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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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NASA NTRS2018

A Deep X-Ray View of the Synchrotron-Dominated Supernova Remnant G330.2+1.0

We present moderately deep (125 ks) XMM-Newton observations of supernova remnant G330.2+1.0. This remnant is one of only a few known that fall into the "synchrotron-dominated" category, with the emission almost entirely dominated by a nonthermal continuum. Previous X-ray observations could only characterize the spectra of a few regions. Here, we examine the spectra from 14 regions surrounding the entire rim, finding that the spectral properties of the nonthermal emission do not vary significantly in any systematic way from one part of the forward shock to another, unlike several other remnants of this class. We confirm earlier findings that the power-law index, Γ, ranges from about 2.1-2.5, while the absorbing column density is generally between (2.0-2.6) × 10(exp 22) cm(exp -2). Fits with the srcut model find values of the roll-off frequency in the range of 10(exp 17.1)-10(exp 17.5) Hz, implying energies of accelerated electrons of approximately 100 TeV. These values imply a high shock velocity of approximately 4600 km s(exp -1), favoring a young age of the remnant. Diffuse emission from the interior is nonthermal in origin as well, and fits to these regions yield similar values to those along the rim, also implying a young age. Thermal emission is present in the east, and the spectrum is consistent with approximately 650 km s(exp -1) shock wave encountering interstellar or circumstellar material with a density of approximately 1 cm(exp -3).

Williams, Brian J.↗
NASA NTRS2017

Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars. II. Planetary Systems Observed During Campaigns 1-7

We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically validate 17 planets (7 of which were previously unpublished), confirm the earlier validation of 22 planets, and announce 17 newly discovered planet candidates. Revising the properties of the associated planet candidates based on the updated host star characteristics and refitting the transit photometry, we find that our sample contains 21 planets or planet candidates with radii smaller than 1.25 solar radii, 18 super-Earths (1.25-2 solar radii), 21 small Neptunes (2-4 solar radii), three large Neptunes (4-6 solar radii), and eight giant planets (greater than 6 solar radii). Most of these planets are highly irradiated, but EPIC 206209135.04 (K2-72e, 1.29 from plus 0.19 to minus 0.18 solar radii), EPIC 211988320.01 (perihelion radius equals 2.86 from plus 0.16 to minus 0.15 solar radii), and EPIC 212690867.01 (2.20 from plus 0.19 to minus 0.18 solar radii) orbit within optimistic habitable zone boundaries set by the "recent Venus" inner limit and the "early Mars" outer limit. In total, our planet sample includes eight moderately irradiated 1.5-3 solar radii planet candidates (planetary flux greater than or approximately 20 times Earth's flux) orbiting brighter stars (Ks less than 11) that are well-suited for atmospheric investigations with the Hubble, Spitzer, and/or James Webb Space Telescopes. Five validated planets orbit relatively bright stars (Kp less than 12.5) and are expected to yield radial velocity semi-amplitudes of at least 2 meters per second. Accordingly, they are possible targets for radial velocity mass measurement with current facilities or the upcoming generation of red optical and near-infrared high-precision RV (Radial Velocity) spectrographs.

Dressing, Courtney D.↗
NASA NTRS2012

A Newton-Raphson Method Approach to Adjusting Multi-Source Solar Simulators

NASA Glenn Research Center has been using an in house designed X25 based multi-source solar simulator since 2003. The simulator is set up for triple junction solar cells prior to measurements b y adjusting the three sources to produce the correct short circuit current, lsc, in each of three AM0 calibrated sub-cells. The past practice has been to adjust one source on one sub-cell at a time, iterating until all the sub-cells have the calibrated Isc. The new approach is to create a matrix of measured lsc for small source changes on each sub-cell. A matrix, A, is produced. This is normalized to unit changes in the sources so that Ax(delta)s = (delta)isc. This matrix can now be inverted and used with the known Isc differences from the AM0 calibrated values to indicate changes in the source settings, (delta)s = A ·'x.(delta)isc This approach is still an iterative one, but all sources are changed during each iteration step. It typically takes four to six steps to converge on the calibrated lsc values. Even though the source lamps may degrade over time, the initial matrix evaluation i s not performed each time, since measurement matrix needs to be only approximate. Because an iterative approach is used the method will still continue to be valid. This method may become more important as state-of-the-art solar cell junction responses overlap the sources of the simulator. Also, as the number of cell junctions and sources increase, this method should remain applicable.

