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Precision Lunar Laser Ranging For Lunar and Gravitational Science

Laser ranging to retroreflector arrays placed on the lunar surface by the Apollo astronauts and the Soviet Lunar missions over the past 39 years have dramatically increased our understanding of gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics. Significant advances in these areas will require placing modern retroreflectors and/or active laser ranging systems at new locations on the lunar surface. Ranging to new locations will enable better measurements of the lunar librations, aiding in our understanding of the interior structure of the moon. More precise range measurements will allow us to study effects that are too small to be observed by the current capabilities as well as enabling more stringent tests of Einstein's theory of General Relativity. Setting up retroreflectors was a key part of the Apollo missions so it is natural to ask if future lunar missions should include them as well. The Apollo retroreflectors are still being used today, and nearly 40 years of ranging data has been invaluable for scientific as well as other studies such as orbital dynamics. However, the available retroreflectors all lie within 26 degrees latitude of the equator, and the most useful ones within 24 degrees longitude of the sub-earth meridian. This clustering weakens their geometrical strength.

Merkowitz, S. M.↗

Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.

Attitude determination and control↗

Interaction dynamics of on-orbit construction

Deployment and assembly of large structures in orbit is a critical technology to the overall problem of orbital construction. The attendant large configuration changes of structures will cause significant changes in the dynamic characteristics of the entire system, and perturbation to the orbital dynamics of the spacecraft from which the structures are deployed and/or assembled. To better design structures for deployment and assembly, and to better design controlled deployment/assembly processes, accurate modeling techniques are absolutely essential. The problem of modeling the dynamics of deploying and retrieving beam-like structures from a rotating base was addressed. A methodology for discrete modeling, and a computational procedure were developed. These results give us the capability of understanding and predicting the effects on the overall satellite motion of deploying flexible appendages. This is an initial step towards a general capability of treating axially moving three-dimensional beams. The interaction dynamics of the orbiter, its flexible manipulator, and the structures to be assembled/deployed, as a prerequisite in order to simulate incremental in-space structural construction processes are investigated. Preliminary results so obtained indicate that, as the inertia properties of the flexible large space structure under construction change during the space assembly/construction process, the interaction dynamics undergo significant changes in their characteristics, thus revealing the need for a variety of control strategies throughout construction.

Park, K. C.↗

Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields

We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in Ricketson and Chacón (2020) to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. Finally, the results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thorium Enrichment within the Procellarum KREEP Terrane: The Record in Surface Deposits and Significance for Thermal Evolution

