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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

The determination of physical and dynamical parameters of Pluto/Charon and binary asteroids by least-square formation of a matched filter for a time series of images. I - The operational theory

A theory is derived for the determination of the masses, radii, and orbital elements of the Pluto/Charon, or similar, system based on the prediction of an image distribution over space and time and its comparison with observation. The comparison may be ultimately through the theory of least squares or the application of a matched filter to the observations as a three-dimensional signal stream at an initial or intermediate state. The theory is an approximation correct to fifth order in the diameters of celestial bodies. The theory of astronomical seeing that is used is based on Kolmogorov turbulence in the long-exposure limit. The images must be photometric. Linear tracking errors that can be removed are preferable to either automatic or manual guiding, in the collection of candidate observations.

Wildey, R. L.↗
DOE OSTI2025

SSAPy - Space Situational Awareness for Python

SSAPy is a fast and flexible orbit modeling and analysis tool for orbits spanning from low-Earth into the cislunar regime. Orbits can be flexibly specified from common input formats such as Keplerian elements or two-line element (TLE) data files. SSAPy allows users to model satellites and specify parameters such as satellite area, mass, and drag coefficients. SSAPy includes a customizable force-propagation with a range of Earth, Lunar, radiation, atmospheric, and maneuvering models. SSAPy makes use of various community integration methods and can calculate time-evolved orbital quantities, including satellite magnitudes and state vectors. Users can specify various space- and ground-based observation models with support for multiple coordinate and reference frames. SSAPy also supports orbit analysis and propagation methods such as multiple hypothesis tracking and has built-in uncertainty quantification. The majority of SSAPy’s methods are vectorized and parallelizable, allowing for effective use of high-performance computer (HPC) systems. Finally, SSAPy has plotting functionality, allowing users to visualize orbits and trajectories. Examples are shown in Figure 1 and Figure 2.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Solar dynamic modules for Space Station Freedom: The relationship between fine-pointing control and thermal loading of the aperture plate

Dynamic simulations of Space Station Freedom (SSF) configured with solar dynamic (SD) power modules were performed. The structure was subjected to Space Shuttle docking disturbances, while being controlled with a 'natural' vibration and tracking control approach. Three control cases were investigated for the purpose of investigating the relationship between actuator effort, SD pointing, and thermal loading on the receiver aperture plate. Transient, one-dimensional heat transfer analyses were performed to conservatively predict temperatures of the multi-layered receiver aperture plate assembly and thermal stresses in its shield layer. Results indicate that the proposed aperture plate is tolerant of concentrated flux impingement during short-lived structural disturbances. Pointing requirements may be loosened and the requirement control torques lessened from that previously specified. Downsizing and simplifying the joint drive system should result in a considerable savings mass.

Quinn, Roger D.↗
NASA NTRS2018

Risk-Based Explosion Assessment Internal Explosion of Exploration Upper Stage in Vehicle Assembly Building

This paper presents risk-based explosion analyses used to determine if an explosion of NASA's Space Launch System (SLS) Exploration Upper Stage (EUS) during fueling in Vehicle Assembly Building (VAB) High Bay 4 can hazard the Space Launch System (SLS) being processed in Bay 3. This paper focuses on blast fragmentation as it was the controlling hazard. An estimate of the amount of Net Explosion Weight (NEW) was used to develop a fragment list (mass, shape, takeoff velocity/angle) given an explosion occurs at ground level in Bay 4. Intervening superstructure that exists between Bay 4 and Bay 3 (that could potentially block EUS fragments) was modeled based on detailed visual images (VISSIM) and AUTOCAD/structural drawings. The fragment list was input to a 3D trajectory application that performs multiple random explosion simulations; each simulation varying fragment ballistic coefficient and takeoff angle/velocity. Individual fragments are tracked until stopped by the intervening superstructure or reach Bay 3, potentially impacting the SLS. The probability of impacting the SLS is then determined from the random simulations; the results are used to help decision-makers determine the efficacy of co-processing within the VAB and decide what mitigations may be appropriate.