Snyder, David B.↗
NASA NTRS2016

First Search for an X-Ray-Optical Reverberation Signal in an Ultraluminous X-Ray Source

Using simultaneous optical (VLT/FORS2) and X-ray (XMM-Newton) data of NGC 5408, we present the first ever attempt to search for a reverberation signal in an ultraluminous X-ray source (NGC 5408 X-1). The idea is similar to active galactic nucleus broad line reverberation mapping where a lag measurement between the X-ray and the optical flux combined with a Keplerian velocity estimate should enable us to weigh the central compact object. We find that although NGC 5408 X-1ʼs X-rays are variable on a timescale of a few hundred seconds (rms of 9.0 +/- 0.5%), the optical emission does not show any statistically significant variations. We set a 3σ upper limit on the rms optical variability of 3.3%. The ratio of the X-ray to the optical variability is an indicator of X-ray reprocessing efficiency. In X-ray binaries, this ratio is roughly 5. Assuming a similar ratio for NGC 5408 X-1, the expected rms optical variability is approximately equal to 2%, which is still a factor of roughly two lower than what was possible with the VLT observations in this study. We find marginal evidence (3 sigma) for optical variability on an approximately 24 hr timescale. Our results demonstrate that such measurements can be made, but photometric conditions, low sky background levels, and longer simultaneous observations will be required to reach optical variability levels similar to those of X-ray binaries.

: accretion↗
NASA NTRS2017

Nano Icy Moons Propellant Harvester

As one of just a few bodies identified in the solar system with a liquid ocean, Europa has become a top priority in the search for life outside of Earth. However, cost estimates for exploring Europa have been prohibitively expensive, with estimates of a NASA Flagship class orbiter and lander approaching $5 billion. ExoTerra's NIMPH offers an affordable solution that can not only land, but return a sample from the surface to Earth. NIMPH combines solar electric propulsion (SEP) technologies being developed for the asteroid redirect mission and microsatellite electronics to reduce the cost of a full sample return mission below $500 million. A key to achieving this order-of-magnitude cost reduction is minimizing the initial mass of the system. The cost of any mission is directly proportional to its mass. By keeping the mission within the constraints of an Atlas V 551 launch vehicle versus an SLS, we can significantly reduce launch costs. To achieve this we reduce the landed mass of the sample return lander, which is the largest multiplier of mission mass, and shrink propellant mass through high efficiency SEP and gravity assists. The NIMPH projects first step in reducing landed mass focuses on development of a micro-In Situ Resource Utilization (micro-ISRU) system. ISRU allows us to minimize landed mass of a sample return mission by converting local ice into propellants. The project reduces the ISRU system to a CubeSat-scale package that weighs just 1.74 kg and consumes just 242 W of power. We estimate that use of this ISRU vs. an identical micro-lander without ISRU reduces fuel mass by 45 kg. As the dry mass of the lander grows for larger missions, these savings scale exponentially. Taking full advantage of the micro-ISRU system requires the development of a micro-liquid oxygen-liquid hydrogen engine. The micro-liquid oxygen-liquid hydrogen engine is tailored for the mission by scaling it to match the scale of the micro-lander and the low gravity of the target moon. We also tailor the engine for a near stoichiometric mixture ratio of 7.5. Most high-performance liquid oxygen-liquid hydrogen engines inject extra liquid hydrogen to lower the average molecular weight of the exhaust, which improves specific impulse. However, this extra liquid hydroden requires additional power and processing time on the surface for the ISRU to create. This increases mission cost, and on missions within high radiation environments such as Europa, increases radiation shielding mass. The resulting engine weighs just 1.36 kg and produces 71.5 newton of thrust at 364 s specific impulse. Finally, the mission reduces landed mass by taking advantage of the SEP modules solar power to beam energy to the surface using a collimated laser. This allows us to replace an 45 kg MMRTG with a 2.5 kg resonant array. By using the combination of ISRU, a liquid oxygen-liquid hydrogen engine, and beamed power, we reduce the initial mass of the lander to just 51.5 kg. When combined with an SEP module to ferry the lander to Europa the initial mission mass is just 6397 kg - low enough to be placed on an Earth escape trajectory using an Atlas V 551 launch vehicle. By comparison, we estimate a duplicate lander using an MMRTG and semi-storable propellants such as liquid oxygen-methane would result in an order of magnitude increase in initial lander mass to 445 kg. Attempting to perform the trajectory with a 450 s liquid oxygen-liquid hydrogen engine would increase initial mass to approximately 135,000 kg. Using an Atlas V 1 U.S. Dollar per kg rate to Earth escape value of $27.7k per kg, just the launch savings are over $3.5 billion.

