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Ultrafast Correlation Energy Estimator

A virtually no-cost method is proposed that can compute the correlation energies of general, covalently bonded, organic, and inorganic molecules (including conjugated π-electron systems) with a well-defined dominant Lewis structure at the accuracy of 99.5% of the near-exact values determined by the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] in the complete-basis-set (CBS) limit. This Correlation Energy Per Bond (CEPB) method assigns a partial correlation energy to each bond type (characterized by the identities of the two atoms forming the bond and its integer bond order) and to a lone pair, regardless of the bond length, bond angle, sp-hybridization, π-electron conjugation, ionicity, noncovalent interactions, etc. At its current stage, the method is mainly suitable for near-equilibrium geometries. The correlation energies per bond are determined by a fit to the CCSD(T)/CBS benchmarks. It can neither improve the equilibrium structures nor discern conformers or positional isomers, yet its accuracy for reaction energies rivals that of the second-order Møller–Plesset perturbation theory, which is far more expensive. Its promising performance underscores the possibility that surprisingly compact, chemically intuitive molecular fragments exist into which correlation energies can be partitioned, leading to various ultrafast correlation-energy estimators tailored to different purposes.

Binding energy↗

The SRG/eROSITA All-Sky Survey: Optical identification and properties of galaxy clusters and groups in the western galactic hemisphere

The first SRG/eROSITA All-Sky Survey (eRASS1) provides the largest intracluster medium-selected galaxy cluster and group catalog covering the western Galactic hemisphere. Compared to samples selected purely on X-ray extent, the sample purity can be enhanced by identifying cluster candidates using optical and near-infrared data from the DESI Legacy Imaging Surveys. Using the red-sequence-based cluster findereROMaPPer, we measured individual photometric properties (redshiftz λ , richnessλ, optical center, and BCG position) for 12000 eRASS1 clusters over a sky area of 13 116 deg 2 , augmented by 247 cases identified by matching the candidates with known clusters from the literature. The median redshift of the identified eRASS1 sample isz= 0.31, with 10% of the clusters atz> 0.72. The photometric redshifts have an accuracy ofδz/(1 +z) ≲ 0.005 for 0.05 specand velocity dispersionσ) were measured a posteriori for a subsample of 3210 and 1499 eRASS1 clusters, respectively, using an extensive compilation of spectroscopic redshifts of galaxies from the literature. We infer that the primary eRASS1 sample has a purity of 86% and optical completeness >95% forz> 0.05. For these and further quality assessments of the eRASS1 identified catalog, we applied our identification method to a collection of galaxy cluster catalogs in the literature, as well as blindly on the full Legacy Surveys covering 24069 deg 2 . Using a combination of these cluster samples, we investigated the velocity dispersion-richness relation, finding that it scales with richness as log(λ norm ) = 2.401 × log(σ) − 5.074 with an intrinsic scatter ofδ in = 0.10 ± 0.01 dex. The primary product of our work is the identified eRASS1 cluster catalog with high purity and a well-defined X-ray selection process, opening the path for precise cosmological analyses presented in companion papers.

Astronomy & Astrophysics↗

Model-based Hierarchical Reinforcement Learning for Improved Physical Security Design: A Prototype

Prior work in FY24 developed an adversarial AI agent aid in path analysis of physical protection systems. This agent, trained using a model-based reinforcement learning algorithm, was able to successfully learn the most vulnerable path in facilities. It was able to extend the current state of practice for physical protection design by exhibiting dynamic behavior based on current environmental conditions. Whereas PathTrace largely performs a static, graph-based analysis, the AI agent was able to make decisions based on relative position in the facility, current conditions (was the adversarial agnet discovered?), and proximity to secondary targets. The agent demonstrated some novel capabilities, but had limitations that need to be resolved before it can be used for production purposes. For example, the adversarial agent generalizes poorly and takes a relatively long time to train. Nonetheless, there is still considerable promise for developing the adversarial agent further in order to explore even richer, more dynamic behaviors (e.g., adversary motivations, environmental debris, and more). This work considers a complementary idea; development of a planning agent. The planning agent is envisioned as an auto-complete-like tool that can help accelerate security system design by human experts. The agent would respect existing barriers and sensors placed by a human expert while offering cost-effective suggestions (i.e., implicitly balancing effectiveness with cost) to improve the design. The goal is for this agent to be part of an expert’s toolbox, not to totally upend the current state-of-practice, or to displace human experts. The ultimate goal would be concurrent training of both the adversarial and planning agent together, to learn entirely through self-play. This would represent an entirely new way of performing system deign. We selected a hierarchical, model-based reinforcement learning algorithm to serve as the planning agent. This is an extension of concepts used in the prior FY24 adversarial agent work. There, we had a single agent acting an environment. Here, we have two different sub-agents (policies), working together, to form a complete agent. There is a manager policy, which can select abstract goals on slower time scales, and a worker, which performs primitive actions to reach goals selected by the manager. It is worth noting that this class of algorithm is challenging to work with. From our understanding, our work is one of the first successful uses of model-based reinforcement learning (MBRL) in nuclear energy1 , and likely the first hierarchical model-based reinforcement learning application in nuclear energy. Further, this work is one of the first known attempts to apply AI to perform a design tasks in nuclear energy. Consequently, there were significant implementation challenges and the bulk of the work was focused on successful implementation and algorithm design. The results presented here are very low technology readiness level as a consequence of the lack of related literature, but still represent a significant step forward in the pursuit of applied AI for design.

