip clearances, acoustic/structure interaction, and hydroelasticity. The process also has to account for complicated cyclic symmetry mode shapes which can be easily mistuned in test, and geometric, boundary condition, and material modifications between the sub-scale inducer used as a test article and the actual flight component. The first phase of the program, documented previously, focused on testing of a cantilever beam in a number of fluids and temperatures to isolate the effects of fluid-added mass and temperature, while the second phase reported here documents the additional issues associated with the more realistic inducer test article. Preliminary structural dynamic analysis of the flight hardware including variability for the above parameters indicated potential severe resonances, requiring implementation of undesired programmatic constraints, so the improved predictive capability may allow removal of these constraints.

Brown, Andrew M.↗
NASA NTRS1972

Electric power processing, distribution and control for advanced aerospace vehicles.

The results of a current study program to develop a rational basis for selection of power processing, distribution, and control configurations for future aerospace vehicles including the Space Station, Space Shuttle, and high-performance aircraft are presented. Within the constraints imposed by the characteristics of power generation subsystems and the load utilization equipment requirements, the power processing, distribution and control subsystem can be optimized by selection of the proper distribution voltage, frequency, and overload/fault protection method. It is shown that, for large space vehicles which rely on static energy conversion to provide electric power, high-voltage dc distribution (above 100 V dc) is preferable to conventional 28 V dc and 115 V ac distribution per MIL-STD-704A. High-voltage dc also has advantages over conventional constant frequency ac systems in many aircraft applications due to the elimination of speed control, wave shaping, and synchronization equipment.

Krausz, A.↗
DOE OSTI2025

Effect of laser melt schedule on the microstructure of additively manufactured IN718 Superalloy

Laser powder bed fusion (L-PBF) has enabled the fabrication of geometrically complex metallic structures and components that are challenging to producing using conventional manufacturing approaches. The site-specific and far from equilibrium thermal conditions of L-PBF offer the potential to facilitate multi-length scale design of structure and properties across the atomic-through macro-levels. However, L-PBF systems face scalability challenges due to throughput constraints. Laser rotary powder bed fusion (L-RPBF) systems are being investigated as a solution to enhance the deposition rates compared to conventional L-PBF. Rotary systems also offer additional flexibility for controlling the time structure of melting through laser interleaving on alternating layers. Here, in this study, IN718 test samples were printed using single-laser or interleaved dual-laser configuration in a L-RPBF system to investigates the effect of process settings and melt-interleaving on as-fabricated microstructure. The microstructural evolution, such as grain size and crystallographic texture, was assessed by determining variations in the melt-pool shapes. Laser interleaving leads to a reduction in average grain size compared to single laser by ∼ 40 % at high power (400 W) and by ∼36 % at medium power (370 W). Results presented here identify key challenge for obtaining uniform microstructures and barriers for the broader adoption of high-deposition rate L-RPBF.

Dual-laser↗
NASA NTRS2004

Physics of Galaxy Clusters and How it Affects Cosmological Tests

The main activities in 2004 were focused on completion of the new 400 square degrees ROSAT PSPC survey for distant galaxy clusters. We observed and reduced optical spectra for all X-ray candidates and now we have complete identification for a statistically complete sample of distant 283 clusters. The papers describing the cluster catalog and first science results are in preparation and will be submitted in early 2005. We also completed a project to measure temperature and density profiles at large radii using Chandra observations of a 11 well exposed low-redshift clusters. We were able to demonstrate that the density, temperature, and total mass profiles are self-similar at large radii. This analysis has led to significant improvements in determination of the cluster baryon fraction as well as cosmologically important scaling relations, such as Mtot-T. The paper describing these results is submitted to ApJ in November, 2004. We continued to study evolution of the cluster scaling relations at high redshifts using Chandra and XMM data. We developed code for image and spectral deconvolution of the XMM observations. This code was used to reconstruct the distribution of baryons and total mass from observations of distant clusters which suffer from the finite size of the XMM PSF. This study allowed us to derive a high-redshift relation between cluster temperature and mass and compare it with the local relation obtained. The paper describing the first results is submitted to the ApJ. However, the project is still on-going as more distant cluster observations enter XMh4 and Chandra public data archives. We continued our work on improving techniques for accurate measurements of the cluster mass function and obtaining cosmological constraints from such observations. We published (ApJ, 601, 610) a study in which we derived the baryon mass function for a complete sample of low-redshift clusters. These papers argued that it was an excellent proxy for the total mass function. The baryon mass function can be used to constrain the amplitude and slope of the density fluctuation power spectrum on cluster scales. This method does not use observational determinations of the total mass and thus bypasses major uncertainties in the traditional analyses based on the X-ray temperature function. We derived the measurements for the amplitude of density perturbations, sigma8 = 0.72 +/- 0.04 and the shape parameter Omega*h = 0.l3 +/- 0.07, in good agreement with a number of independent methods.