The nearside-farside structural and compositional asymmetry of the Moon was recognized during the early days of Apollo and the suggestion was made that the migration of mantle melts to the nearside would have been favored by early Earth-Moon orbital dynamics and nonuniform planetesimal bombardment. Recent global geochemical mapping by Lunar Prospector has provided additional data, particularly in the Th distribution, that strongly supports the notion of global, preferential melt migration, which led in part to the development of the Procellarum KREEP Terrane (PKT) [2-5]. The surface distribution of Th was then reshaped by basin-forming impacts into the PKT, especially the Imbrium impact, which was the last and largest to strike in that region. The Imbrium event probably excavated material from a partially molten zone deep in the crust and delivered Th-rich ejecta Moon-wide. A fundamentally important but poorly understood aspect of the global Th distribution is the concentration of Th in the subsurface rocks of the PKT crustal section. For example, depending on what assumptions are made, the PKT crustal section, which is about 12% of the crust and only about 1.2% of the whole Moon, may contain as much as 40% of the Moon's entire Th budget. Such a distribution of Th and related heat-producing elements would have had a profound effect on melting, mixing, and the thermal evolution of the PKT and the underlying mantle. In this abstract, we examine the compositions of terra formations within the PKT and relate them to some of the Th-bearing rock types known from the Apollo samples. It appears that the existence of the PKT may be a unifying concept for a number of petrologic and geochemical observations. From the initial Lunar Prospector gamma-ray spectrometer data(-about 5 deg. resolution) and from the preliminary low-orbit data, there appears to be a number of relatively hotter "spots" within the PKT in terms of Th concentration. Some of the hotter spots correspond to intermediate-sized craters that penetrated volcanic flows and excavated Th-rich, submare material, such as Aristarchus, Aristillus, and Kepler. Other spots, however, correspond to surficial formations that constitute mainly rough topography associated with Imbrium ejecta or circum-Imbrium ring mountains and do not necessarily imply the presence of exposed KREEP basalts. The Fra Mauro Formation south of Copernicus toward the Apollo 14 site and regions of the Alpes Formation southwest of Copernicus in the vicinity of Reinhold lie within the most prominent hotspot; here them concentration is consistent with that found in the Apollo 14 soils (about 12-13 ppm) when the proportions of Fra Mauro Formation and mare basalt are considered. The area between Copernicus and Kepler and northwest of Copernicus in terra extending to the Carpathians is similarly enriched in Th. The Apennines from Eratosthenes toward the Apollo 15 site contain elevated Th concentrations, as does the northwestern quadrant of circum-Imbrium terra, especially between (but not including) La Condamine and Plato, and in the region northwest of the Jura mountains extending southward past Mairan to the Gruithuisen-Domes region. Within the main topographic rim of Imbrium, the Apennine Bench formation south of Archimedes appears to have relatively elevated Th concentration. Comparing the map of Th distribution to a digital-elevation map derived from Clementine altimetry, it appears that most of the areas richest in Th occur where the surface is elevated relative to the majority of PKT volcanic plains. Not all rough topography within the PKT has such elevated Th, however. Based on an analysis of the 5 deg. data, and using the calibration of, the mean Th concentrations for mainly volcanic-resurfaced terrain and rugged terrain are similar (about 5.5 ppm). This occurs in part because craters that penetrated mare basalt excavated Th-rich material. Even so, there appear to be extensive areas of volcanic resurfacing that have no obvious extrinsic source of Th-rich material, suggesting that the basalts, themselves, may contain as much as 5-6 ppm Th. High-FeO concentrations (18 to >20 wt%) indicate that these are not KREEP basalts but mare basalts. If so, this is surprising because most of the Apollo-sampled mare basalts have very low-Th (typically <2 ppm). A variety of Th-rich materials occur in the sample collection, particularly in the samples from the Apollo 12,14, and 15 sites. The most abundant Th-rich rock types are the mafic impact-melt breccias, which although found at all sites, are most abundant at Apollo 14, where they dominate the rock samples and make up some 40% of the rock particles in the soil. These have Th concentrations ranging up to about 30 ppm and averaging about 18 ppm. The Apollo 14 soils contain about 13 ppm Th, reflecting the high abundance of this melt-breccia component. At the nearby Apollo 12 site, the rocks consist mainly of mare basalts, and these have low-Th concentrations, mostly <1 ppm. Among the nonmare rocks, however, a few such as complex breccia 12013 contain a variety of evolved lithologies and represent potential sources of Th-rich components ranging from 17 to 50 ppm. A single fragment of KREEP basalt from the Apollo 12 soil contains about 50 ppm Th. Despite the identification of highly Th-enriched lithologic components at the Apollo 12 site, the soils there vary linearly in composition so as to extrapolate to a moderate Th KREEP-basalt component or a composition like that of the Fra Mauro formation as reflected by Apollo 14 soil (14 ppm Th at 10 wt% FeO). The nearby Lansberg Crater (39-km diameter) is a likely candidate to have delivered submare material such as buried Fra Mauro or Alpes material to the Apollo 12 site. Additional information contained in the original.

Jolliff, B. L.↗

Dust-void evolution driven by turbulent dust flux can induce runaway migration of Earth-mass planets

Torques from asymmetric dust structures (so-called dust-void and filamentary structures) formed around low-mass planets embedded in a nonturbulent dust-gas disk can exceed the torques produced by the gas disk component and then go on to dominate the planet’s orbital dynamics. Here, we investigate how these structures (hence the dust torque) change when the effect of turbulent dust diffusion and dust feedback are included, along with the direct implications on the migration of Earth-like planets. Using the FARGO3D code, we performed 2D and 3D multifluid hydrodynamic simulations, focusing on a non-migrating planet with a mass of M p = 1.5 M ⊕ in 2D and on migrating planets with M p ∈ [1.5, 12] M ⊕ in 3D. We varied the δ-dimensionless diffusivity parameter in the range [0, 3 × 10 −3 ] and considered three different Stokes numbers, St = {0.04, 0.26, 0.55}, which are representative of the gas-dominated, the transitional, and the gravity-dominated regimes, respectively. In our 2D models, we find that turbulent diffusion of dust prevents the formation of the dust-void and filamentary structures when δ > 3 × 10 −4 . Otherwise, dust structures survive turbulent diffusion flow. However, dust and total torques become positive only in transitional and gravity-dominated regimes. In our 3D models, we find that the dust-void is drastically modified and the high-density ring-shaped barrier delineating the dust-void disappears if δ ≳ 10 −4 , due to the effect of dust turbulent diffusion along with the back-reaction of the dust. For all values of δ, the filament in front of the planet is replaced by a low-density trench. Remarkably, as we have allowed the planets to migrate, the evolving dust-void can drive either runaway migration or outward (inward) oscillatory-torque migration. Our study thus suggests that low-mass Earth-like planets can undergo runaway migration in dusty disks.