42 ENGINEERING↗

Optical testing cryogenic thermal vacuum facility

The construction of a turnkey cryogenic vacuum test facility was recently completed. The facility will be used to measure and record the surface profile of large diameter and 540 kg optics under simulated space conditions. The vacuum test chamber is a vertical stainless steel cylinder with a 3.5 diameter and a 7 m tangent length. The chamber was designed to maximize optical testing quality by minimizing the vibrations between the laser interferometer and the test specimen. This was accomplished by designing the chamber for a high natural frequency and vibration isolating the chamber. An optical test specimen is mounted on a movable presentation stage. During thermal vacuum testing, the specimen may be positioned to + or - 0.00025 cm accuracy with a fine adjustment mechanism. The chamber is evacuated by a close coupled Roots-type blower and rotary vane pump package and two cryopumps. The chamber is equipped with an optically dense gaseous nitrogen cooled thermal shroud. The thermal shroud is used to cool or warm the optical test specimen at a controlled rate. A control system is provided to automatically evacuate the chamber and cooldown the test specimen to the selected control temperature.

Dohogne, Patrick W.↗

Initial drop size and velocity distributions for airblast coaxial atomizers

Phase Doppler measurements were used to determine initial drop size and velocity distributions after a complete disintegration of coaxial liquid jets. The Sauter mean diameter (SMD) distribution was found to be strongly affected by the structure and behavior of the preceding liquid intact jet. The axial measurement stations were determined from the photographs of the coaxial liquid jet at very short distances (1-2 mm) downstream of the observed break-up locations. Minimum droplet mean velocities were found at the center, and maximum velocities were near the spray boundary. Size-velocity correlations show that the velocity of larger drops did not change with drop size. Drop rms velocity distributions have double peaks whose radial positions coincide with the maximum mean velocity gradients.

Eroglu, H.↗

Microbiological methods for the water recovery systems test, revision 1.1

Current microbiological parameters specified to verify microbiological quality of Space Station Freedom water quality include the enumeration of total bacteria, anaerobes, aerobes, yeasts and molds, enteric bacteria, gram positives, gram negatives, and E. coli. In addition, other parameters have been identified as necessary to support the Water Recovery Test activities to be conducted at the NASA/MSFC later this year. These other parameters include aerotolerant eutrophic mesophiles, legionellae, and an additional method for heterotrophic bacteria. If inter-laboratory data are to be compared to evaluate quality, analytical methods must be eliminated as a variable. Therefore, each participating laboratory must utilize the same analytical methods and procedures. Without this standardization, data can be neither compared nor validated between laboratories. Multiple laboratory participation represents a conservative approach to insure quality and completeness of data. Invariably, sample loss will occur in transport and analyses. Natural variance is a reality on any test of this magnitude and is further enhanced because biological entities, capable of growth and death, are specific parameters of interest. The large variation due to the participation of human test subjects has been noted with previous testing. The resultant data might be dismissed as 'out of control' unless intra-laboratory control is included as part of the method or if participating laboratories are not available for verification. The purpose of this document is to provide standardized laboratory procedures for the enumeration of certain microorganisms in water and wastewater specific to the water recovery systems test. The document consists of ten separate cultural methods and one direct count procedure. It is not intended nor is it implied to be a complete microbiological methods manual.