Oliversen, Ronald J.↗
DOE OSTI2021

Where Is the Water? Jupiter-like C/H Ratio but Strong H{sub 2}O Depletion Found on τ Boötis b Using SPIRou

The present-day envelope of gaseous planets is a relic of how these giant planets originated and evolved. Measuring their elemental composition therefore presents a powerful opportunity to answer long-standing questions regarding planet formation. Obtaining precise observational constraints on the elemental inventory of giant exoplanets has, however, remained challenging owing to the limited simultaneous wavelength coverage of current space-based instruments. Here, we present thermal emission observations of the nontransiting hot Jupiter τ Boo b using the new wide wavelength coverage (0.95–2.50 μm) and high spectral resolution (R = 70,000) CFHT/SPIRou spectrograph. By combining a total of 20 hr of SPIRou data obtained over five nights in a full atmospheric retrieval framework designed for high-resolution data, we constrain the abundances of all the major oxygen- and carbon-bearing molecules and recover a noninverted temperature structure using a new free-shape, nonparametric temperature–pressure profile retrieval approach. We find a volume mixing ratio of log(CO) = -2.46{sub -0.29}{sup +0.25} and a highly depleted water abundance of less than 0.0072 times the expected value for a solar composition envelope. Combined with upper limits on the abundances of CH{sub 4}, CO{sub 2}, HCN, TiO, and C{sub 2}H{sub 2}, this results in a gas-phase C/H ratio of 5.85{sub -2.82}{sup +4.44} × solar, consistent with the value of Jupiter, and an envelope C/O ratio robustly greater than 0.60, even when taking into account the oxygen that may be sequestered out of the gas phase. Combined, the inferred supersolar C/H, O/H, and C/O ratios on τ Boo b support a formation scenario beyond the water snowline in a disk enriched in CO owing to pebble drift.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2000

X-Ray Constraints on the Warm-Hot Intergalactic Medium

Three observational constraints can be placed on a warm-hot intergalactic medium (WHIM) using ROSAT Position Sensitive Proportional Counter (PSPC) pointed and survey data, the emission strength, the energy spectrum, and the fluctuation spectrum. The upper limit to the emission strength of the WHIM is 7.5 +/- 1.0 keV/(s*sq cm*sr*keV) in the 3/4 keV band, an unknown portion of which value may be due to our own Galactic halo. The spectral stape of the WHIM emission can be described as thermal emission with logT = 6.42, although the true spectrum is more likely to come from a range of temperatures. The values of emission strength and spectral shape are in reasonable agreement with hydrodynamical cosmological models. The autocorrelation function in the 0.44 keV < E < 1.21 keV band range, w(theta), for the extragalactic soft X-ray background (SXRB) which includes both the WHIM and contributions due to point sources, is approx. < 0.002 for 10 min < 0 < 20 min in the 3/4 keV band. This value is lower than the Croft et al. (2000) cosmological model by a factor of approx. 5, but is still not inconsistent with cosmological models. It is also found that the normalization of the extragalactic power law component of the soft X-ray background spectrum must be 9.5 +/- 0.9 keV/(s*sq cm*sr*keV) to be consistent with the ROSAT All-Sky Survey.

Kuntz, K. D.↗
DOE OSTI2020

The Coupled Influence of Thermal Physiology and Biotic Interactions on the Distribution and Density of Ant Species along an Elevational Gradient

A fundamental tenet of biogeography is that abiotic and biotic factors interact to shape the distributions of species and the organization of communities, with interactions being more important in benign environments, and environmental filtering more important in stressful environments. This pattern is often inferred using large databases or phylogenetic signal, but physiological mechanisms underlying such patterns are rarely examined. We focused on 18 ant species at 29 sites along an extensive elevational gradient, coupling experimental data on critical thermal limits, null model analyses, and observational data of density and abundance to elucidate factors governing species’ elevational range limits. Thermal tolerance data showed that environmental conditions were likely to be more important in colder, more stressful environments, where physiology was the most important constraint on the distribution and density of ant species. Conversely, the evidence for species interactions was strongest in warmer, more benign conditions, as indicated by our observational data and null model analyses. Our results provide a strong test that biotic interactions drive the distributions and density of species in warm climates, but that environmental filtering predominates at colder, high-elevation sites. Such a pattern suggests that the responses of species to climate change are likely to be context-dependent and more specifically, geographically-dependent.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1984

