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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Simulating Z 2 lattice gauge theory on a quantum computer

The utility of quantum computers for simulating lattice gauge theories is currently limited by the noisiness of the physical hardware. Various quantum error mitigation strategies exist to reduce the statistical and systematic uncertainties in quantum simulations via improved algorithms and analysis strategies. We perform quantum simulations of Z 2 gauge theory with matter to study the efficacy and interplay of different error mitigation methods: readout error mitigation, randomized compiling, rescaling, and dynamical decoupling. We compute Minkowski correlation functions in this confining gauge theory and extract the mass of the lightest spin-1 state from fits to their time dependence. Quantum error mitigation extends the range of times over which our correlation function calculations are accurate by a factor of 6 and is therefore essential for obtaining reliable masses.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Inverse kinematics study of the energy levels of 21 Ne populated with the 20 Ne +𝑑 reaction

In recent years there has been significant experimental effort aimed at studying the impact of 16 O neutron poisoning on the weak 𝑠 process in rotating massive stars. Improving the understanding of energy levels in 21 Ne is crucial to reducing uncertainties in the rates of the 𝛼-induced reactions on 17 O that determine the overall efficiency of the weak 𝑠 process. This paper reports on one such experiment: a study of the 20 Ne (𝑑,𝑝)⁢ 21 Ne reaction in inverse kinematics. Deduced spin-parity assignments were made based on adiabatic distorted-wave approximation analysis and neutron partial widths were estimated by comparison with a previous experiment. Of particular significance for nuclear astrophysics is the resulting neutron partial width for the 7820-keV energy level, estimated to be 12 200 ⁢(2900)⁢ eV, and an upper limit of ≤ 9300 eV for that of the 7749-keV energy level. These results are in tension with previous studies and therefore this paper also discusses the current state of the research into the astrophysically relevant energy levels and highlights both areas of agreement and areas of disagreement between this and various other studies that have investigated this nucleus.

direct reactions↗
DOE OSTI2022

Technical and personal remembrances of David A. Shirley in studies of surface magnetism, photoelectron spectroscopy, EUV lithography, and hydrogen storage

This article describes the influence of Professor David A. Shirley on the research science of one of his Ph.D. students in the diverse areas of surface magnetism, x-ray photoelectron spectroscopy (XPS), spin-resolved XPS (SRXPS), extreme ultraviolet (EUV) lithography, and hydrogen storage materials science. Examples are given from the author's work on Cr(001) surface magnetism, XPS, and SRXPS studies of multiplet-splitting in core-level photoemission from Fe. In addition, Dave's influence in understanding the radiation-induced deposition of carbon on EUV optics is described, along with the use of XPS in deciphering how hydrogen storage materials are modified by repeated hydrogen adsorption/desorption cycling. The current status of these particular topics is briefly summarized. These technical remembrances are combined with some fond personal stories about Dave, in recognition of his passing on March 29, 2021.

Klebanoff, L. E.↗
NASA NTRS1999

Practical Application of Model Checking in Software Verification

This paper presents our experiences in applying the JAVA PATHFINDER (J(sub PF)), a recently developed JAVA to SPIN translator, in the finding of synchronization bugs in a Chinese Chess game server application written in JAVA. We give an overview of J(sub PF) and the subset of JAVA that it supports and describe the abstraction and verification of the game server. Finally, we analyze the results of the effort. We argue that abstraction by under-approximation is necessary for abstracting sufficiently smaller models for verification purposes; that user guidance is crucial for effective abstraction; and that current model checkers do not conveniently support the computational models of software in general and JAVA in particular.

