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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

MW-Class SOFC Pilot System Development

The overall objective of this project is to develop a low-cost, efficient, and reliable MWe-class Solid Oxide Fuel Cell (SOFC) power system towards commercial deployment in natural-gas fueled distributed generation applications. This report details the successful completion of all project objectives. The main goals of the project were to develop the conceptual design of a MWe-class SOFC power system, and to complete a techno-economic analysis (TEA) to determine system costs at low-volume production levels of >100MW per year. The combination of the BoP equipment cost and SOFC stack module factory cost provided the net fabrication cost of the selected 1MW SOFC system configuration. The results of the study showed that the cost target of less than $6000/kW is achievable for a FOAK 1MW SOFC system, exclusive of the first-time engineering cost. Also, the project included an exploratory analysis of the factory cost of next generation stack technology based on the Compact Solid-oxide Architecture (CSA) design at a high annual manufacturing rate of one-GW produced in a giga-factory. The BoP capital cost for one giga-watt power production was estimated using learning-curve analysis based on the historical manufacturing cost data related to similar high temperature Molten Carbonate fuel cell systems built by FuelCell Energy (FCE). The giga-factory manufactured SOFC cost estimate combined with the BoP cost at high production rates led to the estimation of entire system capital cost. Ultimately, a Cost of Electricity (COE) analysis was performed including natural gas fuel prices, installation and O&M costs, and stack replacement cost. The results of the techno-economic analysis were summarized by parametric estimation of COE for 1MW SOFC NOAK (Nth-of-a-Kind) system with natural gas prices as a variable parameter.

08 HYDROGEN↗
DOE OSTI2024

The Role of Low-Carbon Fuels and Carbon Capture in Decarbonizing the U.S. Clinker Manufacturing for Cement Production: CO2 Emissions Reduction Potentials

Low-carbon fuels, feedstocks, and energy sources can play a vital role in the decarbonization of clinker production in cement manufacturing. Fuel switching with renewable natural gas, green hydrogen, and biomass can provide a low-carbon energy source for the high-temperature process heat during the pyroprocessing steps of clinker production. However, up to 60% of CO2 emissions from clinker production are attributable to process-related CO2 emissions, which will need the simultaneous implementation of other decarbonization technologies, such as carbon capture. To evaluate the potential of fuel switching and carbon capture technologies in decarbonizing the cement industry, a study of the facility-level CO2 emissions is necessary. This study evaluates the potential for using a single low-carbon fuel as an energy source in clinker production for cement manufacturing compared to conventional clinker production (which uses a range of fuel mixes). In addition, conventional carbon capture (operated with natural gas-based steam for solvent regeneration) and electrified carbon capture configurations were designed and assessed for net-zero emission targets. Carbon emissions reductions with and without biogenic emissions credits were analyzed to ascertain their impact on the overall carbon accounting. Results show that carbon emissions intensity of cement can vary from 571 to 784 kgCO2eq/metric ton of cement without carbon capture and from 166.33 to 438.66 kgCO2eq/metric ton of cement with carbon capture. We find that when biogenic carbon credits are considered, cement production with a sustainably grown biomass as fuel source coupled with conventional carbon capture can lead to a net-negative emission cement (−271 kgCO2eq/metric ton of cement), outperforming an electrified capture design (35 kgCO2eq/metric ton of cement). The carbon accounting for the Scope 1, 2, and biogenic emissions conducted in this study is aimed at helping researchers and industry partners in the cement and concrete sector make an informed decision on the choice of fuel and decarbonization strategy to adopt.

42 ENGINEERING↗
NASA NTRS1987

Effective collision strengths for electron impact excitations in S II

Electron impact collision strengths for forbidden, semiforbidden, and allowed transitions in S II calculated using the R-matrix method are presented. Configuration interaction wave functions are used to represent the six target states included in the calculation. At low impact energies the collision strengths are dominated by resonances for several transitions. The contribution from higher partial waves is obtained in the close-coupling approximation with exchange terms omitted. Results are presented for the effective collision strengths over a wide temperature range (5000-150,000 K) of astrophysical interest. The present results for the 4S(0) yields 2P(0) transition are 20-30 percent lower than previous calculations, while for the 4S(0) yields 2D(0) transition they are in good agreement. The results are approximately 30 percent higher than those of Ho and Henry (1983) for the 4S(0) yields 2P(0) transition at 80,000 K, and the difference between the two results increases with decreasing temperatures (under 80,000 K).

