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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 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

MHD modelling of the earth's magnetosphere

Attention is given to the shock capturing technique, nonuniform grid system, and multiple time scale problem aspects of a global MHD model of the earth's magnetosphere that uses numerical methods. Because of the fast Alfven waves near the earth, the model is more difficult to solve than problems of hydrodynamic flow past bodies. The Rusanov (1962) scheme, which is a variant of the Lax (1954) method that maintains viscosity at a minimum value except where a large one is required, is used. The magnetosphere shape obtained by these means is noted.

Wu, C. C.↗
NASA NTRS1986

Approximate methods for finding CO2 15-micron band transmission in planetary atmospheres

Physical band models that use simplifying assumptions about the structure of the CO2 15-micron band are described and compared with the accurate line-by-line model of Fels and Schwarzkopf (1981). The methods have application to the models of the atmospheres of Venus, earth, and Mars. The narrow-band methods include a general random model and techniques employing the Malkmus (1967) line-strength distribution, and the accuracy of these models at low pressure is found to be sensitive to the line-strength distribution and the line shape. When combined with a simple Voigt parameterization, the more efficient approximate methods represented by an exponential wideband model are found to be almost as accurate as the expensive narrow-band models. Empirical logarithmic wideband models used in climate-modeling studies are found to be very efficient, but of limited range of validity.

Crisp, David↗
NASA NTRS1989

Aerobraking orbital transfer vehicle

An aerobraking orbital transfer vehicle which includes an aerobraking device which also serves as a heat shield in the shape of a raked-off elliptic or circular cone with a circular or elliptical base, and with an ellipsoid or other blunt shape nose. The aerobraking device is fitted with a toroid-like skirt and is integral with the support structure of the propulsion system and other systems of the space vehicle. The vehicle is intended to be transported in components to a space station in lower earth orbit where it is assembled for use as a transportation system from low earth orbit to geosynchronous earth orbit and return. Conventional guidance means are included for autonomous flight.

Scott, Carl D.↗
NASA NTRSDate not supplied

Geopolymer Concrete – A greener alternative on Earth and a feasible material for the Moon

This research is focused on designing in-situ-based concrete material for extraterrestrial construction. Five regolith lunar simulants varying in their compositions were tested and their mechanical performance tested. The results have shown that the lunar regolith simulants are feasible for such concrete technology but exhibit variability due to their mineralogy, amorphous (glass) content, and particle size and shape distributions.

Peter J Collins↗
NASA NTRS1985

Sea floor swells and mantle plumes

Most of the intraplate oceanic hot spots are located on the crest of broad topographic swells in the sea floor. These swells have Gaussian shaped profiles, with up to 1.6 km of relief and half widths of 200 to 300 km. Swells are accompanied by positive geoid height anomalies with amplitudes of 6 to 8 m. In the Atlantic and Pacific basins swells cover an area equal to 10% of the Earth's surface. Next to boundary layer contraction, swells are the most important cause of uplift and subsidence in oceanic lithosphere. Calculation of buoyancy supported topography and geoid height were combined with uplift data from laboratory experiments to assess whether sea floor swell can be produced by mantle plumes. The critical constraints are: (1) swell topographic profiles; (2) geoid height/topographic height ratios; and (3) uplift rates, estimated to be 0.2 km/ma.

Olson, P.↗
NASA NTRS1990

Auroral kilometric radiation - An example of relativistic wave-particle interaction in geoplasma

The earth's auroral kilometric radiation (AKR) is believed to be produced by the electron-cyclotron maser instability. This instability is the result of a wave-particle interaction in which relativistic effects are crucial. An explanation is given as to how these relativistic effects alter the shape of the resonance curve in velocity space and modify the R - X mode wave dispersion near the electron cyclotron frequency compared to the results obtained in the nonrelativistic limit and from cold-plasma theory. The properties of the cyclotron maser instability in a driven system are illustrated using two-dimensional electromagnetic particle simulations which incorporate a continual flow of primary energetic electrons along the magnetic field.