Havelund, Klaus↗
NASA NTRS2004

Lithium Polymer Electrolytes and Solid State NMR

Research is being done at the Glenn Research Center (GRC) developing new kinds of batteries that do not depend on a solution. Currently, batteries use liquid electrolytes containing lithium. Problems with the liquid electrolyte are (1) solvents used can leak out of the battery, so larger, more restrictive, packages have to be made, inhibiting the diversity of application and decreasing the power density; (2) the liquid is incompatible with the lithium metal anode, so alternative, less efficient, anodes are required. The Materials Department at GRC has been working to synthesize polymer electrolytes that can replace the liquid electrolytes. The advantages are that polymer electrolytes do not have the potential to leak so they can be used for a variety of tasks, small or large, including in the space rover or in space suits. The polymers generated by Dr. Mary Ann Meador's group are in the form of rod -coil structures. The rod aspect gives the polymer structural integrity, while the coil makes it flexible. Lithium ions are used in these polymers because of their high mobility. The coils have repeating units of oxygen which stabilize the positive lithium by donating electron density. This aids in the movement of the lithium within the polymer, which contributes to higher conductivity. In addition to conductivity testing, these polymers are characterized using DSC, TGA, FTIR, and solid state NMR. Solid state NMR is used in classifying materials that are not soluble in solvents, such as polymers. The NMR spins the sample at a magic angle (54.7') allowing the significant peaks to emerge. Although solid state NMR is a helpful technique in determining bonding, the process of preparing the sample and tuning it properly are intricate jobs that require patience; especially since each run takes about six hours. The NMR allows for the advancement of polymer synthesis by showing if the expected results were achieved. Using the NMR, in addition to looking at polymers, allows for participation on a variety of other projects, including aero-gels and carbon graphite mat en als. The goals of the polymer electrolyte research are to improve the physical properties of the polymers. This includes improving conductivity, durability, and expanding the temperature range over which it is effective. Currently, good conductivity is only present at high temperatures. My goals are to experiment with different arrangements of rods and coils to achieve these desirable properties. Some of my experiments include changing the number of repeat units in the polymer, the size of the diamines, and the types of coil. Analysis of these new polymers indicates improvement in some properties, such as lower glass transition temperature; however, they are not as flexible as desired. With further research we hope to produce polymers that encompass all of these properties to a high degree.

Berkeley, Emily R.↗
NASA NTRSDate not supplied

The Land Surface in Current and Planned MERRA Reanalysis Products

Current global atmospheric reanalysis products such as the European Centre for Medium-Range Weather Forecasts Reanalysis version 5 (ERA5), the NASA Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2), and the Japanese Reanalysis for Three Quarters of a Century (JRA-3Q) provide estimates of land surface states and fluxes, including soil moisture, soil temperature, snow mass, latent and sensible heat fluxes, and runoff, that are widely used in research and applications. These land surface estimates are based on land surface process models and, depending on the reanalysis product, on precipitation observations or the assimilation of land surface observations of soil moisture, soil temperature, snow conditions, and screen-level air temperature and humidity from satellite observations and in situ measurements. In this presentation, we review the land surface modeling and data assimilation components of the suite of current and planned MERRA reanalysis products. In addition to MERRA-2, we will discuss the latest NASA reanalysis, MERRA for the 21st century (M21C), which is currently under production, as well as the development and planning of the next version of the MERRA reanalysis, tentatively labeled MERRA-3. In MERRA-2, observations-based precipitation data products are used to correct the precipitation falling on the land surface. Outside of the high-latitudes and Africa, the daily, 0.5-degree, gauge-based Climate Prediction Center (CPC) Unified (CPCU) product is used. In Africa, the pentad, 2.5-degree, satellite- and gauge-based CPC Merged Analysis of Precipitation (CMAP) product is used. Poleward of 62.5 degrees latitude, the land surface sees the precipitation generated by the atmospheric model in the cycling data assimilation system. This configuration provides improved soil moisture estimates compared to those of the original (version 1) MERRA estimates, which did not benefit from the use of precipitation observations. Moreover, the use of precipitation observations facilitates a seamless spin-up of the land surface initial conditions across the MERRA-2 production streams. The use of a gauge-only precipitation product in MERRA-2 across much of the globe, however, adversely impacts the quality of the MERRA-2 land surface estimates in regions with poor gauge coverage, including most of South America and Australia. Therefore, the forthcoming M21C reanalysis uses satellite- and gauge-based precipitation from the Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement Mission (IMERG). This change results in significant improvements in the quality of the M21C soil moisture estimates in the Southern Hemisphere compared to those from MERRA-2. Planning for MERRA-3 focuses on the assimilation of soil moisture observations from the Soil Moisture Active Passive (SMAP) mission and the Advanced Scatterometer (ASCAT), along with snow cover area fraction observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) to further improve the quality of the land surface estimates from the reanalysis. As a first step towards the assimilation of land surface observations in MERRA-3, the offline (land-only) M21C-Land reanalysis is currently under development as a supplemental M21C product that includes the assimilation of SMAP, ASCAT, and MODIS observations. Preliminary results from M21C and M21C-Land will be discussed in the context of MERRA-2 and plans for MERRA-3.