Tayal, S. S.↗
NASA NTRS1999

Orientation Effects in ZnO Films Using Off-Axis Sputtering Deposition

ZnO is a wide-band-gap oxide material and has been used in numerous applications. It is also a good substrate for fabricating GaN-based (a blue laser candidate) devices. Off-axis sputtering technique is one of the best techniques in synthesizing oxide materials because negative ion bombardment and particle kinetic energy is greatly reduced when adatoms condense on substrates. Since the sputtered material from the target arrive on the substrate surface at a 90 deg. configuration, which differs from the normal sputtering geometry, it is expected that the film uniformity and composition distributions will be affected. However, the details of these properties and mechanisms have not been well studied. ZnO films are synthesized on (0001) sapphire and quartz substrates by off-axis sputtering deposition in various oxygen/argon mixture ratios and pressures at different temperatures. Substrates and sputtering sources are placed at three different orientations that are orthogonal to each other. The normal direction of a substrate is parallel to the gravity vector and the other is perpendicular to it. Film thickness profiles at different growth orientations are determined using a profimeter. All films grown at high temperatures have highly textured structures on quartz substrates and epitaxially grow on sapphire substrates. Because of this process, the film surface is very smooth. X-ray diffraction, scanning probe microscopy, and Fourier transfer infrared spectroscopy, and electrical measurements will be used to characterize these films. Detailed results will be discussed in the presentation.

Zhu, Shen↗
NASA NTRS2003

Computational Hemodynamic Simulation of Human Circulatory System under Altered Gravity

A computational hemodynamics approach is presented to simulate the blood flow through the human circulatory system under altered gravity conditions. Numerical techniques relevant to hemodynamics issues are introduced to non-Newtonian modeling for flow characteristics governed by red blood cells, distensible wall motion due to the heart pulse, and capillary bed modeling for outflow boundary conditions. Gravitational body force terms are added to the Navier-Stokes equations to study the effects of gravity on internal flows. Six-type gravity benchmark problems are originally presented to provide the fundamental understanding of gravitational effects on the human circulatory system. For code validation, computed results are compared with steady and unsteady experimental data for non-Newtonian flows in a carotid bifurcation model and a curved circular tube, respectively. This computational approach is then applied to the blood circulation in the human brain as a target problem. A three-dimensional, idealized Circle of Willis configuration is developed with minor arteries truncated based on anatomical data. Demonstrated is not only the mechanism of the collateral circulation but also the effects of gravity on the distensible wall motion and resultant flow patterns.

Kim. Chang Sung↗
NASA NTRS2004

Simulation of Spatial and Temporal Radiation Exposures for ISS in the South Atlantic Anomaly

The International Space Station (ISS) living areas receive the preponderance of ionizing radiation exposure from Galactic Cosmic Rays (GCR) and geomagnetically trapped protons. Practically all trapped proton exposure occurs when the ISS passes through the South Atlantic Anomaly (SAA) region. The fact that this region is in proximity to a trapping mirror point indicates that the proton flux is highly directional. The inherent shielding provided by the ISS structure is represented by a recently-developed CAD model of the current 11-A configuration. Using modeled environment and configuration, trapped proton exposures have been analytically estimated at selected target points within the Service and Lab Modules. The results indicate that the directional flux may lead to substantially different exposure characteristics than the more common analyses that assume an isotropic environment. Additionally, predictive capability of the computational procedure should allow sensitive validation with corresponding on-board directional dosimeters.