Rhoads, Tim↗

The stability of hibonite, melilite and other aluminous phases in silicate melts: Implications for the origin of hibonite-bearing inclusions from carbonaceous chondrites

Phase fields in which hibonite and silicate melt coexist with spinel CaAl4O7, gehlenitic melilite, anorthite or corundum at 1 bar in the system CaO-MgO-Al2O3-SiO2-TiO2 were determined. The hibonites contain up to 1.7 wt% SiO2. For TiO2, the experimentally determined partition coefficients between hibonite and coexisting melt D(sub i)(sup Hib/L), vary from 0.8 to 2.1 and generally decrease with increasing TiO2 in the liquid. Based on Ti partitioning between hibonite and melt, bulk inclusion compositions and hibonite-saturated liquidus phase diagrams, the hibonite in hibonite-poor fluffy Type A inclusions from Allende and at least some hibonite from hibonite-rich inclusions is relict, although much of the hibonite from hibonite-glass spherules probably crystallized metasably from a melt. Bulk compositions for all of these CAIs are consistent with an origin as melite + hibonite + spinel + perovskite phase assembalges that were partially altered and in some cases partially or completely melted. The duration of the melting event was sufficient to remove any Na introduced by the alteration process but frequently insufficient to dissolve all of the original hibonite. Simple thermochemical models developed for meteoritic melilite and hibonite solid solutions were used to obtain equilibration temperatures of hibonite-bearing phase assemblages with vapor. Referenced to 10(exp -3) atm, hibonite + corundum + vapor equilibrated at approximately 1260 C and hibonite + spinel +/- melilite + vapor at 1215 +/- 10 C. If these temperatures reflect condensation in a cooling gas of solar composition, then hibonite +/- corundum condensed first, followed by spinel and then melilite. The position of perovskite within this sequence is uncertain, but it probably began to condense before spinel. This sequence of phase appearances and relative temperatures is generally consistent with observed textures but differs from expectations based on classical condensation calculations in that equilibration temperatures are generally lower than predicted and melilite initially condenses with or even after spinel. Simple thermochemical modes for the substitution of trace elements into the Ca site of meteoritic hibonites suggest that virtually all Eu is divalent in early condensate hibonites but that Eu(2+)/Eu(#+) decreases by a factor of 20 or more during the course of condensation primarily because the ratio is proportional to the partial pressure of Al, which decreases dramatically as aluminous phase condense. The relative sizes of Eu and Yb anomalies in meteoritic hibonites and inclusions may be partly due to this effect.

Beckett, J. R.↗

A Comparison of Three Determinants of an Engagement Index for Use in a Simulated Flight Environment

The following report details a project design that is to be completed by the end of the year. Determining how engaged a person is at a task is rather difficult. There are many different ways to assess engagement. One such method is to use psychophysical measures. The current study focuses on three determinants of an engagement index proposed by researchers at NASA-Langley (Pope, A. T., Bogart, E. H., and Bartolome, D. S., 1995). The index (20 Beta/(Alpha+Theta)) uses EEG power bands to determine a person's level of engagement while performs a compensatory tracking task. The tracking task switches between manual and automatic modes. Participants each experience both positive and negative feedback within each trial of the three trials. The tracking task is altered in terms of difficulty depending on the participants current engagement index. The rationale of this study is to determine the optimal level of engagement to gain peak performance. The three determinants are based on an absolute index which differs from the past research which uses a slope index.

Hitt, James M., II↗

NASA/University Joint Venture in Space Science (JOVE)

The spectra of the Ring Nebula at position angle 124 degrees, covering a spectral range from [O III] 3727 A to [S II] 6723 A is obtained using McDonald Observatory's 82-inch telescope (operated by the University of Texas at Austin). This work was carried out in September of 1991. During the 1992 summer, the analysis of the McDonald spectra were carried out and compared the results with the IUE (UV) spectra of the Ring Nebula. In addition, IRAF was successfully installed on NASA/Jove Sun IPC workstation (polaris) during September 1993 and the installation of three additional Sun workstations (mizar, dubhe, and merak) is about to be completed.