Joined-wing research airplane feasibility study

The joined wing is a new type of aircraft configuration which employs tandem wings arranged to form diamond shapes in plan view and front view. Wind-tunnel tests and finite-element structural analyses have shown that the joined wing provides the following advantages over a comparable wing-plus-tail system; lighter weight and higher stiffness, higher span-efficiency factor, higher trimmed maximum lift coefficient, lower wave drag, plus built-in direct lift and direct sideforce control capability. To verify these advantages at full scale a manned research airplane is required. A study has therefore been performed of the feasibility of constructing such an airplane, using the fuselage and engines of the existing NAA AD-1 oblique-wing airplane. Cost and schedule constraints favored converting the AD-1 rather than constructing a totally new airframe. By removing the outboard wing panels the configuration can simulate wings joined at 60, 80, or 100 percent of span. For maximum versatility the aircraft has alternative control surfaces (such as ailerons and elevators on the front and/or rear wings), and a removeable canard to explore canard/joined-wing interactions at high-lift conditions. Design, performance, and flying qualities are discussed.

Wolkovitch, J.↗
NASA NTRS2006

High-Strain-Rate Compression Testing of Ice

In the present study a modified split Hopkinson pressure bar (SHPB) was employed to study the effect of strain rate on the dynamic material response of ice. Disk-shaped ice specimens with flat, parallel end faces were either provided by Dartmouth College (Hanover, NH) or grown at Case Western Reserve University (Cleveland, OH). The SHPB was adapted to perform tests at high strain rates in the range 60 to 1400/s at test temperatures of -10 and -30 C. Experimental results showed that the strength of ice increases with increasing strain rates and this occurs over a change in strain rate of five orders of magnitude. Under these strain rate conditions the ice microstructure has a slight influence on the strength, but it is much less than the influence it has under quasi-static loading conditions. End constraint and frictional effects do not influence the compression tests like they do at slower strain rates, and therefore the diameter/thickness ratio of the samples is not as critical. The strength of ice at high strain rates was found to increase with decreasing test temperatures. Ice has been identified as a potential source of debris to impact the shuttle; data presented in this report can be used to validate and/or develop material models for ice impact analyses for shuttle Return to Flight efforts.

Shazly, Mostafa↗
DOE OSTI2026

Determination of nuclear PDFs using Markov chain Monte Carlo methods

Global QCD analyses of nuclear parton distribution functions (nPDFs) have traditionally relied on the Hessian method for uncertainty estimation. However, the inherent Gaussian approximation and reliance on local curvature often prove insufficient for nPDF fits, which are frequently characterized by limited data constraints and non-Gaussian likelihoods. In this paper, we present the first nPDF determination based on Markov Chain Monte Carlo (MCMC) techniques, implemented within the nCTEQ framework using an adaptive Metropolis-Hastings algorithm. The MCMC approach enables a direct mapping of the posterior distribution and reveals a highly nontrivial parameter-space structure, including multiple modes and pronounced non-Gaussian behavior, particularly for the valence PDFs. We perform the first single-nucleus global analysis of lead PDFs using exclusively lead data and compare it to a multi-nuclei fit employing a standard analytic A dependence. The inclusion of lighter nuclei reduces quark uncertainties and modifies the shape of the lead PDFs, while leaving the gluon distribution largely unaffected. A complementary Hessian analysis exposes systematic limitations of the Gaussian approximation. Our results demonstrate that MCMC methods provide a more reliable framework for uncertainty quantification in nPDF determinations.