Anderson, Brooke M.↗
NASA NTRS2008

Spacecraft Formation Control: Managing Line-of-Sight Drift Based on the Dynamics of Relative Motion

In a quest to improve space-based observational capability, an increasing number of investigators are proposing missions with precision formation flying architectures. Typical missions include the Micro- Arcsecond X-ray Imaging Mission (MAXIM), Stellar Imager (SI), and the New Worlds Observer (NWO). Missions designed to explore targets in deep-space generally require holding a formation configuration fixed in inertial space during science observation. Analysis in this paper is specifically aimed at the NWO architecture, characterizing the natural drift of the line-of-sight and the separation range for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2) libration point. Analysis employs a linear form of the relative dynamics associated with an n-body gravity field. The study is designed to identify favorable observation directions, characterized by minimal line-of-sight drift, along the mission timeline.

Luquette, Richard J.↗
NASA NTRS2008

Simulating Operation of a Complex Sensor Network

Simulation Tool for ASCTA Microsensor Network Architecture (STAMiNA) ["ASCTA" denotes the Advanced Sensors Collaborative Technology Alliance.] is a computer program for evaluating conceptual sensor networks deployed over terrain to provide military situational awareness. This or a similar program is needed because of the complexity of interactions among such diverse phenomena as sensing and communication portions of a network, deployment of sensor nodes, effects of terrain, data-fusion algorithms, and threat characteristics. STAMiNA is built upon a commercial network-simulator engine, with extensions to include both sensing and communication models in a discrete-event simulation environment. Users can define (1) a mission environment, including terrain features; (2) objects to be sensed; (3) placements and modalities of sensors, abilities of sensors to sense objects of various types, and sensor false alarm rates; (4) trajectories of threatening objects; (5) means of dissemination and fusion of data; and (6) various network configurations. By use of STAMiNA, one can simulate detection of targets through sensing, dissemination of information by various wireless communication subsystems under various scenarios, and fusion of information, incorporating such metrics as target-detection probabilities, false-alarm rates, and communication loads, and capturing effects of terrain and threat.

Jennings, Esther↗
NASA NTRS2011

Fuel Efficiencies Through Airframe Improvements

The factors of continuing strong growth in air traffic volume, the vital role of the air transport system on the economy, and concerns about the environmental impact of aviation have added focus to the National Aeronautics Research Policy. To address these concerns in the context of the National Policy, NASA has set aggressive goals in noise reduction, emissions, and energy consumption. With respect to the goal of reducing energy consumption in the fleet, the development of promising airframe technologies is required to realize the significant improvements that are desired. Furthermore, the combination of advances in materials and structures with aerodynamic technologies may lead to a paradigm shift in terms of potential configurations for the future. Some of these promising airframe technologies targeted at improved efficiency are highlighted.

Bezos-O'Connor, Gaudy M.↗
NASA NTRS2012

Sofia Observatory Performance and Characterization

The Stratospheric Observatory for Infrared Astronomy (SOFIA) has recently concluded a set of engineering flights for Observatory performance evaluation. These in-flight opportunities have been viewed as a first comprehensive assessment of the Observatory's performance and will be used to address the development activity that is planned for 2012, as well as to identify additional Observatory upgrades. A series of 8 SOFIA Characterization And Integration (SCAI) flights have been conducted from June to December 2011. The HIPO science instrument in conjunction with the DSI Super Fast Diagnostic Camera (SFDC) have been used to evaluate pointing stability, including the image motion due to rigid-body and flexible-body telescope modes as well as possible aero-optical image motion. We report on recent improvements in pointing stability by using an Active Mass Damper system installed on Telescope Assembly. Measurements and characterization of the shear layer and cavity seeing, as well as image quality evaluation as a function of wavelength have been performed using the HIPO+FLITECAM Science Instrument configuration (FLIPO). A number of additional tests and measurements have targeted basic Observatory capabilities and requirements including, but not limited to, pointing accuracy, chopper evaluation and imager sensitivity. SCAI activities included in-flight partial Science Instrument commissioning prior to the use of the instruments as measuring engines. This paper reports on the data collected during the SCAI flights and presents current SOFIA Observatory performance and characterization.