Quigley, Robert J.↗

Constellation Program Lessons Learned: Detailed Lessons Learned - Volume 2

These lessons learned are part of a suite of hardware, software, test results, designs, knowledge base, and documentation that comprises the legacy of the Constellation Program. The context, summary information, and lessons learned are presented in a factual format, as known and described at the time. While our opinions might be discernable in the context, we have avoided all but factually sustainable statements. Statements should not be viewed as being either positive or negative; their value lies in what we did and what we learned that is worthy of passing on. The lessons include both "dos" and "don ts." In many cases, one person s "do" can be viewed as another person s "don t"; therefore, we have attempted to capture both perspectives when applicable and useful. While Volume I summarizes the views of those who managed the program, this Volume II encompasses the views at the working level, describing how the program challenges manifested in day-to-day activities. Here we see themes that were perhaps hinted at, but not completely addressed, in Volume I: unintended consequences of policies that worked well at higher levels but lacked proper implementation at the working level; long-term effects of the "generation gap" in human space flight development, the need to demonstrate early successes at the expense of thorough planning, and the consequences of problems and challenges not yet addressed because other problems and challenges were more immediate or manifest. Not all lessons learned have the benefit of being operationally vetted, since the program was cancelled shortly after Preliminary Design Review. We avoid making statements about operational consequences (with the exception of testing and test flights that did occur), but we do attempt to provide insight into how operational thinking influenced design and testing. The lessons have been formatted with a description, along with supporting information, a succinct statement of the lesson learned, and recommendations for future programs and projects that may be placed in similar circumstances.

Jennifer Rhatigan↗

Chirped-Superlattice, Blocked-Intersubband QWIP

An Al(x)Ga(1-x)As/GaAs quantum-well infrared photodetector (QWIP) of the blocked-intersubband-detector (BID) type, now undergoing development, features a chirped (that is, aperiodic) superlattice. The purpose of the chirped superlattice is to increase the quantum efficiency of the device. A somewhat lengthy background discussion is necessary to give meaning to a brief description of the present developmental QWIP. A BID QWIP was described in "MQW Based Block Intersubband Detector for Low-Background Operation" (NPO-21073), NASA Tech Briefs Vol. 25, No. 7 (July 2001), page 46. To recapitulate: The BID design was conceived in response to the deleterious effects of operation of a QWIP at low temperature under low background radiation. These effects can be summarized as a buildup of space charge and an associated high impedance and diminution of responsivity with increasing modulation frequency. The BID design, which reduces these deleterious effects, calls for a heavily doped multiple-quantum-well (MQW) emitter section with barriers that are thinner than in prior MQW devices. The thinning of the barriers results in a large overlap of sublevel wave functions, thereby creating a miniband. Because of sequential resonant quantum-mechanical tunneling of electrons from the negative ohmic contact to and between wells, any space charge is quickly neutralized. At the same time, what would otherwise be a large component of dark current attributable to tunneling current through the whole device is suppressed by placing a relatively thick, undoped, impurity-free AlxGa1 x As blocking barrier layer between the MQW emitter section and the positive ohmic contact. [This layer is similar to the thick, undoped Al(x)Ga(1-x)As layers used in photodetectors of the blocked-impurity-band (BIB) type.] Notwithstanding the aforementioned advantage afforded by the BID design, the responsivity of a BID QWIP is very low because of low collection efficiency, which, in turn, is a result of low electrostatic- potential drop across the superlattice emitter. Because the emitter must be electrically conductive to prevent the buildup of space charge in depleted quantum wells, most of the externally applied bias voltage drop occurs across the blocking-barrier layer. This completes the background discussion. In the developmental QWIP, the periodic superlattice of the prior BID design is to be replaced with the chirped superlattice, which is expected to provide a built-in electric field. As a result, the efficiency of collection of photoexcited charge carriers (and, hence, the net quantum efficiency and thus responsivity) should increase significantly.

Gunapala, Sarath↗

Illuminating the Photophysics of Oxygen Atom Transfer in Rare Earth Metal-Organic Complexes

