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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Impact of Climatic Variability on Atmospheric Mass Distribution and GRACE-Derived Gravity Fields

During the period we calculated the atmospheric data sets related to its mass and angular momentum distribution. For mass, we determined the various harmonics from the NCEP-NCAR reanalysis, especially the low-order harmonics that are useful in studying the gravitation distribution as will be determined from the GRACE mission. Atmospheric mass is also related to the atmospheric loading on the solid Earth; we cooperated with scientists who needed the atmospheric mass information for understanding its contributions to the overall loading, necessary for vertical and horizontal coordinate estimation. We calculated atmospheric angular momentum from the NCEP-NCAR reanalyses and 4 operational meteorological centers, based on the motion (wind) terms and the mass (surface pressure) terms. These are associated with motions of the planet, including its axial component causing changes in the length of day, more related to the winds, and the equatorial component related to motions of the pole, more related to the mass. Tasks related to the ocean mass and angular momentum were added to the project as well. For these we have noted the ocean impact on motions of the pole as well as the torque mechanisms that relate the transfer of angular momentum between oceans and solid earth. The activities of the project may be summarized in the following first manuscript written in December 2002, for a symposium that Dr. Salstein attended on Geodynamics. We have continued to assess ocean angular momentum (OAM) quantities derived from bottom pressure and velocity fields estimated with our finite-difference barotropic (single layer) model. Three years of output (1993-95) from a run without any data constraints was compared to output from a corresponding run that was constrained by altimeter data using a Kalman filter and smoother scheme. Respective OAM time series were combined with corresponding atmospheric series and compared to observed polar motion. The constrained OAM series provided slightly better variance reduction than the unconstrained series. Analysis provided a check on the estimation scheme and pointed to further work to improve the determination of OAM using this method. A significant effort was also devoted to quantifying effects of uncertainties in high frequency winds on the mean and seasonal momentum exchange between atmosphere and oceans.

Salstein, David A.↗
NASA NTRS2001

Amyloplast sedimentation dynamics in maize columella cells support a new model for the gravity-sensing apparatus of roots

Quantitative analysis of statolith sedimentation behavior was accomplished using videomicroscopy of living columella cells of corn (Zea mays) roots, which displayed no systematic cytoplasmic streaming. Following 90 degrees rotation of the root, the statoliths moved downward along the distal wall and then spread out along the bottom with an average velocity of 1.7 microm min(-1). When statolith trajectories traversed the complete width or length of the cell, they initially moved horizontally toward channel-initiation sites and then moved vertically through the channels to the lower side of the reoriented cell where they again dispersed. These statoliths exhibited a significantly lower average velocity than those sedimenting on distal-to-side trajectories. In addition, although statoliths undergoing distal-to-side sedimentation began at their highest velocity and slowed monotonically as they approached the lower cell membrane, statoliths crossing the cell's central region remained slow initially and accelerated to maximum speed once they reached a channel. The statoliths accelerated sooner, and the channeling effect was less pronounced in roots treated with cytochalasin D. Parallel ultrastructural studies of high-pressure frozen-freeze-substituted columella cells suggest that the low-resistance statolith pathway in the cell periphery corresponds to the sharp interface between the endoplasmic reticulum (ER)-rich cortical and the ER-devoid central region of these cells. The central region is also shown to contain an actin-based cytoskeletal network in which the individual, straight, actin-like filaments are randomly distributed. To explain these findings as well as the results of physical simulation experiments, we have formulated a new, tensegrity-based model of gravity sensing in columella cells. This model envisages the cytoplasm as pervaded by an actin-based cytoskeletal network that is denser in the ER-devoid central region than in the ER-rich cell cortex and is linked to stretch receptors in the plasma membrane. Sedimenting statoliths are postulated to produce a directional signal by locally disrupting the network and thereby altering the balance of forces acting on the receptors in different plasma membrane regions.