liquid↗
NASA NTRS2016

The XXL Survey I. Scientific Motivations - Xmm-Newton Observing Plan - Follow-up Observations and Simulation Programme

The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have supported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey; it comes at a time when the Planck mission results are being finalized. Aims. We present the XXL Survey, the largest XMM programme totaling some 6.9 Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25 deg2 each at a point-source sensitivity of approx. 5 x 10(exp 15) erg/s/sq cm in the [0.5-2] keV band (completeness limit). The surveys main goals are to provide constraints on the dark energy equation of state from the space-time-distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programs. Methods. We describe the 542 XMM observations along with the associated multi- and numerical simulation programmes. We give a detailed account of the X-ray processing steps and describe innovative tools being developed for the cosmological analysis. Results. The paper provides a thorough evaluation of the X-ray data, including quality controls, photon statistics, exposure and background maps, and sky coverage. Source catalogue construction and multi-associations are briefly described. This material will be the basis for the calculation of the cluster and AGN selection functions, critical elements of the cosmological and science analyses. Conclusions. The XXL multi- data set will have a unique lasting legacy value for cosmological and extragalactic studies and will serve asa calibration resource for future dark energy studies with clusters and other X-ray selected sources. With the present article, we release the XMM XXL photon and smoothed images along with the corresponding exposure maps.

X-rays: general – large-scale structure of Unive↗
NASA NTRS2008

High Power Amplifier and Power Supply

A document discusses the creation of a high-voltage power supply (HVPS) that is able to contain voltages up to -20 kV, keep electrical field strengths to below 200 V/mil (approximately equal to 7.87 kV/mm), and can provide a 200-nanosecond rise/fall time focus modulator swinging between cathode potential of 16.3 kV and -19.3 kV. This HVPS can protect the 95-GHz, pulsed extended interaction klystron (EIK) from arcs/discharges from all sources, including those from within the EIK fs vacuum envelope. This innovation has a multi-winding pulse transformer design, which uses new winding techniques to provide the same delays and rise/fall times (less than 10 nanoseconds) at different potential levels ranging from -20 kV to -16 kV. Another feature involves a high-voltage printed-wiring board that was corona-free at -20 kV DC with a 3- kV AC swing. The corona-free multilayer high-voltage board is used to simulate fields of less than 200 V/mil (approximately equal to 7.87 kV/mm) at 20 kV DC. Drive techniques for the modulator FETs (field-effect transistors) (four to 10 in a series) were created to change states (3,000-V swing) without abrupt steps, while still maintaining required delays and transition times. The packing scheme includes a potting mold to house a ten-stage modulator in the space that, in the past, only housed a four-stage modulator. Problems keeping heat down were solved using aluminum oxide substrate in the high-voltage section to limit temperature rise to less than 10 while withstanding -20 kV DC voltage and remaining corona-free.

Duong, Johnny↗
NASA NTRS2006

The Evolution of the Cluster X-ray Scaling Relations in the Wide Angle ROSAT Pointed Survey Sample at 0.6 < z < 1.0

The X-ray properties of a sample of 11 high-redshift (0.6 < z < 1 .O) clusters observed with Chardm and/or XMM-Newton are used to investigate the evolution of the cluster scaling relations. The observed evolution in the normalization of the L-T, M-T, M(sub 2)-T and M-L relations is consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of the Universe at their redshift of observation. Under the assumption that the model of self-similar evolution is correct and that the local systems formed via a single spherical collapse, the high-redshift L-T relation is consistent with the high-z clusters having virialized at a significantly higher redshift than the local systems. The data are also consistent with the more realistic scenario of clusters forming via the continuous accretion of material. The slope of the L-T relation at high redshift (B = 3.32 +/- 0.37) is consistent with the local relation, and significantly steeper than the self-similar prediction of B = 2. This suggests that the same non-gravitational processes are responsible for steepening the local and high-z relations, possibly occurring universally at z is approximately greater than 1 or in the early stages of the cluster formation, prior to their observation. The properties of the intracluster medium at high redshift are found to be similar to those in the local Universe. The mean surface-brightness profile slope for the sample is Beta = 0.66 +/- 0.05, the mean gas mass fractions within R(sub 2500(z)) and R(200(z)) are 0.069 +/- 0.012 and 0.11 +/- 0.02, respectively, and the mean metallicity of the sample is 0.28 +/- 0.11 Z(sub solar).