Industrial separations of rare earth metals are reliant on selectivity based on ionic radii, which are time, energy, and resource consuming.1 The unique and discontinuous manifold of energy states associated with the f-electron configurations of the rare earth ions2 offer an opportunity to overcome some of these limitations by incorporating light into the separation process. Here, we use transient absorption spectroscopy to understand the differences in mechanism of light-initiated oxygen atom transfer (OAT) in yttrium (Y) and dysprosium (Dy) rare earth complexes. These metal-organic complexes are functionalized with hexfluoroacetyl-acetonate (hfac) and 4-methylmorpholine-N-oxide (NMMO). After light absorption in the presence of triphenyl phosphine (TPP), the NMMO in the Y-NMMO complex is replaced by the TPPO OAT reaction product. Because the Dy f-electron manifold is accessible to the ligand excited states, while there are no accessible states associated with f-electrons for Y, there are significant differences in reactivity. Transient absorption spectroscopy (TAS) was used to monitor changes after 340 nm photoexcitation of Dy/Y-NMMO or the product complex Dy/Y-TPPO. TAS is a pump-probe technique where a white light probe pulse is delayed relative to a visible pump pulse, which photoexcites a sample. Differences between the ground and excited states are monitored over time. With TAS, we access time scales from 100 fs-400 us to determine the photophysics of the complexes of interest. Photoexcitation of Y-NMMO (Fig. 1A) creates a broad photoinduced absorption (PIA) that evolves into a sharp positive feature over 4.2 ps centered at 450 nm. A secondary feature centered at 550 nm grows in with a 200 ps time constant and remains through the 5 ns time window of our experiment. Control experiments for Y-TPPO reveal that the feature at 450 nm is due to internal dynamics of the hfac ligand, while the 550 nm shoulder is due to the presence of the NMMO. Comparing kinetics at 550 nm for Y-NMMO and Dy-NMMO (Fig. 1B) shows that while Y exhibits a distinct growth in the NMMO feature, the Dy decays almost completely within 5 ns. Control experiments with Dy-TPPO prove that the ligand excited states centered on the hfac ligand are deactivated via energy transfer to the Dy manifold within 200 ps. This deactivation leads to significant differences in OAT reactivity between Y and Dy.

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS↗

ATR Fuel Management

The sixth Core Internals Changeout (CIC) of ATR was completed on March 21, 2022, and Nuclear Testing (NT) commenced shortly thereafter. In support of NT, 235U flux wires were attached to flux wands using electrical tape and installed in water channels 2, 6, 11, 15 and 19 in each of the 40 ATR Mark VII fuel elements that comprise an ATR core to perform low power flux measurements during ATR Cycle 170CIC NT-3. The flux wands were fabricated from Poly (Methyl Methacrylate), or PMMA. Irradiated cobalt capsules were loaded in the ATR Northeast Irradiation Housing Assembly (NEIHA), the East Flux Trap (EFT), South Flux Trap (SFT), inboard A-positions and various H-positions as a 170CIC NT-3 core reactivity hold-down mechanism. The PMMA flux wands received significant gamma dose from the irradiated cobalt during NT-3 which caused discoloration, embrittlement and swelling of the flux wands. The removal of the degraded flux wands from the 0.078 in. wide by 50 in. long fuel element coolant channels has been a unique challenge. This presentation summarizes the cleaning techniques used to remove the flux wand debris from the elements, an aggressive PMMA irradiation experiment performed concomitantly with initial cleaning efforts, and planned inspection and qualification techniques that will be applied in the future to potentially requalify the impacted elements for re-use.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Amino acids of the Murchison meteorite. I - Six carbon acyclic primary alpha-amino alkanoic acids

Six of the seven chain isomers of six-carbon acyclic primary alpha-amino alkanoic acids (leucine isomers) have been either identified or confirmed in hot-water extracts of the Murchison meteorite using combined gas chromatography-mass spectrometry (GC-MS) and ion exchange chromatography. 2-Amino-2-ethylbutyric acid, 2-amino-2,3-dimethylbutyric acid, pseudoleucine, and 2-methylnorvaline were positively identified by GC-MS. These amino acids have not been previously reported to occur in natural materials and may be uniquely meteoritic in origin. The presence of leucine and isoleucine (including the diastereoisomer, alloisoleucine) was confirmed. Peaks corresponding to norleucine were seen by ion-exchange and gas chromatography but characteristic mass spectra were not obtained. The alpha-branched chain isomers in this series are quantitatively the most significant. These results are compared with literature data on amino acid synthesis by electrical discharge and Fischer-Tropsch-type catalysis. Neither model system produces an amino acid suite that is completely comparable to that found in the Murchison meteorite.