Explosion Assessment↗
NASA NTRS1995

Fast Track Lunar NTR Systems Assessment for NASA's First Lunar Outpost and Its Evolvability to Mars

Integrated systems and missions studies are presented for an evolutionary lunar-to-Mars space transportation system (STS) based on nuclear thermal rocket (NTR) technology. A 'standardized' set of engine and stage components are identified and used in a 'building block' fashion to configure a variety of piloted and cargo, lunar and Mars vehicles. The reference NTR characteristics include a thrust of 50 thousand pounds force (klbf), specific impulse (I(sub sp)) of 900 seconds, and an engine thrust-to-weight ratio of 4. 3. For the National Aeronautics and Space Administrations (NASA) First Lunar Outpost (FLO) mission, and expendable NTR stage powered by two such engines can deliver approximately 96 metric tonnes (t) to trans-lunar injection (TLI) conditions for an initial mass in low Earth orbit (IMLEO) of approximately 198 t compared to 250 t for a cryogenic chemical system. The stage liquid hydrogen (LH2) tank has a diameter, length, and capacity of 10 m, 14.5 m and 66 t, respectively. By extending the stage length and LH2 capacity to approximately 20 m and 96 t, a single launch Mars cargo vehicle could deliver to an elliptical Mars parking orbit a 63 t Mars excursion vehicle (MEV) with a 45 t surface payload. Three 50 klbf engines and the two standardized LH2 tanks developed for the lunar and Mars cargo vehicles are used to configure the vehicles supporting piloted Mars missions as early as 2010. The 'modular' NTR vehicle approach forms the basis for an efficient STS able to handle the needs of a wide spectrum of lunar and Mars missions.

Borowski, Stanley K.↗
NASA NTRS1991

Final STS-35 Columbia descent BET products and results for LaRC OEX investigations

Final STS-35 'Columbia' descent Best Estimate Trajectory (BET) products have been developed for Langley Research Center (LaRC) Orbiter Experiments (OEX) investigations. Included are the reconstructed inertial trajectory profile; the Extended BET, which combines the inertial data and, in this instance, the National Weather Service atmospheric information obtained via Johnson Space Center; and the Aerodynamic BET. The inertial BET utilized Inertial Measurement Unit 1 (IMU1) dynamic measurements for deterministic propagation during the ENTREE estimation process. The final estimate was based on the considerable ground based C-band tracking coverage available as well as Tracking Data and Relay Satellite System (TDRSS) Doppler data, a unique use of the latter for endo-atmospheric flight determinations. The actual estimate required simultaneous solutions for the spacecraft position and velocity, spacecraft attitude, and six IMU parameters - three gyro biases and three accelerometer scale factor correction terms. The anchor epoch for this analysis was 19,200 Greenwich Mean Time (GMT) seconds which corresponds to an initial Shuttle altitude of approximately 513 kft. The atmospheric data incorporated were evaluated based on Shuttle derived considerations as well as comparisons with other models. The AEROBET was developed based on the Extended BET, the measured spacecraft configuration information, final mass properties, and the final Orbiter preoperation databook. The latter was updated based on aerodynamic consensus incrementals derived by the latest published FAD. The rectified predictions were compared versus the flight computed values and the resultant differences were correlated versus ensemble results for twenty-two previous STS entry flights.

Oakes, Kevin F.↗
NASA NTRS2012

Spinoff 2011

Topics include: Bioreactors Drive Advances in Tissue Engineering; Tooling Techniques Enhance Medical Imaging; Ventilator Technologies Sustain Critically Injured Patients; Protein Innovations Advance Drug Treatments, Skin Care; Mass Analyzers Facilitate Research on Addiction; Frameworks Coordinate Scientific Data Management; Cameras Improve Navigation for Pilots, Drivers; Integrated Design Tools Reduce Risk, Cost; Advisory Systems Save Time, Fuel for Airlines; Modeling Programs Increase Aircraft Design Safety; Fly-by-Wire Systems Enable Safer, More Efficient Flight; Modified Fittings Enhance Industrial Safety; Simulation Tools Model Icing for Aircraft Design; Information Systems Coordinate Emergency Management; Imaging Systems Provide Maps for U.S. Soldiers; High-Pressure Systems Suppress Fires in Seconds; Alloy-Enhanced Fans Maintain Fresh Air in Tunnels; Control Algorithms Charge Batteries Faster; Software Programs Derive Measurements from Photographs; Retrofits Convert Gas Vehicles into Hybrids; NASA Missions Inspire Online Video Games; Monitors Track Vital Signs for Fitness and Safety; Thermal Components Boost Performance of HVAC Systems; World Wind Tools Reveal Environmental Change; Analyzers Measure Greenhouse Gasses, Airborne Pollutants; Remediation Technologies Eliminate Contaminants; Receivers Gather Data for Climate, Weather Prediction; Coating Processes Boost Performance of Solar Cells; Analyzers Provide Water Security in Space and on Earth; Catalyst Substrates Remove Contaminants, Produce Fuel; Rocket Engine Innovations Advance Clean Energy; Technologies Render Views of Earth for Virtual Navigation; Content Platforms Meet Data Storage, Retrieval Needs; Tools Ensure Reliability of Critical Software; Electronic Handbooks Simplify Process Management; Software Innovations Speed Scientific Computing; Controller Chips Preserve Microprocessor Function; Nanotube Production Devices Expand Research Capabilities; Custom Machines Advance Composite Manufacturing; Polyimide Foams Offer Superior Insulation; Beam Steering Devices Reduce Payload Weight; Models Support Energy-Saving Microwave Technologies; Materials Advance Chemical Propulsion Technology; and High-Temperature Coatings Offer Energy Savings.