Temi, Pasquale↗
NASA NTRS2020

An Experimental Approach to a Rapid Propulsion and Aeronautics Concepts Testbed

Modern aircraft design tools have limitations for predicting complex propulsion-airframe interactions. The demand for new tools and methods addressing these limitations is high based on the many recent Distributed Electric Propulsion (DEP) Vertical Take-Off and Landing (VTOL) concepts being developed for Urban Air Mobility (UAM) markets. We propose that low cost electronics and additive manufacturing can support the conceptual design of advanced autonomy-enabled concepts, by facilitating rapid prototyping for experimentally driven design cycles. This approach has the potential to reduce complex aircraft concept development costs, minimize unique risks associated with the conceptual design, and shorten development schedule by enabling the determination of many "unknown unknowns" earlier in the design process and providing verification of the results from aircraft design tools. A modular testbed was designed and built to evaluate this rapid design-build-test approach and to support aeronautics and autonomy research targeting UAM applications utilizing a complex, transitioning-VTOL aircraft configuration. The testbed is a modular wind tunnel and flight model. The testbed airframe is approximately 80% printed, with labor required for assembly. This paper describes the design process, fabrication process, ground testing, and initial wind tunnel structural and thermal loading of a proof-of-concept aircraft, the Langley Aerodrome 8 (LA-8).

McSwain, Robert G.↗
NASA NTRS2026

Prototype Demonstration of Solar-Carbothermal System to Extract Oxygen From Regolith

The Carbothermal Reduction Demonstration (CaRD) project was an effort to develop a prototype system to demonstrate the extraction of oxygen from simulated lunar regolith using concentrated solar energy and a carbothermal reaction. The prototype consisted of a deployable solar concentrator capable of tracking the sun, carbothermal reactor, fluid system, gas analysis, and a solar concentrator control system consisting of avionics and software. These subsystems were developed by multiple NASA centers and a private industry partner, Sierra Space. The various teams worked together to define requirements and interfaces to successfully assemble the complex system and demonstrate an integrated solar carbothermal process. The solar concentrator developed at Glenn Research Center (GRC) was designed to be stowed for a launch environment then deployed on the lunar surface. It utilized a crossed dragone configuration of composite mirrors to direct horizontal sunlight onto a target 90° from the incoming sunlight. The key performance parameters for the solar concentrator were efficiency and power density. The carbothermal reactor was developed by Sierra Space through a separate project called the Carbothermal Oxygen Production Reactor (COPR) where it successfully demonstrated a fully automated process in a thermal vacuum environment [1]. The fluid system needed for the carbothermal reaction was also developed by Sierra Space and successfully demonstrated in the same thermal vacuum test. The gas analysis system was developed at Kennedy Space Center (KSC) and was required to determine the amount of oxygen extracted during each test. The gas analysis system was based on the Mass Spectrometer Observing Lunar Operations (MSOLO) instrument. Avionics and software for the CaRD prototype were also developed at KSC and based on experience with MSOLO avionics and software. The control system was designed to stow, deploy, track the sun, and perform beam alignment of the concentrated light. The prototype subsystems were integrated and tested at Johnson Space Center’s (JSC) Energy Systems Test Area. A heliostat was used to direct sunlight toward the prototype in a way that is representative of the sunlight conditions at the south pole of the Moon. When concentrated sunlight was focused on simulated lunar regolith within the reactor, the gas analysis team confirmed the presence of carbon monoxide gas, which confirmed that a solar carbothermal reaction took place. The key performance parameter for the integrated prototype was grams of oxygen extracted per kilowatt hour of energy arriving at the concentrator primary mirror. The prototype design successfully demonstrated end-to-end capability and further steps to achieve a flight capable system have been defined. With lunar data, engineers would be able to design a scaled-up system capable of extracting oxygen from regolith at useful quantities for crew life support and rocket propellant. On the long term, this method of In-Situ Resource Utilization could be used to drastically reduce the cost and risk of a sustained human presence on the Moon by reducing the amount of oxygen that would have to be delivered.