Rolf Reichle↗
DOE OSTI2024

Incorporation of rare earth elements $\text{Sc}$, $\text{Y}$ and $\text{La}$ into gibbsite

Rare earth elements (REE) are increasingly critical resources in technological applications, but the current understanding of their separation by uptake into minerals remains limited. We examined the adsorption and solubilization of scandium (Sc), yttrium (Y), and lanthanum (La) into aluminum hydroxide (gibbsite, Al(OH) 3 ). Based on spectroscopic investigations such as inductively coupled plasma-optical emission spectroscopy (ICP-OES) and time of flight-secondary ion mass spectrometry (ToF-SIMS), only Sc exhibited favorable incorporation and adsorption (0.66 and 0.06 atom%, respectively). Analysis of solid state 45 Sc magic angle spinning-nuclear magnetic resonance spectroscopy (MAS-NMR) indicated that Sc exhibits an octahedral coordination consistent with isolated substitutions for Al in the gibbsite structure, leading to a increase in lattice constants detectable by X-ray diffraction. Density functional theory (DFT) calculations reinforced this interpretation by reproducing the detected structural distortion as well as demonstrating the relatively favorable energetic basis for Sc incorporation into gibbsite by substitution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Experimental scheme for polarizing boron nuclei

Unraveling the internal structure of hadrons and nuclei in terms of the quarks and gluons of quantum chromodynamics is a central focus of current nuclear physics research. Directly observing gluonic states in the nucleus would be groundbreaking and is an objective of the future Electron-Ion Collider (EIC). Over 30 years ago, Jaffe and Manohar [R. L. Jaffe and A. Manohar, Phys. Lett. B 223 , 218 (1989)] identified a new double-helicity flip structure function, directly sensitive to exotic gluons. They pointed out that this could be measured in inclusive high-energy electron scattering from a transversely polarized nuclear target with spin 𝐼 ≥ 1. Here, in this work, we identify the spin-3 nucleus boron-10 as a particularly interesting system to search for exotic gluons. Leveraging technical advances in atomic physics over the past decade, we outline an experimental scheme to directly optically pump a beam of stable boron atoms to polarize the nuclear spin. Technical challenges to realize a spin-polarized beam of boron-10 in the EIC are discussed. The proposed scheme will also polarize the 11 B nucleus, which could significantly enhance the proton-boron fusion cross section.

atomic spectra↗
DOE OSTI2022

Terahertz nano-imaging of metal-insulator transition in Cd 2 Os 2 O 7

The osmate pyrochlore Cd 2 Os 2 O 7 supports an antiferromagnet insulator ground state with an all-in/all-out (AIAO) spin ordering at low temperature. Above 225 K, Cd 2 Os 2 O 7 becomes a paramagnetic metal whereas the mechanism of this metal-to-insulator transition (MIT) remains elusive. In this letter, we use cryogenic near-field technique operating at terahertz frequencies to study the evolution of low-energy response across the MIT. We observed a systematic variation of the magnitude of nano-THz signal across the transition, consistent with the trend in the direct-current conductivity. Conducting domain walls that dominate the nano-scale landscape of the conductivity of a closely related AIAO system Nd 2 Ir 2 O 7 are not apparent in Cd 2 Os 2 O 7

36 MATERIALS SCIENCE↗
NASA NTRS2002

Evaluation of the Effect of Water Vapor On the Performance of NASA's NMRO Catalysts for Carbon Monoxide Oxidation

The Noble Metal Reducible Oxide (NMRO) catalysts for the low temperature oxidation of carbon monoxide were developed by NASA for the reoxidation of carbon monoxide which forms by the dissociation of carbon dioxide during the operation of sealed carbon dioxide lasers. The NMRO catalyst, which consists of a noble metal in conjunction with a reducible metal oxide, was evaluated under conditions that will be encountered in a CO2 laser operation, namely temperatures in the range 298 to 373 K and no significant reaction gas components other than CO, CO2 and O2. The NMRO catalysts may have significant potential for spin-off applications such as the prevention of carbon monoxide build-up in closed spaces as in space vehicle cabins or submarines, and the elimination of the cold start-up problem of automobile exhaust catalysts. The most significant difference in the conditions of these possible future applications is the high moisture content of the gases to be processed. Lack of understanding of the effects of water vapor and high temperature on catalyst activity and operation for extended periods are currently the main stumbling blocks for the transfer of this NASA technology to be used for commercial purposes. In the original proposal the following objectives were stated: To obtain experimental data on the adsorption, desorption and reaction characteristics of CO and CO2 the catalysts under high moisture conditions; to collect evidence on the presence of carbonate and hydroxyl surface species and their involvement in the CO oxidation mechanism; and to model the reaction system using a Monte-Carlo simulation to gain insight on the various steps involved. After the work has commenced the NASA technical monitor Mr. David Scheyer informed us that there was increased interest in the possible use of the NMRO catalysts as automobile exhaust catalysts and therefore NASA wanted to know whether the catalysts can operate at high temperatures as well as with high moisture gases. At that meeting it was decided that investigation of the high temperature performance of the NMRO catalysts should be given priority and replace the Monte-Carlo simulation objective. As a result, the modified objectives of the investigation were taken as the investigation of the high-temperature activity of the NMRO catalysts, and the effect of water vapor on the performance of these catalysts.