NASA Program Fundamental Space Biology↗
NASA NTRS1994

Method development for compensating temperature effects in pressure sensitive paint measurements

Pressure sensitive luminescent paints (PSP) have recently emerged as a viable technique for aerodynamic pressure measurements. The technique uses a surface coating which contains probe molecules that luminesce when excited by light of an appropriate wavelength. The photoluminescence of these materials is known to be quenched by the presence of molecular oxygen. Since oxygen is a fixed mole fraction of the air, the coating's luminescence intensity varies inversely with air pressure. Digital imaging of the luminescence varying across a coated surface produces a pressure distribution map over that surface. One difficulty encountered with this technique is the temperature effect on the luminescence intensity. Present PSP formulations have significant sensitivity to temperature. At the moment, the most practical way of correcting for temperature effects is to calibrate the paint in place at the operating temperatures by using a few well-placed pressure taps. This study is looking at development of temperature indicating coatings that can be applied and measured concurrently with PSP, and use the temperature measurement to compute the correct pressure. Two methods for this dual paint formulation are proposed. One method will use a coating that consists of temperature sensitive phosphors in a polymer matrix. This is similar in construction to PSP, except that the probe molecules used are selected primarily for their temperature sensitivity. Both organic phosphors (e.g., europium thenoyltrifluoroacetonate, bioprobes) and inorganic phosphors (e.g., Mg4(F)GeO6:Mn, La2O2S:Eu, Radelin Type phosphors, Sylvania Type phosphors) will be evaluated for their temperature sensing potential. The next method will involve a novel coating composing of five membered heterocyclic conducting polymers which are known to show temperature dependent luminescence (e.g., poly(3-alkylthiopene), poly(3-alkylselenophene), poly(3-alkylfuran)). Both methods will involve applying a bottom layer of temperature sensitive coating followed by a top coating of PSP. An oxygen-impermeable polymer can be used as the temperature sensitive coating matrix, or it can be layered in between the coatings to prevent oxygen quenching of the bottom coating's luminescence. The probe molecules of the coatings will be excited by a broad band of light, with the different emissions detected and measured at their distinct wavelengths. Developmental research of these coatings is still in progress; however, preliminary results look very promising.

Demandante, Carlo Greg N.↗
DOE OSTI2023

Revisiting the definition of field capacity as a functional parameter in a layered agronomic soil profile beneath irrigated maize

The soil water content at the condition of field capacity (θ FC ) is a key parameter in irrigation scheduling and has been suggested to be determined by running a synthetic drainage experiment until the flux rate (q) at the bottom of the soil profile achieves a predefined negligible value (q FC ). We question the impact of q FC on the assessment of field capacity. Moreover, calculating θ FC as the integral mean of the water content profile when q is equal to q FC is strictly valid only for uniform soil profiles. By contrast, this practice is ambiguous and biased for stratified soil profiles due to the soil water content discontinuity at the layer interfaces. In this study, the concept of field capacity was revisited and adapted to practical agronomic heuristics. By resorting to the assessment of root-zone water storage capacity (W), we envision field capacity as a functional hydraulic parameter derived from synthetic irrigation scheduling scenarios to minimize drought stress, drainage, and nitrate leachate below the root zone. A functional analysis was carried out on a 135-cm-thick layered soil profile beneath maize in eastern Nebraska. On-farm irrigation scheduling applications and agricultural practices were recorded for 20 years (2001–2020) at a daily time step. Hydrus-1D was calibrated and validated with direct measurements of the soil water retention curve and soil water content data, respectively, in each soil layer. A set of functional field capacity values was derived from 24 irrigation scheduling scenarios, and the optimal water storage capacity at field capacity (W FC ) was approximately 50 cm (corresponding to about 80% saturation in the soil profile). An average irrigation amount of 217.5 mm distributed over 21 events was obtained by using optimal irrigation scheduling, which was initiated when the matric pressure head took on a value of –700 cm and the irrigation rate was set at 1.0 cm d –1 . This irrigation practice ensured water storage at approximately the same level (ideally at W FC ) by sustaining only evapotranspiration fluxes in the uppermost portion of the root zone and by limiting excessive drainage. This protocol can be transferred to other agricultural fields.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2017