Maughan, B. J.↗
NASA NTRS2007

Evidence for a Broad Relativistic Iron Line from the Neutron Star LMXB Ser X-1

We report on an analysis of XMM-Newton data from the neutron star low mass X-ray binary (LMXB) Serpens X-1 (Ser X-1). Spectral analysis of EPIC PN data indicates that the previously known broad iron Ka emission line in this source has a significantly skewed structure with a moderately extended red wing. The asymmetric shape of the line is well described with the laor and diskline models in XSPEC, which strongly supports an inner accretion disk origin of the line. To our knowledge this is the first strong evidence for a relativistic line in a neutron star LMXB. This finding suggests that the broad lines seen in other neutron star LMXBs likely originate from the inner disk as well. Detailed study of such lines opens up a new way to probe neutron star parameters and their strong gravitational fields. The laor model describes the line from Ser X-1 somewhat better than diskline, and suggests that the inner accretion disk radius is less than 6GM/c(exp 2). This is consistent with the weak magnetic fields of LMXBs, and may point towards a high compactness and rapid spin of the neutron star. Finally, the inferred source inclination angle in the approximate range 50-60 deg is consistent with the lack of dipping from Ser X-1.

Bhattacharyya, Sudip↗
NASA NTRS1990

An adaptive grid algorithm for one-dimensional nonlinear equations

Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and less computation time than required by the tridiagonal method. The performance of the adaptive grid method tends to degrade as the solution process proceeds in time, but still remains faster than the tridiagonal scheme.

Gutierrez, William E.↗
NASA NTRS2004

An Extreme, Blueshifted Iron Line in the Narrow Line Seyfert 1 PG 1402+261

We report on a short, XMM-Newton observation of the radio-quiet Narrow Line Seyfert 1 PG 1402+261. The EPIC X-ray spectrum of PG 1402+261 shows a strong excess of counts between 6 - 9 keV in the rest frame. This feature can be modeled by an unusually strong (equivalent width 2 keV) and very broad energy at 7.3 keV appears blue-shifted with respect to the iron Kalpha emission band between 6.4 - 6.97 keV, whilst the blue-wing of the line extends to 9 keV in the quasar rest frame. The line profile can be fitted by reflection from the inner accretion disk, but an inclination angle of greater than 60 degrees is required to model the extreme blue-wing of the line. Furthermore the extreme strength of the line requires a geometry whereby the hard X-ray emission from PG1402+261 above 2 keV is dominated by the pure-reflection component from the disk, whilst little or none of the direct hard power-law is observed. Alternatively the spectrum above 2 keV may instead be explained by an ionized absorber, if the column density is sufficiently high (NH greater than 3 x 10(exp 23) per square centimeter) and if the matter is ionized enough to produce a deep (tau approximately equal to 1) iron K-shell absorption edge at 9 keV. This absorber could originate in a large column density, high velocity outflow, perhaps similar to those which appear to be observed in several other high accretion rate AGN. Further observations, especially at higher spectral resolution, are required to distinguish between the accretion disk reflection or outflow scenarios.

Reeves, J. N.↗
NASA NTRS2007

A Stellar-mass Black Hole in the Ultra-luminous X-ray Source M82 X-1

We have analyzed the archival XMM-Newton data of the archetypal Ultra-Luminous X-ray Source (ULX) M82 X-1 with an LO5 ksec exposure when the source was in the steady state. Thanks to the high photon statistics from the large effective area and long exposure, we were able to discriminate different X-ray continuum spectral models. Neither the standard accretion disk model (where the radial dependency of the disk effective temperature is T(r) proportional to r(sup -3/4)) nor a power-law model gives a satisfactory fit. In fact, observed curvature of the M82 X-1 spectrum was just between those of the two models. When the exponent of the radial dependence (p in T(r) proportional to r(sup -P)) of the disk temperature is allowed to be free, we obtained p = 0.61 (sup +0.03)(sub -0.02). Such a reduction of p from the standard value 3/4 under extremely high mass accretion rates is predicted from the accretion disk theory as a consequence of the radial energy advection. Thus, the accretion disk in M82 X-1 is considered to be in the Slim disk state, where an optically thick Advection Dominant Accretion Flow (ADAF) is taking place. We have applied a theoretical slim disk spectral model to M82 X-1, and estimated the black hole mass approximately equal to 19 - 32 solar mass. We conclude that M82 X-1 is a stellar black hole which has been produced through evolution of an extremely massive star, shining at a several times the super-Eddington luminosity.