Derakhshanian, N. [Institute of Nuclear Physics Po↗
NASA NTRS2007

Development of a HTSMA-Actuated Surge Control Rod for High-Temperature Turbomachinery Applications

In recent years, a demand for compact, lightweight, solid-state actuation systems has emerged, driven in part by the needs of the aeronautics industry. However, most actuation systems used in turbomachinery require not only elevated temperature but high-force capability. As a result, shape memory alloy (SMA) based systems have worked their way to the forefront of a short list of viable options to meet such a technological challenge. Most of the effort centered on shape memory systems to date has involved binary NiTi alloys but the working temperatures required in many aeronautics applications dictate significantly higher transformation temperatures than the binary systems can provide. Hence, a high temperature shape memory alloy (HTSMA) based on NiTiPdPt, having a transformation temperature near 300 C, was developed. Various thermo-mechanical processing schemes were utilized to further improve the dimensional stability of the alloy and it was later extruded/drawn into wire form to be more compatible with envisioned applications. Mechanical testing on the finished wire form showed reasonable work output capability with excellent dimensional stability. Subsequently, the wire form of the alloy was incorporated into a benchtop system, which was shown to provide the necessary stroke requirements of approx.0.125 inches for the targeted surge-control application. Cycle times for the actuator were limited to ~4 seconds due to control and cooling constraints but this cycle time was determined to be adequate for the surge control application targeted as the primary requirement was initial actuation of a surge control rod, which could be completed in approximately one second.

Padula, Santo, II↗
DOE OSTI2020

Validation of gyrokinetic simulations in NSTX and projections for high-k turbulence measurements in NSTX-U

An extensive validation effort performed for a modest-beta NSTX NBI-heated H-mode discharge predicts that electron thermal transport can be entirely explained by electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in conditions of strong and weak ETG turbulence drive. Thermal power-balance estimates computed by TRANSP as well as the shape of the high-k density fluctuation wavenumber spectrum and the fluctuation level ratio between strongly driven and weakly driven ETG-turbulence conditions can be matched by nonlinear gyrokinetic simulations and a synthetic diagnostic for high-k scattering. Linear gyrokinetic simulations suggest that the ion-scale instability in the weak ETG condition is close to the critical threshold for the kinetic ballooning mode instability, and nonlinear ion-scale gyrokinetic simulations show that turbulence might be in a state reminiscent of a Dimits' shift regime, opening speculation on the role that ion-scale turbulence might play for the weak ETG condition. A simulation that matched all experimental constraints is chosen to project high-k turbulence spectra in NSTX-U, revealing that the new high-k system [R. Barchfeld et al., Rev. Sci. Instrum. 89, 10C114 (2018)] should be sensitive to density fluctuations from radially elongated streamer structures. In this study, two schemes are designed to characterize the radial and poloidal wavenumber dependence of the density fluctuation wavenumber power spectrum around the streamer peak, suggesting future high-k fluctuation measurements could be sensitive to an asymmetry in the k r spectrum introduced due to the presence of strong background flow shear.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

Isotopic Constraints on the Genesis of Carbonates in Martian Meteorite ALH 84001

Oxygen isotopic analyses in approximately 20 micrometer spots in a chemically diverse suite of carbonates from ALH 84001 show highly variable delta(exp 18)O values from +5.4 to +25.3%. The isotopic data are correlated with the major element composition of the carbonate. The earliest forming (Ca-rich) carbonates have the lowest delta(exp 18)O values and the late-forming Mg-rich carbonates have the highest delta(exp 18)O values. Two models that can explain the isotopic variation were investigated. The carbonates could have formed in a water-rich environment at relatively low, but highly variable temperatures. In this open-system case the lower limit to the temperature variation is approximately 125 C, with fluctuations of over 250 C possible within the constraints of the model, depending on fluid composition. Alternatively the data can be explained by a closed-system model in which carbonates precipitated from a limited amount of a CO2-rich fluid. This scenario can reproduce the range of isotopic values observed, even at relatively high temperatures (greater than 500 C). Thus, the oxygen isotopic compositions do not provide unequivocal evidence for formation of the carbonates at low temperature. Neither of these scenarios is consistent with a biological origin of the carbonates and their associated features. Olivine from ALH 84001 occurs as clusters within orthopyroxene adjacent to fractures containing disrupted carbonate globules and feldspathic shock glass. The inclusions are irregular in shape and range in size from approximately 40 micrometers to submicrometer. The olivine exhibits a limited range of chemical composition from Fo(sub 65) to Fo(sub 66). We measured delta(exp 18)O values of the olivine to be +5.1 +/- 1.4%, indistinguishable within uncertainty from the host orthopyroxene. The data suggest that the olivine formed at high temperature (greater than 800 C), and is probably unrelated to carbonate formation. Instead the olivine probably formed by metamorphic reactions involving either dehydration of hydrous silicates or reduction of opx + spinel. If the reactions took place after carbonate formation, they could have caused devolatilization of siderite, producing the magnetite in the ALH carbonate globules. This scenario is also inconsistent with a biological origin for the features in ALH 84001.