Pritchett, P. L.↗
NASA NTRS1991

Hoop column soil moisture spacecraft in low Earth orbit for global change monitoring

A subset of the total Global Change Technology Initiative instruments are required to be in low Earth, sunsynchronous orbits. There is one instrument, however, that requires its own specialized spacecraft; the Soil Moisture Microwave Radiometer (SMMR). The characteristic structure of the instrument is the 118 m hoop column support structure. The hoop is supported by an axially placed column. Tension cables support and shape an electromagnetically reflective mesh surface. The instrument is capable of detecting frequencies in the 1.4 GHz range (Soil Moisture and Sea Salinity). Three apertures are used to reduce the degree of paraboloid offset and improve the beam quality. The spacecraft configuration is determined by the instrument support requirements and the requirement that it can fit into the Titan IV cargo bay. The configuration is derived by cross referencing the instrument performance requirements with the performance of the spacecraft. The spacecraft design is similar with the Multi-mission Modular Spacecraft in terms of size and packaging. A description of the spacecraft's features will yield a summary of the technologies needed for the SMMR spacecraft.

Ferebee, Melvin J., Jr.↗
NASA NTRS1992

Atomic oxygen undercutting of LDEF aluminized-Kapton multilayer insulation

Atomic oxygen undercutting is a potential threat to vulnerable spacecraft materials which have atomic oxygen protective coatings. Such undercutting is due to atomic oxygen attack of oxidizable materials at microscopic defects in the protective coatings. These defects occur during fabrication and handling, or from micrometeoroid and debris bombardment in space. An aluminized-polyimide Kapton multilayer insulation sample that was located on the leading edge of the Long Duration Exposure Facility (LDEF) was used to study low Earth orbit directed ram atomic oxygen undercutting. Cracks in the aluminized coatings located around vent holes provided excellent defect sites for evaluation of atomic oxygen undercutting. The experimentally observed undercutting profiles were compared to predictions from Monte Carlo models for normal incident ram atomic oxygen attack. The shape of the undercut profile was found to vary with crack width, which is proportional to the number of oxygen atoms entering the crack. The resulting profiles of atomic oxygen which occurred on LDEF indicated wide undercut cavities in spite of the fixed ram orientation. Potential causes of the observed undercutting are presented. Implications of the undercutting profiles relevant to the Space Station Freedom are also discussed.

Degroh, Kim K.↗
NASA NTRS1992

Attitude stability of LDEF: Refinement of results from the silver pinhole camera

A measurement was previously described of the angular offset and attitude stability of the LDEF spacecraft using a simple pinhole camera device in the UAH experiment A0114. This device uses a silver surface to record the impact zone of atmospheric atomic oxygen passing through a small pinhole on the front surface of the satellite. The shape and size of this zone are well defined if the satellite velocity and gas temperature are known. The circular symmetry of the zone would be distorted by oscillation of the LDEF about its stable attitude, or by the effect of the co-rotation of the Earth's atmosphere for cases of satellites in nonequatorial orbits. The observed ellipticity of 1.05 with the major axis in the yaw direction is equivalent to an oscillation of + or - 0.2 deg about the stable attitude. The uncertainty in that measurement was estimated at about 0.1 deg. A refined analysis based on summing distributions of flux versus incidence angle for a large number of orbital positions, and including a co-rotating atmosphere, indicates that the combined distributions produce a result consistent with the measured exposed spot. It is suggested that, within the precision of the measurements, no actual oscillation of the LDEF is required to produce the results. Thus, the LDEF may have maintained a stable attitude to better than 0.1 deg, even under conditions of maximum aerodynamic perturbation when the silver oxygen record was made. This error is some two orders of magnitude lower than the predicted uncertainty in yaw oscillation and may indicate that the predict methodologies are too conservative.