Cronin, J. R.↗

EMU Shoulder Injury Tiger Team Report

The number and complexity of extravehicular activities required for the completion and maintenance of the International Space Station is unprecedented. It is not surprising that training to perform these space walks presents a risk of overuse musculoskeletal injuries. The goal of this tiger team, created in December 2002, was to identify the different factors contributing to the risk of EVA training-related shoulder injury in the Neutral Buoyancy Lab at the Sonny Carter Training Facility and to make recommendations that would either significantly reduce or eliminate those risks. Since 1999, concerns have been expressed about the risk of shoulder injury associated with EVA training at the NBL, particularly in inverted body positions (McMonigal, 1999). A survey was developed and administered to 42 astronauts and astronaut candidates; the results suggest a causal relationship between EVA training at the NBL and the observed injuries. Also, during the tiger team review, it became evident that training in the extravehicular mobility unit may also result in other types of injuries, including fingernail delamination, elbow pain, knee pain, foot pain, and nerve compression leading to transient loss of sensation in certain areas of the upper or lower extremity. A multi-directorate team to detect, evaluate and respond to the medical issues associated with EVA training should be implemented immediately and given the appropriate resources and authority to reduce the risk of injury to crew during training to a level as low as reasonably achievable.

Williams, David R.↗

Raman spectroscopic characterization of SiO 2 phase transformation and Si substrate stress relevant to EBC performance

To accurately model the long-term durability of environmental barrier coatings (EBCs), a more complete understanding of the phase composition and transformations of the thermally grown oxide SiO 2 (TGO) is desired. For the TGO formed during thermal cycling in steam, cristobalite formation and the subsequent β- to α-cristobalite transformation has been identified as a potentially life-limiting mechanism. In this study, Raman micro-spectroscopy was used to quantify the cristobalite transformation on a polycrystalline Si coupon that was exposed to steam at 1350°C for 100 h. The phase transformation was mapped at 200–260°C on the TGO surface at different ramp rates using a heating stage and a micro-positioning stage. The stress in the Si substrate was also determined using Raman spectroscopy by measuring the stress induced peak shift. The α→β phase transformation produced a 300–500 MPa tensile stress in the Si substrate, which compared well to the stress predicted from the volumetric expansion of the cristobalite. In conclusion, quantifying the phase transformation and residual stress are critical tools in developing the next generation of high performance EBCs.

36 MATERIALS SCIENCE↗

Cargo systems manual: Heat Pipe Performance (HPP) STS-66

The purpose of the cargo systems manual (CSM) is to provide a payload reference document for payload and shuttle flight operations personnel during shuttle mission planning, training, and flight operations. It includes orbiter-to-payload interface information and payload system information (including operationally pertinent payload safety data) that is directly applicable to the Mission Operations Directorate (MOD) role in the payload mission. The primary objectives of the heat pipe performance (HPP) are to obtain quantitative data on the thermal performance of heat pipes in a microgravity environment. This information will increase understanding of the behavior of heat pipes in space and be useful for application to design improvements in heat pipes and associated systems. The purpose of HPP-2 is to establish a complete one-g and zero-g data base for axial groove heat pipes. This data will be used to update and correlate data generated from a heat pipe design computer program called Grooved Analysis Program (GAP). The HPP-2 objectives are to: determine heat transport capacity and conductance for open/closed grooved heat pipes and different Freon volumes (nominal, under, and overcharged) using a uniform heat load; determine heat transport capacity and conductance for single/multiple evaporators using asymmetric heat loads; obtain precise static, spin, and rewicking data points for undercharged pipes; investigate heat flux limits (asymmetric heat loads); and determine effects of positive body force on thermal performance.

Napp, Robert↗

Estimates of Minimum Energy Requirements for Range-Controlled Return of a Nonlifting Satellite from a Circular Orbit

Existing expressions are used to obtain the minimum propellant fraction required for return from a circular orbit as a function of vacuum trajectory range. trajectory are matched to those of the atmospheric trajectory to obtain a complete return from orbit to earth. The results are restricted by the assumptions of (1) impulsive velocity change, (2) nearly circular transfer trajectory, ( 3) spherical earth, atmosphere, and gravitational field, (4) exponential atmospheric density variation with attitude, and (5) a nonrotating atmosphere. The solutions for the parameters of the vacuum Calculations are made t o determine the effects of longitudinal and lateral range on required propeUant fraction and reentry loading for a nonrotating earth and for several orbital altitudes. the single- and two-impulse method of return is made and the results indicate a "trade off" between propellant fraction required and landing- position accuracy. A comparison of An example of a return mission from a polar orbit is discussed where the initial deorbit point is the intersection of the North Pole horizon with the satellite orbit. Some effects of a rotating earth are also considered. It is found that, for each target-orbital-plane longitudinal difference, there exists a target latitude for which the required propellant fraction is a minimum.

Jackson, Charlie M., Jr.↗