79 ASTRONOMY AND ASTROPHYSICS↗

Planetary waves can activate resonant drag instabilities in 3D dusty gaseous discs

Resonant drag instabilities (RDIs) in protoplanetary discs are driven by the aerodynamic back-reaction of dust on gas and occur when the relative dust-gas motion resonate with a wave mode intrinsic to the gas fluid. Axisymmetric models indicate that the RDI generates filamentary perturbations, leading to grain clumping and planetesimal formation. Motivated by these findings, we investigate the dust–gas interaction in a non-axisymmetric inviscid protoplanetary disc with an embedded low-mass planet ($M_{\mathrm{p}}\in [0.3, 3] \, \rm M_{\oplus }$, here $\, \rm M_{\oplus }$ is the Earth mass). We conduct global 3D high-resolution two-fluid simulations, with the dust being parametrized by the Stokes number $\mathrm{St}\in [0.01,0.5]$. We find that planetary waves (PWs; also known as Rossby waves), which propagate along the downstream separatrices of the horseshoe region, resonate with the streaming motion and trigger the RDI. The consequent development of a global-scale filamentary dust distribution does not sensitively depend on the Stokes number, nor does it depend on the fast dust settling that takes place in an inviscid disc. The rapid onset of this instability, which is comparable to the dynamical orbital time-scale, suppresses the formation of asymmetric structures in the dust in the vicinity of the planet (such as dust voids and filaments). Additionally, we find that the dust feedback enables buoyancy resonances in an otherwise non-buoyant (globally isothermal) disc. Therefore, our results provide the first numerical evidence of RDIs generation driven by planetary waves.

79 ASTRONOMY AND ASTROPHYSICS↗

Optical Properties of the Infinite-Layer La 1-x Sr x NiO 2 and Hidden Hund's Physics

We investigate the optical properties of the normal state of the infinite-layer La 1-x Sr x NiO 2 using density functional theory plus dynamical mean-field theory. We find a correlated metal which exhibits substantial transfer of spectral weight to high energies relative to the density functional theory. The correlations are not due to Mott physics, which would suppress the charge fluctuations and the integrated optical spectral weight as we approach a putative insulating state. Instead, we find the unusual situation, that the integrated optical spectral weight decreases with doping and increases with increasing temperature. We contrast this with the coherent component of the optical conductivity, which decreases with increasing temperature as a result of a coherence-incoherence crossover. Our studies reveal that the effective crystal field splitting is dynamical and increases strongly at low frequency. This leads to a picture of a Hund's metallic state, where dynamical orbital fluctuations are visible at intermediate energies, while at low energies a Fermi surface with primarily d x 2 -y 2 character emerges. The infinite-layer nickelates are thus in an intermediate position between the iron based high temperature superconductors where multiorbital Hund's physics dominates and a one-band system such as the cuprates. To capture this physics we propose a low-energy two-band model with atom centered e g states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Does a continuous solid nucleus exist in comets.

The implication of actual cometary observations for the physical nature of comets is briefly reviewed, bringing out the complete conflict with observation of the ice-dust solid nucleus model put forward in recent years as representing the fundamental structure of comets. That under increasing solar heat the nucleus develops an expanding atmosphere is inconsistent with the well-established phenomenon that the coma contracts with decreasing distance from the sun. Several comets remaining always beyond Mars have nevertheless been strongly active and produced fine tails. That some comets show at times a star-like point of light is readily explicable on the dust-cloud structure and by no means establishes that a solid nucleus exists. With the nucleus-area corresponding not to a small solid mass but to an optical phenomenon, there would be no reason to expect that it would describe a precise dynamical orbit. On the hypothesis of a nucleus, it is necessary to postulate further some internal jet-propulsion mechanism to account for the orbital deviations.

Lyttleton, R. A.↗

C-band station coordinate determination for the GEOS-C altimeter calibration area

Dynamical orbital techniques were employed to estimate the center-of-mass station coordinates of six C-band radars located in the designated primary GEOS-C radar altimeter calibration area. This work was performed in support of the planned GEOS-C mission (December, 1974 launch). The sites included Bermuda, Grand Turk, Antigua, Wallops Island (Virginia), and Merritt Island (Florida). Two sites were estimated independently at Wallops Island yielding better than 40 cm relative height recovery, with better than 10 cm and 1 m (relative) recovery for phi and gamma respectively. Error analysis and comparisons with other investigators indicate that better than 2 m relative recovery was achieved at all sites. The data used were exclusively that from the estimated sites and included 18 orbital arcs which were less than two orbital revolutions in length, having successive tracks over the area. The techniques employed here, given their independence of global tracking support, can be effectively employed to improve various geodetic datums by providing very long and accurate baselines. The C-band data taken on GEOS-C should be employed to improve such geodetic datums as the European-1950 using similar techniques.