Peters, P. N.↗
NASA NTRS2002

A Closed-Loop Hardware Simulation of Decentralized Satellite Formation Control

In recent years, there has been significant interest in the use of formation flying spacecraft for a variety of earth and space science missions. Formation flying may provide smaller and cheaper satellites that, working together, have more capability than larger and more expensive satellites. Several decentralized architectures have been proposed for autonomous establishment and maintenance of satellite formations. In such architectures, each satellite cooperatively maintains the shape of the formation without a central supervisor, and processing only local measurement information. The Global Positioning System (GPS) sensors are ideally suited to provide such local position and velocity measurements to the individual satellites. An investigation of the feasibility of a decentralized approach to satellite formation flying was originally presented by Carpenter. He extended a decentralized linear-quadratic-Gaussian (LQG) framework proposed by Speyer in a fashion similar to an extended Kalman filter (EKE) which processed GPS position fix solutions. The new decentralized LQG architecture was demonstrated in a numerical simulation for a realistic scenario that is similar to missions that have been proposed by NASA and the U.S. Air Force. Another decentralized architecture was proposed by Park et al. using carrier differential-phase GPS (CDGPS). Recently, Busse et al demonstrated the decentralized CDGPS architecture in a hardware-in-the-loop simulation on the Formation Flying TestBed (FFTB) at Goddard Space Flight Center (GSFC), which features two Spirent Cox 16 channel GPS signal generator. Although representing a step forward by utilizing GPS signal simulators for a spacecraft formation flying simulation, only an open-loop performance, in which no maneuvers were executed based on the real-time state estimates, was considered. In this research, hardware experimentation has been extended to include closed-loop integrated guidance and navigation of multiple spacecraft formations using GPS receivers and real-time vehicle telemetry. A hardware closed-loop simulation has been performed using the decentralized LQG architecture proposed by Carpenter in the GPS test facility at the Center for Space Research (CSR). This is the first presentation using this type of hardware for demonstration of closed-loop spacecraft formation flying.

Ebimuma, Takuji↗
NASA NTRS2004

A New View of Mars

During the last 8 years the US has successfully sent 2 major spacecraft to Mars 1z?der= planet. The Mars Global Surveyor spacecraft (IGS), which started operating at Mars in Sept 1977 and Mars Odyssey spacecraft that started operating in Jan 2002, are both operational and collecting data, including 1.5 meter pixel imagery, them spectrometry, magnetometry, altimeter/radiometry, gamma ray and neutron counts. imaging spectrometry, and gravity. The two orbiters are conceptually similar to Earth orbiting spacecraft in that their primary purpose is to observe, monitor, and measure a variety of parameters about the planet and report any changes that might be occurring on the surfaces and in the atmosphere. As a result we now have detailed physical descriptions of the shape, topography, magnetism. surface roughness, thermal inertia, atmospheric pressure and temperature, the distribution of hydrogen in the top meter of the crust, models for the planetary interior based upon data, and an image set that portrays much of the history of the past 3 billion years. understand how the planet came to be this way.

Smith, David E.↗
NASA NTRS2005

Salt Kinematics and InSAR

As part of a long-term attempt to learn how the climatic and tectonic signal interact to shape a steady state mountain monitored displacement of a markers in SE termination and also near the summit of a small viscous salt fountain extruding onto the Central plateau of Iran. The marker displacements relate to the first InSAR interferograms of salt extrusion (980913 to 990620) calculated Earth tides, winds, air pressures and temperatures. In the first documented staking exercise, hammered wooden stakes vertically through the surgical marl (c. 1 Ocm deep) onto the top of crystalline salt. These stakes installed in an irregular array elongate E-W along the c.50 m high cliff marking the effective SE terminus of the glacier at Qum Kuh(Centra1 Iran) ,just to the E of a NE trending river cliff about 40 m high. We merely measured the distances between pairs of stakes with known azimuth about 2 m apart to calculate sub horizontal strain in a small part of Qum Kuh. Stakes moved and micro strains for up to 46 pairs of stakes (p strain= ((lengthl-length2)/1engthl) x 10-1) was calculated for each seven stake epochs and plotted against their azimuth on simplified array maps. The data fit well the sine curves cxpected of the maximum and minimum strain ellipses. The first documented stakes located on the SE where the InSAR image show -1 1 to 0 mm pink to purple, 0 to lOmm purple to blue, and show high activity of salt in low activity area of the InSAR image (980913 to 990620).Short term micro strains of stake tie lines record anisotropic expansions due to heating and contraction due to cooling. All epochs changed between 7 to 1 17 days (990928 to000 1 16), showed 200 to 400 micro strain lengthening and shortening. The contraction and extension existed in each epoch, but the final strain was extension in E-W in Epoch land 6, contraction in E-W direction during epochs 2-3-4-5 and 7. The second pair of stakes hammered about 20 cm deep into the deep soils(more than 1 m) , near summit, where the colors change between 19 to 29mm in InSAR image(9809 13 to 990620). Additional information is included in the original abstract.