Akyurtlu, Ates↗
NASA NTRS2011

Orbit Determination of Spacecraft in Earth-Moon L1 and L2 Libration Point Orbits

The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.

Woodard, Mark↗
DOE OSTI2020

First-principles study of magnetism and electric field effects in 2D systems

This review article provides a bird's-eye view of what first-principles based methods can contribute to next-generation device design and simulation. After a brief overview of methods and capabilities in the area, the authors focus on published work by their group since 2015 and current work on CrI3. The authors introduce both single- and dual-gate models in the framework of density functional theory and the constrained random phase approximation in estimating the Hubbard U for 2D systems vs their 3D counterparts. A wide range of systems, including graphene-based heterogeneous systems, transition metal dichalcogenides, and topological insulators, and a rich array of physical phenomena, including the macroscopic origin of polarization, field effects on magnetic order, interface state resonance induced peak in transmission coefficients, spin filtration, etc., are covered. For CrI3, the authors present their new results on bilayer systems such as the interplay between stacking and magnetic order, pressure dependence, and electric field induced magnetic phase transitions. The authors find that a bare bilayer CrI3, graphene|bilayer CrI3|graphene, hexagonal boron nitride (h-BN)|bilayer CrI3|h-BN, and h-BN|bilayer CrI3|graphene all have a different response at high field, while at small field, the difference is small except for graphene|bilayer CrI3|graphene. The authors conclude with discussion of some ongoing work and work planned in the near future, with the inclusion of further method development and applications.

Cheng, Hai-Ping (ORCID:0000000159901725)↗
NASA NTRS1983

Use of VAS multispectral data for sea surface temperature determination

The Visible Infrared Spin Scan Radiometer Atmospheric Sounder (VAS) is a radiometer possessing eight visible channel detectors and six thermal detectors that sense infrared radiation in 12 spectral bands. Housed in the GOES satellite, VAS spins in a west to east direction at 100 rpm and achieves spatial coverage at resolutions of 1 km in the visible and 7 or 14 km in the infrared by stepping a scan mirror in a north to south direction. Designed for multipurpose applications, the VAS can be operated in two different modes: (1) a multi-spectral imaging (MSI) mode, and (2) a dwell sounding (DS) mode. The MSI mode of operation is used for sea surface temperature (SST) determination. Currently, a full-disk MSI image for SST determination is received every hour, 18 hours a day during weekdays. This MSI mode of operation for SST consists of data obtained from wavelengths centered at 3.9 microns (channel 12), 11.6 microns (channel 8), and 12.6 microns (channel 7) as well as visible data.

Bates, J.↗
DOE OSTI2020

Time resolved electrical, optical, and thermal probes of topological spin textures in magnetic nanostructures

This project is a fundamental study of magnetization dynamics in nanoscale spin textures with topological properties. One example is magnetic skyrmions that form in chiral ferromagnetic material systems that lack inversion symmetry. We have concentrated on the scalable chiral magnetic metal B20 FeGe thin film that has an asymmetric exchange interaction due to non-centrosymmetric cubic lattice. While the asymmetric exchange interaction can be found at the interface of a ferromagnet and a heavy metal, manipulation of skyrmions at these interfaces is non-trivial due to pinning and it requires higher critical current. In contrast, B20 materials such as FeGe have superior material quality to offer pinning-free and low-current skyrmion motion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Correcting the PFNS for more consistent fission modeling