Krabill, W. B.↗

Analysis of RAE-1 inversion

The RAE-1 spacecraft inversion performed October 31, 1972 is described based upon the in-orbit dynamical data in conjunction with results obtained from previously developed computer simulation models. The computer simulations used are predictive of the satellite dynamics, including boom flexing, and are applicable during boom deployment and retraction, inter-phase coast periods, and post-deployment operations. Attitude data, as well as boom tip data, were analyzed in order to obtain a detailed description of the dynamical behavior of the spacecraft during and after the inversion. Runs were made using the computer model and the results were analyzed and compared with the real time data. Close agreement between the actual recorded spacecraft attitude and the computer simulation results was obtained.

Hedland, D. A.↗

C-band station coordinate determination for the Geos-C altimeter calibration area

Dynamical orbital techniques were employed to estimate the center-of-mass station coordinates of six C-band radars located in the designated primary Geos-C radar altimeter calibration area. This work was performed in support of the planned Geos-C mission (December 1974 launch). The sites included Bermuda, Grand Turk, Antigua, Wallops Island (Virginia), and Merritt Island (Florida). Two sites were estimated independently at Wallops Island yielding better than 40 cm relative height recovery, with better than 10 cm and 1m (relative) recovery for phi and lambda, respectively. The tracking data used in this analysis were taken during 1969 when the radars tracked the Geos-II transponder. In all, over 120 passes of data were used. Range biases were estimated. Error analysis and comparisons with other investigators indicate that better than 2m (1 sigma) relative recovery has been achieved at all sites.

Klosko, S. M.↗

Analysis of structural dynamic data from Skylab. Volume 1: Technical discussion

A compendium of Skylab structural dynamics analytical and test programs is presented. These programs are assessed to identify lessons learned from the structural dynamic prediction effort and to provide guidelines for future analysts and program managers of complex spacecraft systems. It is a synopsis of the structural dynamic effort performed under the Skylab Integration contract and specifically covers the development, utilization, and correlation of Skylab Dynamic Orbital Models.

Demchak, L.↗

Long duration exposure facility - A multipurpose free-flying experiment carrier

The Long Duration Exposure Facility (LDEF) is being developed to accommodate, using the Shuttle, a class of technology, science, and applications experiments which do not require a sophisticated or dedicated satellite. The LDEF is a simple reusable structure approximately 4.3 m in diameter and 9 m in length. The basic LDEF consists of a structural framework whose cross section is a 12-sided regular polygon. A facility description is provided, taking into account the structure, aspects of attitude stabilization, the experiment trays, the experiment exposure control canister, the environment monitoring system, and Shuttle bay environment measurements. Missions and questions of experiment selection are discussed, giving attention to orbits, dynamic motions, a space debris damage experiment, thermal coating experiments, the solar cells and arrays experiment, and the active optical components experiment.

Kinard, W. H.↗

Vibration detection of component operability

In order to prevent catastrophic failure and eliminate unnecessary periodic maintenance in the Space Shuttle Orbiter dynamic components, instrumentation for detecting incipient failure in these components is required. This study investigated the utilization of vibrational phenomena as one of the principal physical parameters on which to base the design of this instrumentation. Baseline vibration data was collected from three aircraft type fans and two aircraft type pumps over a frequency range from a few Hertz to greater than 300 kHz. The baseline data included spectrum analysis of the vibration and detected carrier signals, as well as several non-spectrum parameters. Several defects were introduced into the five test items, and all defects were detected by at least one of the parameters with a margin of at least 2:1 over the worst case baseline.

Baird, B.↗

GEOS-3 coherent C-band tracking data reduction and analysis

The availability of a coherent C-Band transponder on an orbiting vehicle has permitted the development of calibration techniques for C-Band radars. Prior coherent tracking was limited to test vehicles in powered flight or skin tracking of orbiting spacecraft. The pulse Doppler range rate data available concurrently and independently with normal range and angle data provides an extremely useful data set for assessing the internal consistency of the radars measurements, particularly when coupled with a trajectory well constrained by orbit dynamics. In order to further assess the precision of the range rate data, a technique was developed to numerically integrate the rate measurements into a pseudo-range data set showing extremely low noise and high sensitivity to systematic radar errors. Evaluation of integrated range data led to improvements in calibration of both the rate and conventional range data. In particular, proper evaluation of the very sensitive integrated ranges required the development of a processing correction for beacon delay variation with signal strength, a significant error in the conventional ranging data.

Krabill, W. B.↗