Source record↗
NASA NTRSDate not supplied

Post-Flight Reconstruction Approach for Space Launch System Artemis I Mission

Upon completion of the first Space Launch System flight, NASA personnel will begin post-flight analyses. Telemetry from across the vehicle will be combined with external radar tracking and environmental observation data in order to close validation criteria and generate a best estimated trajectory (BET). This paper will describe the approach taken by the SLS team to integrate flight data from multiple flights sources into BET, pre-flight simulation and testing results, primary sources of uncertainty, and path towards processing flight results. This paper also includes a brief description of algorithms and approaches to estimate as-flown vehicle parameters such as booster specific impulse, booster (and core) thrust multipliers and dry mass.

Evan John Anzalone↗
NASA NTRSDate not supplied

Investigating Risks Due to Artemis EVA Tempo Via Probabilistic Risk Assessment

Spaceflight operations pose unique challenges to crew health, safety, and resource management. As space agencies and private companies continue to push the boundaries of human exploration, it is essential to understand the risks associated with Extravehicular Activities (EVAs) and develop strategies to mitigate them. The tempo at which EVAs are conducted – the total number and frequency of these activities – can have a profound impact on medical risks, resource consumption, and overall mission success. Probabilistic risk assessment (PRA) provides a powerful framework for evaluating complex systems and identifying potential hazards. Our work employs the Medical Extensible Dynamic Probabilistic Risk Assessment Tool (MEDPRAT) [1] to simulate mission events, occurrence and treatment of medical conditions, and track the utilization of resources. Coupled with the Evidence Library [2], a medical evidence base for exploration-class missions developed by the Exploration Medical Capability within NASA’s Human Research Program, we can estimate these risks with increased fidelity and optimize medical kit contents to meet specific mission requirements. This presentation provides a detailed examination of how EVA tempo influences medical risk estimates for a lunar surface design reference mission. A comprehensive analysis is conducted to assess the additional mass and volume burden imposed on medical kits required to maintain adequate levels of risk mitigation. Furthermore, we estimate the distribution of the number of successful EVAs completed based on the level of task impairment imposed by medical events and flight rules related to specific medical events, such as decompression sickness.

Modeling↗
NASA NTRS2017

Chondrules: Ubiquitous Chondritic Solids Tracking the Evolution of the Solar Protoplanetary Disk

Chondrite meteorites are samples of primitive asteroidal bodies thathave escaped melting and differentiation. The only record of our Solar System’sformative stages comes from the earliest solids preserved in chondrites, namelymillimetre- to centimetre-sized calcium-aluminium-rich inclusions (CAIs) andchondrules. These solids formed by transient heating events during the lifetimeof the solar protoplanetary disk. Collectively, CAIs and chondrules provide time-sequenced samples allowing us to probe the composition of the disk material thataccreted to form planetesimals and planets. Here, we showcase the current state-of-the-art data with respect to the chronology and stable isotopic compositions ofindividual chondrules from various chondrite groups and discuss how these datacan be used to provide novel insights into the thermal and chemical evolution of thesolar protoplanetary disk, including mass transport processes.

Martin Bizzarro↗
NASA NTRS1992

Grasp force control in telemanipulation

This paper presents two experiments which focus upon the issue of grasp force control in telemanipulation. The first experiment examines the ability to control and stabilize master-controller grasp force during a 30-s compensatory tracking task under different levels of master controller digit mass, friction, and backlash. The second experiment explores the potential for substituting tactile feedback in lieu of direct force-feedback to gage and control remote grasp force. Results show that subjects were better able to control force when mass and friction levels were increased. Even when perceptual gains between tactile and direct force feedback displays were matched, force reflection produced better grasp control. The lack of backlash effects and improvements in performance with direct force reflection in comparison to tactile feedback are attributable to reflexive short-loop adjustment of grasp tension afforded by the muscle's length-tension control system. The criterion of acceptable operator performance, dependent upon both the quality of the transmission of control commands and feedback, and the response of the remote device, is discussed.