Koorosh R Araghi↗
NASA NTRS2026

Prototype Demonstration of Solar Carbothermal System to Extract Oxygen from Regolith

The Carbothermal Reduction Demonstration (CaRD) project was an effort to develop a prototype system to demonstrate the extraction of oxygen from simulated lunar regolith using concentrated solar energy and a carbothermal reaction. The prototype consisted of a deployable solar concentrator capable of tracking the sun, carbothermal reactor, fluid system, gas analysis, and a solar concentrator control system consisting of avionics and software. These subsystems were developed by multiple NASA centers and a private industry partner, Sierra Space. The various teams worked together to define requirements and interfaces to successfully assemble the complex system and demonstrate an integrated solar carbothermal process. The solar concentrator developed at Glenn Research Center (GRC) was designed to be stowed for a launch environment then deployed on the lunar surface. It utilized a crossed dragone configuration of composite mirrors to direct horizontal sunlight onto a target 90° from the incoming sunlight. The key performance parameters for the solar concentrator were efficiency and power density. The carbothermal reactor was developed by Sierra Space through a separate project called the Carbothermal Oxygen Production Reactor (COPR) where it successfully demonstrated a fully automated process in a thermal vacuum environment. The fluid system needed for the carbothermal reaction was also developed by Sierra Space and successfully demonstrated in the same thermal vacuum test. The gas analysis system was developed at Kennedy Space Center (KSC) and was required to determine the amount of oxygen extracted during each test. The gas analysis system was based on the Mass Spectrometer Observing Lunar Operations (MSOLO) instrument. Avionics and software for the CaRD prototype were also developed at KSC and based on experience with MSOLO avionics and software. The control system was designed to stow, deploy, track the sun, and perform beam alignment of the concentrated light. The prototype subsystems were integrated and tested at Johnson Space Center’s (JSC) Energy Systems Test Area. A heliostat was used to direct sunlight toward the prototype in a way that is representative of the sunlight conditions at the south pole of the Moon. When concentrated sunlight was focused on simulated lunar regolith within the reactor, the gas analysis team confirmed the presence of carbon monoxide gas, which confirmed that a solar carbothermal reaction took place. The key performance parameter for the integrated prototype was grams of oxygen extracted per kilowatt hour of energy arriving at the concentrator primary mirror. The prototype design successfully demonstrated end-to-end capability and further steps to achieve a flight capable system have been defined. With lunar data, engineers would be able to design a scaled-up system capable of extracting oxygen from regolith at useful quantities for crew life support and rocket propellant. On the long term, this method of In-Situ Resource Utilization could be used to drastically reduce the cost and risk of a sustained human presence on the Moon by reducing the amount of oxygen that would have to be delivered.

Aaron Paz↗
NASA NTRS2026

Prototype Demonstration of an Integrated Solar Concentrator System and Carbothermal Reactor Using Solar Energy to Extract Oxygen from Regolith