Leshin, Laurie A.↗
NASA NTRS1994

The power spectrum of galaxies in the nearby universe

We compute the power spectrum of galaxy density fluctuations in a recently completed Southern Sky Redshift Survey of optically selected galaxies (SSRS2). The amplitude and shape of the SSRS2 power spectrum are consistent with results of the Center for Astrophysics redshift survey of the northern hemisphere (CfA2), including the abrupt change of slope on a scale of 30-50/h Mpc; these results are reproducible for independent volumes of space, and variations are consistent with the errors estimated from mock surveys. Taken together, the SSRS2 and the CfA2 form a complete sample of 14,383 galaxies which covers one-third of the sky. The power spectrum of this larger sample continues to rise on scales up to approximately 200/h Mpc, with weak evidence for flattening on the largest scales. The SSRS2 + CfA2 power spectrum and the power spectrum constraints implied by COBE are well matched by an Omega(h) is approximately 0.2, Omega + lambda(sub 0) = 1 cold dark matter model with minimal biasing of optically selected galaxies.

Da Costa, L. Nicolaci↗
NASA NTRS2017

Endogenous Lunar Volatiles

The chapter will begin with an introduction that defines magmatic volatiles (e.g., H, F, Cl, S) versus geochemical volatiles (e.g., K, Rb, Zn). We will discuss our approach of understanding both types of volatiles in lunar samples and lay the ground work for how we will determine the overall volatile budget of the Moon. We will then discuss the importance of endogenous volatiles in shaping the "Newer Views of the Moon", specifically how endogenous volatiles feed forward into processes such as the origin of the Moon, magmatic differentiation, volcanism, and secondary processes during surface and crustal interactions. After the introduction, we will include a re-view/synthesis on the current state of 1) apatite compositions (volatile abundances and isotopic compositions); 2) nominally anhydrous mineral phases (moderately to highly volatile); 3) volatile (moderately to highly volatile) abundances in and isotopic compositions of lunar pyroclastic glass beads; 4) volatile (moderately to highly volatile) abundances in and isotopic compositions of lunar basalts; 5) volatile (moderately to highly volatile) abundances in and isotopic compositions of melt inclusions; and finally 6) experimental constraints on mineral-melt partitioning of moderately to highly volatile elements under lunar conditions. We anticipate that each section will summarize results since 2007 and focus on new results published since the 2015 Am Min review paper on lunar volatiles [9]. The next section will discuss how to use sample abundances of volatiles to understand the source region and potential caveats in estimating source abundances of volatiles. The following section will include our best estimates of volatile abundances and isotopic compositions (where permitted by available data) for each volatile element of interest in a number of important lunar reservoirs, including the crust, mantle, KREEP, and bulk Moon. The final section of the chapter will focus upon future work, outstanding questions, and any in-sights on the types of samples or experimental studies that will be needed to answer these questions.

McCubbin, F. M.↗
NASA NTRS1996

Radar Observations of Asteroid 1620 Geographos

Goldstone radar observations of Geographos from August 28 through September 2, 1994 yield over 400 delay-Doppler images whose linear spatial resolutions range from approx. 75 to approx. 151 in, and 138 pairs of dual-polarization (OC, SC) spectra with one-dimensional resolution of 103 m. Each data type provides thorough rotational coverage. The images contain an intrinsic north/south ambiguity, but the equatorial view allows accurate determination of the shape of the radar-facing part of the asteroid's pole-on silhouette at any rotation phase. Sums of co-registered images that cover nearly a full rotation have defined the extremely elongated shape of that silhouette. Here we present individual images and co-registered sums over approx. 30 deg of rotation phase that show the silhouette's structural characteristics in finer detail and also reveal numerous contrast features "inside" the silhouette. Those features include several candidate craters as well as indications of other sorts of large-scale topographic relief, including a prominent central indentation. Protuberances at the asteroid's ends may be related to the pattern of ejecta removal and deposition caused by the asteroid's gravity field. The asteroid's surface is homogeneous and displays only modest roughness at centimeter-to-meter scales. Our estimates of radar cross section and the currently available constraints on the asteroid's dimensions are consistent with a near-surface bulk density between 2 and 3 g/cu cm. The delay-Doppler trajectory of Geographos' center of mass has been determined to about 200 m on August 28 and to about 100 m on August 31, an improvement of two orders of magnitude over pre-observation ephemerides.

Ostro, Steven J.↗