Wiker, Steven F.↗
NASA NTRS1999

Modeling Studies of PVT Growth of ZnSe: Current Status and Future Course

Bulk growth of wide band gap II-VI semiconductors by physical vapor transport (PVT) has been developed and refined over the past several years at NASA Marshall Space Flight Center. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using a two-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and a compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles are provided. The simulations show that the Stefan flux dominates the system flow field and the subtle gravitational effects can be gauged by subtracting this flux from the calculated profiles. Shear flows, due to solutal buoyancy, of the order of 50 microns/s for the liorizont,-d growth orientation and 10 microns/s for the vertical orientation are predicted. Whether these flows can fully account for the observed gravity related growth morphological effects and inhomogeneous solute and dopant distributions is a matter of conjecture. A template for future modeling efforts in this area is suggested which incorporates a mathematical approach to the tracking of the growth front based on energy of formation concepts.

Ramachandran, N.↗
NASA NTRS2008

NASA Tech Briefs, August 2008

Customizable Digital Receivers for Radar Two-Camera Acquisition and Tracking of a Flying Target Visual Data Analysis for Satellites A Data Type for Efficient Representation of Other Data Types Hand-Held Ultrasonic Instrument for Reading Matrix Symbols Broadband Microstrip-to-Coplanar Strip Double-Y Balun A Topographical Lidar System for Terrain-Relative Navigation Programmable Low-Voltage Circuit Breaker and Tester Electronic Switch Arrays for Managing Microbattery Arrays Topics covered include: Lower-Dark-Current, Higher-Blue-Response CMOS Imagers; Fabricating Large-Area Sheets of Single-Layer Graphene by CVD; Support for Diagnosis of Custom Computer Hardware; Providing Goal-Based Autonomy for Commanding a Spacecraft; Dynamic Method for Identifying Collected Sample Mass; Optimal Planning and Problem-Solving; Attitude-Control Algorithm for Minimizing Maneuver Execution Errors; Grants Document-Generation System; Heat-Storage Modules Containing LiNO3 3H2O and Graphite Foam; Precipitation-Strengthened, High-Temperature, High-Force Shape Memory Alloys; Improved Relief Valve Would Be Less Susceptible to Failure; Safety Modification of Cam-and-Groove Hose Coupling; Using Composite Materials in a Cryogenic Pump; Using Electronic Noses to Detect Tumors During Neurosurgery; Producing Newborn Synchronous Mammalian Cells; Smaller, Lower-Power Fast-Neutron Scintillation Detectors; Rotationally Vibrating Electric-Field Mill; Estimating Hardness from the USDC Tool-Bit Temperature Rise; Particle-Charge Spectrometer; Automated Production of Movies on a Cluster of Computers; FIDO-Class Development Rover; and Tone-Based Command of Deep Space Probes Using Ground Antennas.

Source record↗
NASA NTRS1994

Fast Track NTR Systems Assessment for NASA's First Lunar Outpost Scenario

Integrated systems and mission study results are presented which quantify the rationale and benefits for developing and using nuclear thermal rocket (NTR) technology for returning humans to the moon in the early 2000's. At present, the Exploration Program Office (ExPO) is considering chemical propulsion for its 'First Lunar Outpost' (FLO) mission, and NTR propulsion for the more demanding Mars missions to follow. The use of an NTR-based lunar transfer stage, capable of evolving to Mars mission applications, could result in an accelerated schedule, reduced cost approach to moon/Mars exploration. Lunar mission applications would also provide valuable operational experience and serve as a 'proving ground' for NTR engine and stage technologies. In terms of performance benefits, studies indicate that an expendable NTR stage powered by two 50 klbf engines can deliver approximately 96 metric tons (t) to trans-lunar injection (TLI) conditions for an initial mass in low earth orbit (IMLEO) of approximately 199 t compared to 250 t for a cryogenic chemical TLI stage. The NTR stage liquid hydrogen (LH2) tank has a 10 m diameter, 14.8 m length, and 68 t LH2 capacity. The NTR utilizes a 'graphite' fuel form consisting of coated UC2 particles in a graphite substrate, and has a specific impulse capability of approximately 870 s, and an engine thrust-to-weight ratio of approximately 4.8. The NTR stage and its piloted FLO lander has a total length of approximately 38 m and can be launched by a single Saturn V-derived heavy lift launch vehicle (HLLV) in the 200 to 250 t-class range. The paper summarizes NASA's First Lunar Outpost scenario, describes characteristics for representative engine/stage configurations, and examines the impact on engine selection and vehicle design resulting from a consideration of alternative NTR fuel forms and lunar mission profiles.