Okajima, Takashi↗
NASA NTRS1982

Application of strong fluctuation random medium theory to scattering of electromagnetic waves from a half-space of dielectric mixture

The strong fluctuation random medium theory is applied to calculate scattering from a half-space of dielectric mixture. The first and second moments of the fields are calculated, respectively, by using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. Expressions for the effective permittivity for the full space case are derived. It is shown that the derived result of the effect permittivity is identical to that of the Polder and van Santern mixing formula. The correlation function of the random medium is obtained by using simple physical arguments and is expressed in terms of the fractional volumes and particle sizes of the constituents of the mixture. Backscattering coefficients of a half-space dielectric mixture are also calculated. Numerical results of the effective permittivity and backscattering coefficients are illustrated using typical parameters encountered in microwave remote sensing of dry and wet snow. It is also shown that experimental data can be matched with the theory by using physical parameters of the medium as obtained from ground truth measurements.

Tsang, L.↗
NASA NTRS2004

Over-Luminous Elliptical Galaxies

The first paper from our work has been completed and accepted for publication. Another paper presents a study of the ESO 30601 70 galaxy group, combining Chandra, XMM-Newton, and optical observations. We find that the system is a true fossil galaxy group - a group whose optical light is dominated by a single galaxy. The group X-ray emission is composed of a central, dense, cool core (10 kpc in radius) and an isothermal medium beyond the central 10 kpc. The region between 10 and 50 kpc (the cooling radius) has the same temperature as the gas from 50 to 400 kpc, although the gas cooling time between 10 and 50 kpc (2-6 Gyr) is shorter than the Hubble time. Thus, the ESO 3060170 group does not have a group-sized cooling core. We suggest that the group cooling core may have been heated by a central active galactic nucleus (AGN) outburst in the past and that the small, dense, cool core is the truncated relic of a previous cooling core. The Chandra observations also reveal a variety of X-ray features in the central region, including a finger, an edge-like feature, and a small tail, all aligned along a north-south axis, as are the galaxy light and group galaxy distribution. The proposed AGN outburst may cause gas to slosh around the center and produce these asymmetric features. The observed flat temperature profile to 1/3rvir is not consistent with the predicted temperature profile in recent numerical simulations. We compare the entropy profile of the ESO 3060170 group with those of three other groups and find a flatter relation than that predicted by simulations involving only shock heating, S approximately r approximately 0.85. This is direct evidence of the importance of non-gravitational processes in group centers. We derive the mass profiles within 1/3rvir and find that the ESO 3060170 group is the most massive fossil group known.

Forman, William↗
NASA NTRS2015

Is Ice-Rafted Sediment in a North Pole Marine Record Evidence for Perennial Sea-ice Cover?

Ice-rafted sediments of Eurasian and North American origin are found consistently in the upper part (13 Ma BP to present) of the Arctic Coring Expedition (ACEX) ocean core from the Lomonosov Ridge, near the North Pole (approximately 88 degrees N). Based on modern sea-ice drift trajectories and speeds, this has been taken as evidence of the presence of a perennial sea-ice cover in the Arctic Ocean from the middle Miocene onwards. However, other high latitude land and marine records indicate a long-term trend towards cooling broken by periods of extensive warming suggestive of a seasonally ice-free Arctic between the Miocene and the present. We use a coupled sea-ice slab-ocean model including sediment transport tracers to map the spatial distribution of ice-rafted deposits in the Arctic Ocean. We use 6 hourly wind forcing and surface heat fluxes for two different climates: one with a perennial sea-ice cover similar to that of the present day and one with seasonally ice-free conditions, similar to that simulated in future projections. Model results confirm that in the present-day climate, sea ice takes more than 1 year to transport sediment from all its peripheral seas to the North Pole. However, in a warmer climate, sea-ice speeds are significantly faster (for the same wind forcing) and can deposit sediments of Laptev, East Siberian and perhaps also Beaufort Sea origin at the North Pole. This is primarily because of the fact that sea-ice interactions are much weaker with a thinner ice cover and there is less resistance to drift. We conclude that the presence of ice-rafted sediment of Eurasian and North American origin at the North Pole does not imply a perennial sea-ice cover in the Arctic Ocean, reconciling the ACEX ocean core data with other land and marine records.

Palaeoclimate↗
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↗