Sample Processor for Life on Icy Worlds (SPLIce): Design and Test Results

We report the design, development, and testing of the Sample Processor for Life on Icy Worlds (SPLIce) system, a microfluidic sample processor to enable autonomous detection of signatures of life and measurements of habitability parameters in Ocean Worlds. This monolithic fluid processing-and-handling system (Figure 1; mass 0.5 kg) retrieves a 50-L-volume sample and prepares it to supply a suite of detection instruments, each with unique preparation needs. SPLIce has potential applications in orbiter missions that sample ocean plumes, such as found in Saturns icy moon Enceladus, or landed missions on the surface of icy satellites, such as Jupiters moon Europa. Answering the question Are we alone in the universe? is captivating and exceptionally challenging. Even general criteria that define life very broadly include a significant role for water [1,2]. Searches for extinct or extant life therefore prioritize locations of abundant water whether in ancient (Mars), or present (Europa and Enceladus) times. Only two previous planetary missions had onboard fluid processing: the Viking Biology Experiments [3] and Phoenixs Wet Chemistry Laboratory (WCL) [4]. SPLIce differs crucially from those systems, including its capability to process and distribute L-volume samples and the integration autonomous control of a wide range of fluidic functions, including: 1) retrieval of fluid samples from an evacuated sample chamber; 2) onboard multi-year storage of dehydrated reagents; 3) integrated pressure, pH, and conductivity measurement; 4) filtration and retention of insoluble particles for microscopy; 5) dilution or vacuum-driven concentration of samples to accommodate instrument working ranges; 6) removal of gas bubbles from sample aliquots; 7) unidirectional flow (check valves); 8) active flow-path selection (solenoid-actuated valves); 9) metered pumping in 100 nL volume increments. The SPLIce manifold, made of three thermally fused layers of precision-machined cyclo-olefin polymer, supports all fluidic components (Figure 1) and integrated microchannels (125 x 250 m). Fluid is pumped by a stepper-motor-driven pump (Lee Co.). The functionality of the integrated MEMS pressure sensor (Honeywell) and passive check valves (Figure 2) were tested in conjunction with our newly designed integral bubble traps (Figure 3) and hydrophobic membrane-based concentrator (Figure 4). The concentrator (initially tested as a standalone component) demonstrated 5-fold vacuum-evaporative concentration. Polyethylene fused bead beds (PEFBBs; 50 porosity) store drylyophilized buffers, calibrants, and fluorescent dyes, and also promote mixing of sample with calibrant, dye, or H2O. Software-controlled automated tests demonstrated successful 1) fluid delivery to each component 2) valve and pump synchronization 3) sample aliquot delivery to instrument interface ports, and 4) rehydration of vacuum-dried fluorescent dye. In Figure 5, fluorescein on PEFBBs was rehydrated for 15 min using a pump-delivered water aliquot; it is displaced as H2O enters the bottom of the channel and pushes the dye into a check valve. Ultimately, SPLIce will fluorescently label amino acids in the sample for microchip-based electrophoretic (MCE) chiral separation and detection to seek and quantify key organic bio-signatures [5]; it will also deliver sample to a microfluidic version of WCL (mWCL) to measure soluble ions and redox-active species.

Life detection↗
NASA NTRS2013

High Water Contents in the Siberian Cratonic Mantle: An FTIR Study of Udachnaya Peridotite Xenoliths

Water is believed to be a key factor controlling the long-term stability of cratonic lithosphere, but mechanisms responsible for the water content distribution in the mantle remain poorly constrained. Water contents were obtained by FTIR in olivine, pyroxene and garnet for 20 well-characterized peridotite xenoliths from the Udachnaya kimberlite (central Siberian craton) and equilibrated at 2-7 GPa. Water contents in minerals do not appear to be related to interaction with the host kimberlite. Diffusion modeling indicates that the core of olivines preserved their original water contents. The Udachnaya peridotites show a broad range of water contents in olivine (6.5 +/- 1.1 to 323 +- 65 ppm H2O (2 sigma)), and garnet (0 - 23 +/- 6 ppm H2O). The water contents of olivine and garnet are positively correlated with modal clinopyroxene, garnet and FeO in olivine. Water-rich garnets are also rich in middle rare earth elements. This is interpreted as the result of interaction between residual peridotites and water rich-melts, consistent with modal and cryptic metasomatism evidenced in the Siberian cratonic mantle. The most water-rich Udachnaya minerals contain 2 to 3 times more water than those from the Kaapvaal craton, the only craton with an intact mantle root for which water data is available. The highest water contents in olivine and orthopyroxene in this study (>= 300 ppm) are found at the bottom of the lithosphere (> 6.5 GPa). This is in contrast with the Kaapvaal craton where the olivines of peridotites equilibrated at > 6.4 GPa have < 1 ppm H2O. The latter "dry" olivine may make the base of the Kaapvaal cratonic root strong and thus protects it from erosion by the convective mantle The calculated viscosity for water-rich Udachnaya peridotites at > 6 GPa is lower or similar (8.4× 10(exp 16) to 8.0× 10(exp 18) Pa./s) to that of the asthenosphere (<= 3.7x10(exp 18) Pa./s ). Such lithologies would not be able to resist delamination by the convecting asthenosphere. However, seismology studies as well as the high equilibration pressures of our samples indicate that the Udachnaya cratonic lithosphere is 220-250 km thick. Consequently, the water-rich peridotites are likely not representative of the overall Siberian cratonic lithosphere. Their composition is linked to spatially limited melt metasomatism in mantle regions above asthenospheric upwellings responsible for the kimberlite magmatism prior to their ascent and eruption.