Aftabi, Pedarm↗
NASA NTRS2005

The Explorer's Guide to Impact Craters

Impact cratering is a fundamental geologic process of our solar system. It competes with other processes, such as plate tectonics, volcanism, fluvial, glacial and eolian activity, in shaping the surfaces of planetary bodies. In some cases, like the Moon and Mercury, impact craters are the dominant landform. On other planetary bodies impact craters are being continuously erased by the action of other geological processes, like volcanism on Io, erosion and plate tectonics on the Earth, tectonic and volcanic resurfacing on Venus, or ancient erosion periods on Mars. The study of crater populations is one of the principal tools for understanding the geologic history of a planetary surface. Among the general public, impact cratering has drawn wide attention through its portrayal in several Hollywood movies. Questions that are raised after watching these movies include: How do scientists learn about impact cratering? , and What information do impact craters provide in understanding the evolution of a planetary surface? Fundamental approaches used by scientists to learn about impact cratering include field work at known terrestrial craters, remote sensing studies of craters on various solid surfaces of solar system bodies, and theoretical and laboratory studies using the known physics of impact cratering.

Chuang, F.↗
NASA NTRS2018

Star & Planet Formation Studies and Opportunities with SOFIA

Star formation, the most fundamental process in the universe, is linked to planet formation and thus to the origin and evolution of life. We have a general outline of how planets and stars form, yet unraveling the details of the physics and chemistry continues to challenge us. The infrared and submillimeter part of the spectrum hold the most promise for studying the beginnings of star formation. The observational landscape recently shaped by Spitzer, Herschel and ALMA, continues to challenge our current theories. SOFIA, the Stratospheric Observatory for Infrared Astronomy, equipped with state-of-the-art infrared instrumentation to a vantage point at 45,000 feet (13.7 kilometers) flight altitude that is above 99.9 percent of the Earth's water vapor, enables observations in the infrared through terahertz frequencies not possible from the ground. SOFIA is a community observatory, about to start its sixth annual observing cycle. My talk will focus on recent results in advancing star and planet formation processes using SOFIAʼs imaging and polarimetric capabilities, and the upcoming science enabled by the 3rd generation instrument High-Resolution Mid-Infrared Spectrometer (HIRMES) to be commissioned in 2019. I will show how mid-infrared imaging is used to test massive star formation theories, how far-infrared polarimetry on sub-parsec scales is directly testing the role of magnetic fields in molecular clouds, and how velocity-resolved high-resolution spectroscopy will push forward our understanding of proto-planetary disk science. I will also summarize upcoming opportunities with the SOFIA observatory. For the latest news about your flying observatory, see https://sofia.usra.edu/.

Star formation↗
NASA NTRS1999

Osteoblast fibronectin mRNA, protein synthesis, and matrix are unchanged after exposure to microgravity

The well-defined osteoblast line, MC3T3-E1 was used to examine fibronectin (FN) mRNA levels, protein synthesis, and extracellular FN matrix accumulation after growth activation in spaceflight. These osteoblasts produce FN extracellular matrix (ECM) known to regulate adhesion, differentiation, and function in adherent cells. Changes in bone ECM and osteoblast cell shape occur in spaceflight. To determine whether altered FN matrix is a factor in causing these changes in spaceflight, quiescent osteoblasts were launched into microgravity and were then sera activated with and without a 1-gravity field. Synthesis of FN mRNA, protein, and matrix were measured after activation in microgravity. FN mRNA synthesis is significantly reduced in microgravity (0-G) when compared to ground (GR) osteoblasts flown in a centrifuge simulating earth's gravity (1-G) field 2.5 h after activation. However, 27.5 h after activation there were no significant differences in mRNA synthesis. A small but significant reduction of FN protein was found in the 0-G samples 2.5 h after activation. Total FN protein 27.5 h after activation showed no significant difference between any of the gravity conditions, however, there was a fourfold increase in absolute amount of protein synthesized during the incubation. Using immunofluorescence, we found no significant differences in the amount or in the orientation of the FN matrix after 27.5 h in microgravity. These results demonstrate that FN is made by sera-activated osteoblasts even during exposure to microgravity. These data also suggest that after a total period of 43 h of spaceflight FN transcription, translation, or altered matrix assembly is not responsible for the altered cell shape or altered matrix formation of osteoblasts.