Borowski, Stanley K.↗
NASA NTRS1994

Pressure Control System Design for a Closed Crop Growth Chamber

The Controlled Ecological Life Support System (CELSS) is an area of active research at NASA. CELSS is a plant-based bioregenerative life support system for long term manned space flights where resupply is costly or impractical. The plants in a CELSS will function to convert the carbon dioxide (exhaled by the crew) into oxygen, purify non-potable water into potable quality water, and provide food for the crew. Prior to implementing a CELSS life support system, one must have knowledge on growing plants in a closed chamber under low gravity. This information will come from research to be conducted on the CELSS Test Facility that will operate on the Space Station Freedom. Currently a ground-based CELSS Test Facility is being built at NASA Ames Research Center. It is called the EDU (Engineering Development Unit). This system will allow researchers to identify issues that may cause difficulties in the development of the CELSS Test Facility and aid in the development of new needed technologies. The EDU consists of a 1 m2 crop growth chamber that is surrounded by a containment enclosure. The containment enclosure isolates the system so there is very little mass and thermal exchange with the ambient. The leakage rate is on the order of 1 % of the enclosure's volume per day (with 0.2S psi pressure difference). The thermal leakage is less than 0.5% of the electrical power supplied to the system per degree Celsius difference from the surrounding. The pressure in the containment enclosure is regulated at 62.5 Pa below the ambient by an active controller. The goal is to maintain this set point for a variety of conditions, such as a range of operating temperatures, heat load variations that occur when the lights are turned on and off, and fluctuations in ambient pressure. In addition certain transition tracking performance is required. This paper illustrates the application of some advanced systems control methods to the task of synthesizing the EDU's pressure control system.

Tsai, K.↗
NASA NTRS1996

Relativistic Navigation: A Theoretical Foundation

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the relativistic equations of satellite motion in the vicinity of the extended bodies. Anticipating improvements in radio and laser tracking technologies over the next few decades, we apply this method to spacecraft orbit determination. We emphasize the number of feasible relativistic gravity tests that may be performed within the context of the parameterized WFSMA. Based on the planeto-centric equations of motion of a spacecraft around the planet, we suggested a new null test of the Strong Equivalence Principle (SEP). The experiment to measure the corresponding SEP violation effect could be performed with the future Mercury Orbiter mission. We discuss other relativistic effects, including the perihelion advance and the redshift and geodetic precession of the orbiter's orbital plane about Mercury, as well as the possible future implementation of the proposed formalism in software codes developed for solar-system orbit determination. All the important calculations are completely documented, and the references contain an extensive list of cited literature.

Turyshev, Slava G.↗
NASA NTRS2009

The Integrated Medical Model - Optimizing In-flight Space Medical Systems to Reduce Crew Health Risk and Mission Impacts

The Integrated Medical Model (IMM) is a decision support tool used by medical system planners and designers as they prepare for exploration planning activities of the Constellation program (CxP). IMM provides an evidence-based approach to help optimize the allocation of in-flight medical resources for a specified level of risk within spacecraft operational constraints. Eighty medical conditions and associated resources are represented in IMM. Nine conditions are due to Space Adaptation Syndrome. The IMM helps answer fundamental medical mission planning questions such as What medical conditions can be expected? What type and quantity of medical resources are most likely to be used?", and "What is the probability of crew death or evacuation due to medical events?" For a specified mission and crew profile, the IMM effectively characterizes the sequence of events that could potentially occur should a medical condition happen. The mathematical relationships among mission and crew attributes, medical conditions and incidence data, in-flight medical resources, potential clinical and crew health end states are established to generate end state probabilities. A Monte Carlo computational method is used to determine the probable outcomes and requires up to 25,000 mission trials to reach convergence. For each mission trial, the pharmaceuticals and supplies required to diagnose and treat prevalent medical conditions are tracked and decremented. The uncertainty of patient response to treatment is bounded via a best-case, worst-case, untreated case algorithm. A Crew Health Index (CHI) metric, developed to account for functional impairment due to a medical condition, provides a quantified measure of risk and enables risk comparisons across mission scenarios. The use of historical in-flight medical data, terrestrial surrogate data as appropriate, and space medicine subject matter expertise has enabled the development of a probabilistic, stochastic decision support tool capable of optimizing in-flight medical systems based on crew and mission parameters. This presentation will illustrate how to apply quantitative risk assessment methods to optimize the mass and volume of space-based medical systems for a space flight mission given the level of crew health and mission risk.

Kerstman, Eric↗
NASA NTRS1981

Saturn gravity results obtained from Pioneer 11 tracking data and earth-based Saturn satellite data

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

Null, G. W.↗