Doucet, Luc S.↗
NASA NTRSDate not supplied

Habitable Working and Living Spaces in the Deep Space Science Vessel

The Deep Space Science Vessel (DSSV) is a conceptual design of a very large spacecraft intended as a mobile microgravity science platform. It represents an effort to conceptualize the systems and internal architectures needed to support a forty-eight-person crew for multi-year missions throughout the inner solar system and potentially beyond. The general arrangement of the DSSV is a modular spacecraft. Considering only the pressurized, habitable elements, the DSSV includes two large pressurized modules (Hab and Lab) docked together along with eight smaller node modules completing the habitable configuration. The Hab and Lab modules are docked side by side, with the longitudinal axes parallel to each other and a single docking port connecting them. A node module is docked to each dome on the Hab and Lab modules, such that the two small node modules on each end of the large Hab and Lab domes are docked both to each other and to the Hab and Lab. This creates a “racetrack” translation path on the interior. The other four node modules are docked at the center of the Hab and Lab modules, two on each side, creating another “racetrack” translation path perpendicular to the first one. The DSSV has a generally vertical orientation. Within the Hab and Lab modules the decks are perpendicular to the longitudinal axis. The node modules are oriented with their longitudinal axes perpendicular to those of the Hab and Lab modules, so the nodes have a horizontal internal orientation. Decks are numbered one through nine, with decks two and eight representing the “top” and “bottom” domes of the Hab and Lab modules. The Hab Module decks encompass the ship’s galley, crew quarters, waste, hygiene, portions of crew exercise, and group recreation. The Lab Module contains food production facilities, the life science lab, the ship’s infirmary, the physical science lab, and the maintenance and fabrication workshop. The Node Modules serve a number of different functions. The two Exercise Nodes are docked to deck five of both the Hab and Lab modules and contain most of the aerobic and resistive exercise devices. Also docked to deck five but on the opposite side of the Hab and Lab modules are the Observation Deck and Space Café. These two node modules provide social gathering space for small numbers of crew. The Mission Operations Node is on deck nine directly above the Galley and contains spacecraft monitoring and commanding capabilities. Docked to it is the EVA Operations Node, which contains suit maintenance and storage. (The airlock is a separate, external element docked to the EVA Operations Node.) The Subsystems Node is on deck one beneath the maintenance and fabrication workshop. Docked to it is the Stowage Node. This node does not house DSSV primary stowage, but is a staging point where stowage brought in from logistics modules can be sorted, unpacked, or repacked as needed prior to distribution to the appropriate sections of the spacecraft.

Deep Space Habitat↗
NASA NTRS1998

Ma'adim Vallis Estuarine Delta in Elysium Basin and Its Relevance as a Landing Site for Exobiology Exploration on Mars