Flight Experiment↗
NASA NTRS2024

Mineral Dust Optical Properties for Remote Sensing and Global Modeling: A Review

Dust plays a key role in many Earth system processes and is ubiquitous in the Martian atmosphere. Various intensive field campaigns, laboratory analyses, space-based remote sensing missions, and global modeling efforts aim to characterize dust optical properties. This is a bountiful time for dust scientists, and yet the interpretation of retrievals and comparison to models remains complicated by various conflicting assumptions that are part of each algorithm. For example, the conversion of satellite radiance measurements into products like aerosol optical depth for model evaluation depends upon aerosol properties like particle size and shape that are often prescribed and not part of the retrieval. Conversely, the model calculation of aerosol optical depth often uses different assumptions. The goal of this review is to first document algorithmic assumptions by various satellite retrieval products and models, and identify where there is consistency and where there are differences. In general, the differences documented in this paper reflect uncertainties resulting from incomplete observational characterization of dust aerosols and limitations in our understanding. Second, we note what observations might reduce uncertainties in our knowledge and bring greater consistency to retrievals and models, allowing for a more rigorous and harmonious comparison. The lack of comprehensive and realistic shape models for dust is an outstanding issue, such that closure between forward modeling from particle refractive index, shape, and size and observed optical properties cannot be achieved. Limitations in the computational methods that must be applied to model scattering from complex shapes also makes accurate optical modeling for dust challenging. Field observations indicate the persistence of coarse and giant dust particles at higher altitudes and farther downwind from their source than previously expected. Remote sensing retrieval algorithms based on observations at visible wavelengths have limited sensitivity to these particles and generally do not consider them, although a recent product based on longwave radiances is encouraging. Current measurements of the refractive index of bulk dust and fundamental dust minerology components such as hematite vary widely, inhibiting attempts to represent the variability in dust optical properties and forcing, as expected from different major dust source regions on Earth that have varying mineralogical composition. Some remote sensing retrieval algorithms allow for limited refractive index variability in their inversion solutions through mixing with other fine mode aerosol models, or optimizing the single scattering albedo, but Earth system models surveyed for this paper assume a globally uniform, size-invariant refractive index. Although no Martian dust samples have yet been returned to Earth, remote sensing observations indicate that Martian dust is globally homogenous in composition, and a single spectral refractive index assumption has been widely adopted to represent Martian dust. The lack of comprehensive, statistically representative measurements of dust particle microphysical properties (size distribution, morphology, complex index of refraction spectra, internal structure heterogeneity), and the resulting optical properties, limits our ability to verify the fidelity of these assumptions. A chain of measurements is needed, ranging from characterizing individual dust mineralogy components (e.g., pure hematite and goethite) to in situ sampling of complex atmospheric aerosol mixtures. Such results could be applied to both remote sensing retrievals that characterize the optical properties of the total aerosol burden in the atmosphere from total radiance measurements, and to global models that represent the total aerosol burden in the atmosphere by building it up from the balance of individual aerosol sources and sinks.

Aeolian dust↗
NASA NTRS1998

Inferences About the Early Moon From Gravity and Topography

Recent spacecraft missions to the Moon have significantly improved our knowledge of the lunar gravity and topography fields, and have raised some new and old questions about the early lunar history. It has frequently been assumed that the shape of the Moon today reflects an earlier equilibrium state and that the Moon has retained some internal strength. Recent analysis indicating a superisostatic state of some lunar basins lends support to this hypothesis. On its simplest level, the present shape of the Moon is slightly flattened by 2.2 +/- 0.2 km while its gravity field, represented by an equipotential surface, is flattened only about 0.5 km. The hydrostatic component to the flattening arising from the Moon's present day rotation contributes only 7 m. This difference between the topographic shape of the MOon and the shape of its gravitational equipotential has frequently been explained as the "memory" of an earlier moon that was rotating faster and had a correspondingly larger hydrostatic flattening. To obtain this amount of hydrostatic flattening from rotation alone, and accounting for the contribution of the present-day gravity field, the Moon's rotation rate would need to be about 15x greater than at present, leading ot a period of < 2 days. Maintaining its synchronous rotation with Earth would require a radius for the Moon's orbit of approximately 9 Earth Radii. Unfortunately, our confidence in the observed lunar flattening is not as great as we would like. The uncertainty of .02 km may not properly reflect the limitations of the Clementine dataset, which did not sample poleward of latitudes 81 N and 79 S. Also, the large variation of topography +/- 8 km seen on the MOon dwarfs our estimate fo the flattening. Further the lunar south pole is on the edge of, or possibly inside the massive deep, South Pole-Aitken Basin. Thus, polar radii could be underestimated. This would yield a smaller flattening, which would imply a greater lunar rotation period and orbital radius. However, Basin compensation states and analyses of support and relaxation of topography at long wavelengths point to a lunar shape that has retained a flattening from an earlier faster rotation period.

Smith, D. E.↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