The Carbothermal Reduction Demonstration (CaRD) project was an effort to develop a prototype system to demonstrate the extraction of oxygen from simulated lunar regolith using concentrated solar energy and a carbothermal reaction. The prototype consisted of a deployable solar concentrator capable of tracking the sun, carbothermal reactor, fluid system, gas analysis, and a solar concentrator control system consisting of avionics and software. These subsystems were developed by multiple NASA centers and a private industry partner, Sierra Space. The various teams worked together to define requirements and interfaces to successfully assemble the complex system and demonstrate an integrated solar carbothermal process. The solar concentrator developed at Glenn Research Center (GRC) was designed to be stowed for a launch environment then deployed on the lunar surface. It utilized a crossed dragone configuration of composite mirrors to direct horizontal sunlight onto a target 90° from the incoming sunlight. The key performance parameters for the solar concentrator were efficiency and power density. The carbothermal reactor was developed by Sierra Space through a separate project called the Carbothermal Oxygen Production Reactor (COPR) where it successfully demonstrated a fully automated process in a thermal vacuum environment. The fluid system needed for the carbothermal reaction was also developed by Sierra Space and successfully demonstrated in the same thermal vacuum test. The gas analysis system was developed at Kennedy Space Center (KSC) and was required to determine the amount of oxygen extracted during each test. The gas analysis system was based on the Mass Spectrometer Observing Lunar Operations (MSOLO) instrument. Avionics and software for the CaRD prototype were also developed at KSC and based on experience with MSOLO avionics and software. The control system was designed to stow, deploy, track the sun, and perform beam alignment of the concentrated light. The prototype subsystems were integrated and tested at Johnson Space Center’s (JSC) Energy Systems Test Area. A heliostat was used to direct sunlight toward the prototype in a way that is representative of the sunlight conditions at the south pole of the Moon. When concentrated sunlight was focused on simulated lunar regolith within the reactor, the gas analysis team confirmed the presence of carbon monoxide gas, which confirmed that a solar carbothermal reaction took place. The key performance parameter for the integrated prototype was grams of oxygen extracted per kilowatt hour of energy arriving at the concentrator primary mirror. The prototype design successfully demonstrated end-to-end capability and further steps to achieve a flight capable system have been defined. With lunar data, engineers would be able to design a scaled-up system capable of extracting oxygen from regolith at useful quantities for crew life support and rocket propellant. On the long term, this method of In-Situ Resource Utilization could be used to drastically reduce the cost and risk of a sustained human presence on the Moon by reducing the amount of oxygen that would have to be delivered.

Oxygen from Regolith↗
NASA NTRS2010

Selectivity enhancement in photoacoustic gas analysis via phase-sensitive detection at high modulation frequency

A method for detecting a target fluid in a fluid sample comprising a first fluid and the target fluid using photoacoustic spectroscopy (PAS), comprises a) providing a light source configured to introduce an optical signal having at least one wavelength into the fluid sample; b) modulating the optical signal at a desired modulation frequency such that the optical signal generates an acoustic signal in the fluid sample; c) measuring the acoustic signal in a resonant acoustic detector; and d) using the phase of the acoustic signal to detect the presence of the target fluid.

Kosterev, Anatoliy↗
NASA NTRS2018

Range and Intensity Image-Based Terrain and Vehicle Relative Pose Estimation System

A navigation system includes an image acquisition device for acquiring a range image of a target vehicle, at least one processor, a memory including a target vehicle model and computer readable program code, where the processor and the computer readable program code are configured to cause the navigation system to convert the range image to a point cloud having three dimensions, compute a transform from the target vehicle model to the point cloud, and use the transform to estimate the target vehicle's attitude and position for capturing the target vehicle.

Gill, Nathaniel↗
DOE OSTI2026

Superstructure Optimization for Brine Valorization from Brackish Water Desalination

This poster presents preliminary results from a superstructure optimization framework developed to identify cost-optimal brine valorization configurations for brackish water desalination plants across diverse U.S. regional feed chemistries. The study uses brackish groundwater compositions from Arizona, California, Florida, New Mexico, and Texas. Using Pyomo Generalized Disjunctive Programming (GDP) within the WaterTAP modeling environment, the optimization framework simultaneously evaluates thousands of candidate treatment configurations, spanning nanofiltration, reverse osmosis, and chemical precipitation, to minimize the levelized cost of water (LCOW) while meeting water recovery targets and product recovery constraints. Results across eight representative feed clusters demonstrate water recovery rates of 57–87% and net LCOW values ranging from -$0.032/m³ (net revenue-positive) to $0.80/m. Notably, no single process configuration was optimal across all feed types, underscoring the necessity of feed-specific optimization. Products targeted include calcium carbonate (CaCO₃) at $0.01/kg and sodium chloride (NaCl) at $0.10/kg, both at 95% purity, with product revenues offsetting treatment costs in several scenarios. The work advances NAWI's process systems engineering capabilities for multi-configuration screening.

58 GEOSCIENCES↗
NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