The debouche of Ma'adim Vallis in the Elysium Basin generated a transitional transported sediment structure, which planimetric shape is controlled by the enclosing topography of a deep reentrant gulf of the Basin into the highland. We defined it as an estuarine delta. The location and the importance of this estuarine delta is supported by the theoretical model of graded profile constructed for Ma'adim Vallis, and by two approaches: (i) the reconstruction of Ma'adim Vallis downstream course from Gusev to Elysium Basin, and (ii) the survey of the sediment deposit in the alleged estuary. The longitudinal graded profile of Ma'adim Vallis finds its base-level in the Elysium Basin, at a about 1000 m elevation, which is in agreement with the observed Basin shoreline. This model is supported by observational evidence of flow between the northern rim of Gusev crater, and the Elysium Basin shoreline. This downstream course of Ma'adim Vallis can be divided into three hydrogeologic regions. into three hydrogeologic regions. (a) The first region is a flooded plain (Zephiria Mensae), consisting in chaotic terrain formed by highland rocks, and disintegrated lava of the western flank of Apollinaris. Morphologic indicators of the flood process are: (1) the sediment deposit over the Gusev crater northern rim that reflects the overspilling of the crater-lake water through a 40-km wide gap provided by an ancient impact crater, (2) the tear-drop shaped feature on the northeastern flank of Apollinaris Patera, and (3) the chaotic terrain that suggest the emergence of ground water generated by the seepage of the crater lake through high-permeable broken rampart material. This underground water circulation sustained by the hydrostatic pressure of the crater-lake has likely generated a hydrothermal system in the volcanic environment of Apollinaris Patera. The stratigraphy of the flooded area is identified as Hesperian age, with occurrences of Noachian hilly individual features, and as Amazonian flooded plain and chaotic material, (b) The second region is located on the western flank of Apollinaris Patera. It is surrounded by relics of deep valleys that suggest a former downstream course of Ma'adim Vallis. The geologic setting of this region (Lucus Planum) is interpreted to be an Amazonian formation composed by the middle and lower members of the Medusae Formation., c) The third region corresponds to the convergence of the west and east branches of Ma'adirn Vallis into a deep re-entrant wide gulf that penetrates about 100 km into the highland. This topographic depression is delineated by the 1000 in elevation contour. This gulf has formed an estuarine configuration centered at 3S/190W within the Elysium Basin. This configuration has favored the formation of a estuarine sedimentary delta, because of topographically controlled lateral migration. This estuarine structure is strongly dominated by the incoming supply of Ma'adim Vallis fluvial sediment extracted from Zephiria Mensae and Lucus Planum. The obtuse-angle geometry of the estuary increases the sedimentation rate, which is higher than in the course of the channel. The sediment deposition process is governed by the estuarine water circulation. The inflowing loaded fluvial water enters the estuary as a bottom current, and mixes with the relatively less-loaded water of the receiving basin. When they mixed. the inflowing fluvial material, and the landward basin circulating water generate an accumulation of highly-diversified estuarine deposit stratification. This accumulation of material is mostly centered in the transitional zone of the delta. The sediment trapping efficiency of the estuary is function of the energy balance between the inflowing fluvial water, and the ingoing basin current. The submergence of the delta by the rising of the water-level increases the estuary water-depth, and consequently the sediment entrapment is favored. The locus of sediment accumulation moves landward in the zone of inflowing fluvial water. This results in the rising of the channel base-level, thus in the increase of the length of the longitudinal graded-profile. The sediment deposit facies of the zone A shows a generally smooth surface. The longitudinal deposit is bordered by alluvial terraces that reflect the variations of the channel level. The waning of the Elysium Basin caused the erosion of the Basin estuarine zone by small channels, this episode being characterized by dissected tear-drop shaped mesa-like morphologies in the delta. Our estuarine delta model predicts a lithostratigraphic depositional sequence associated with the water submergence and the transgression of Elysium Basin. The thickness of the estuarine sediment corresponds to the Elysium Basin levels changes relatively to the bed floor of the estuary, The depositional sequence of Ma'adim Vallis are described: (1) a pro-current filled region (A), where fluvial are longitudinally accumulated by the inflowing water, (2) inverse current from Elysium Basin (B), where fluvial and lacustrine sediments are accumulated, and (3) zone of current equilibrium (C), where the sediments are distributed as a shoreline at the boundary of the estuarine delta. The estuary sedimentology dynamics collects and keeps the record of the geologic unit material crossed by Ma'adim Vallis, and those of the lakebed deposit of Elysium Basin. The predicted mixed stratigraphic sequence from fluvial and lacustrine sediment makes this site an exceptional environment to concentrate potential multi-origin biologic records. We envision four possible strategies to explore this sedimentologic record: (1) longitudinal surface and subsurface traverses in region A to investigate outcrop levees, (2) exploration of the mesa walls in region B, (3) deep drilling hole lodging of the sequential deposits in the zones A and B, and (4) surface and subsurface exploration of the shoreline delta. The expected results for each of these strategies are: (1) in the deepest layers of region A are predicted frequent and abundant coarse material, sandy lenses lamination grading downward from sand to cobbles. Volcanic debris from the Noachian crustal Plateau unit material, hydrothermal altered rocks, carbonates, Hesperian and possibly Amazonian volcanic material, from Apollinaris Patera, altered rocks and carbonates from Zephiria Mensae are expected. As a favorable environment for inception of life, possible biological records are expected in transported rock, (2) At the surface, and subsurface (<=100 m), large deposits sandy to silted material from Elysium paleolake basin mixed with fine-grained sediments from Ma'adim Vallis are expected mostly in the upstream part of region B, (3) on the shoreline of the estuarine delta, abundant fine material from Elysium paleolake basin (evaporites, carbonates), mostly Amazonian in age are expected. The Ma'adini estuary is a favorable landing site for all the above mentioned science aspects, and .for its location. The site lies near the equator, which is favorable for the rover solar power supply, and at 1000m elevation, which is a favorable configuration for the descent system braking. Another advantage is the extent of the area of high scientific interest (33,000 sq km), which provides a good ellipse, and potential long study traverses.

Grin, E. A.↗
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↗