For FY20, we had a deliverable to write a report detailing efforts to simultaneously evaluate both the prompt neutron multiplicity, $\overline{ν}$, and the prompt neutron fission neutron spectrum, PFNS, using CGMF. CGMF is the LANL-developed fission fragment decay code that consistently evaporates prompt neutrons and γ rays using the Hauser-Feshbach statistical theory of compound reactions. The decay begins by constructing the initial conditions of the fission fragments, then decaying each one from the excited state by neutrons and γ rays, conserving energy, momentum, spin, and parity in each step of the emission. The initial conditions of the fragments, along with the multiplicity, energy, and direction of each emitted neutron or γ ray, are recorded, allowing for the full reconstruction of the fission event. These event histories allow us to reconstruct average quantities, as well as correlations between observables, that can be compared with experimental or evaluated data. In that initial report, although there was already a favorable comparison between $\overline{ν}$ from CGMF, experiment, and the current ENDF/B-VIII.0 evaluation, we showed that there was still significant work to be done to improve the PFNS from CGMF. Historically, the PFNS is calculated too soft by Hauser-Feshbach fission models, and CGMF is no exception. The incorrect shape presents a significant challenge in fission modeling, including for our understanding of the fission process and for our ability to consistently calculate and predict a variety of prompt fission observables (such as fission fragment initial conditions, neutron and γ-ray multiplicities and energies, and the correlations between all observables). In our companion report, we detail our success in using CGMF to evaluate $\overline{ν}$. Although not included in the optimization explicitly, we also keep the initial conditions of the fission fragments physical, along with reproducing reasonably well the neutron multiplicity distribution. As we would expect from the sensitivities calculations from, the average neutron energies change very little from the $\overline{ν}$ optimization along with the PFNS (as will be shown in Sec. 2.6). The conclusion was that the global and statistical models would have to be investigated instead of just the fission fragment initial conditions (as is sufficient for $\overline{ν}$). This report details those efforts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1977

Consequences and inferences from tidal interactions in the solar system

A general theory of the rotation of solid bodies in the solar system leads to the following conclusions: No special initial conditions on the primordial rotation states of most tidally evolved bodies are necessary to account for their present rotation. The possible exception is the rotation of Venus, which must have been initially retrograde unless a liquid core-solid mantle interaction or an accelerating atmospheric tide could dominate the ordinary gravitational tides. Tides eventually drive all bodies in precessing orbits to 'Cassini states', where the spin vector, normal to the orbit and normal to the invariable plane remain coplanar as the first two precess about the latter. The constant obliquity in this configuration, together with the lowest order gravitational harmonics and the amplitude of the physical libration allows the determination of the central condensation and the extent of a liquid-core for Mercury. Criteria for the existence of observable amplitudes of the free wobble, free precession and libration of the moon are established which do not exclude current, non-zero values.

Peale, S. J.↗
NASA NTRS2003

A Solar System Survey of Forced Librations in Longitude

Physical librations in longitude are forced periodic variations of a body's rotation rate. If the torque producing the librations can be calculated, then observations of the phase and amplitude of librations can provide information on mass distribution, and effective strength of the body. In the near future prospects for observing physical librations look quite promising. Radio interferometric observations of Venus and Mercury may yield sufficiently accurate rotational observations that librations there may be visible. Range measurements from Earth to networks of landed instrument packages on Mars are likely to yield librational data there as well. We compute expected libration amplitudes from physical and orbital parameters of a set of planets and satellites partially motivated by a desire to identify candidates for future observations. Solar system bodies occupy one of three general rotation states: non-resonant states, resonant states, and the synchronous resonant state. Analytical treatments of forced librations were initially motivated by the Moon. Lunar librations were predicted by Newton, first detected telescopically by Bessel, and definitively resolved through lunar laser ranging which has led to quite thorough analysis of of librations for the synchronous case. The synchronous resonant state is commonly observed among satellites. The only known body to exist in a non-synchronous resonance is Mercury which exists in a 3:2 resonance, completing three rotations for every two revolutions about the sun. The analysis of Goldreich and Peale has lead to improved understanding of the general case of half integer resonance states. The dynamics of forced librations in non-resonant rotators has received less attention. While there are few cases in which non-resonant forced librations have been observed, Earth is an important exception, and current observing techniques may have the capacity to detect them on Venus. A comprehensive observing program spanning a range of solar system bodies can address an array of geophysical issues involving interior mass distribution of planets, satellites, and asteroids. Calculations of expected librations can supply amplitude estimates helpful in identifying the likelihood of detecting librations observationally. We present a survey of expected libration amplitudes for a subset of solar system bodies, identifying those bodies with amplitudes likely to be detectable, and commenting on spin state, and radial structure implications.

Comstock, R. L.↗