Structure of Jupiter - Chemical composition, contraction, and rotation
Jupiter model construction from improved state equation, considering chemical composition, contraction and rotation
Hubbard, W. B.↗
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Interiors of the giant planets
Various investigations concerning Jupiter, Uranus and Saturn are discussed. Revisions in the Galilean satellite ephemerides led to a new interpretation of earth-based measurements of Jovian oblateness which agrees with Pioneer measurements. In the area of scintillation theory, a semi-qualitative result was obtained for spike profiles produced by finite stellar disks viewed through Kolmogorov turbulence. It was also possible to set limits on the systematic distortion of stellar occulation profiles by turbulence which minimize the systematic distortion problem. The position of Miranda was studied for the purpose of obtaining an accurate prediction of a possible stellar occultation by Miranda in 1977, following an occultation of the same star by Uranus. In addition, using thermodynamic calculations, a model was developed for the adiabiatic cooling of Jovian-type planets and an observational test of the model was proposed. The dynamic structure of Saturn's rings was also studied.
Hubbard, W. B.↗
Possible flyby measurements of Galilean satellite interior structure
Flyby encounters of the Galilean satellites from a Jupiter orbiter spacecraft could yield information about the second-degree gravity harmonics of these satellites. The expected values of these harmonics have been calculated for a range of plausible interior models in hydrostatic equilibrium. Because the satellites respond to comparable perturbations from rotation and tides, an independent test of hydrostatic equilibrium is feasible. For Io and Ganymede, the expected measurement accuracy from a nominal encounter should make possible an excellent discrimination from the ensemble of interior models. For Europa, a qualitative distinction between near-uniform and centrally condensed models seems feasible. Only for Callisto is the proposed experiment of marginal value.
Hubbard, W. B.↗
Two- and three-layer models of Uranus
Simple two-layer models of Uranus with rocky core and polytropic envelope satisfying exactly the observed mass, radius and the gravitational moments are presented. The models show that the value of the fourth order zonal harmonic is less than about -38 x 10 to the -6th, while J(6) is roughly 10 to the -6th. More elaborate three-layer models fail to satisfy the observational constraints of the ice/rock ratio and/or of the rotation period. It is concluded that three-layer models with uniform chemical composition in each layer may be too restrictive. More realistic models should account for variable chemical composition within each layer.
Horedt, G. P.↗
Electrostatic emissions between electron gyroharmonics in the outer magnetosphere
A scheme was constructed and a theoretical model was developed to classify electrostatic emissions. All of the emissions appear to be generated by the same basic mechanism: an unstable electron plasma distribution consisting of cold electrons (less than 100 eV) and hot loss cone electrons (about 1 keV). Each emission class is associated with a particular range of model parameters; the wide band electric field data can thus be used to infer the density and temperature of the cold plasma component. The model predicts that gyroharmonic emissions near the plasma frequency require large cold plasma densities.
Hubbard, R. F.↗
Electrostatic emissions between electron gyroharmonics in the outer magnetosphere
Electrostatic emissions are often observed by spacecraft in the outer magnetosphere at frequencies between low electron gyroharmonics. The emissions include the well-known odd half-harmonic emissions as well as weaker emissions which occur near the electron plasma frequency. A scheme is constructed for classifying the emissions, and it is shown that a theoretical model which has been previously used to explain '3/2' emissions can be extended to the other classes of emissions. All of the emissions therefore appear to be generated by the same basic mechanism: an unstable electron plasma distribution consisting of cold electrons (below 100 eV) and hot loss cone electrons (about 1 keV). Each emission class is associated with a particular range of model parameters; the wide-band electric field data can thus be used to infer the density and temperature of the cold plasma component. The model predicts that gyroharmonic emissions near the plasma frequency require large cold plasma densities.
Hubbard, R. F.↗
Global Aerodynamic Modeling Using Automated Local Model Networks in Real Time
A novel method is presented for automated real-time global aerodynamic modeling using local model networks, known as Smoothed Partitioning with Localized Trees in Real Time (SPLITR), as part of NASA’s Learn-to-Fly technology development initiative. The global nonlinear aerodynamics are partitioned into several local regions known as cells, with the dimension, location, and timing of each partition automatically selected based on a residual characterization procedure, under the constraints of real-time operation. Regression trees represent the successive partitioning of the global flight envelope and describe the evolution of the cell structure. Recursive equation-error least-squares parameter estimation in the time domain is used to estimate a model that represents the local aerodynamics in each region, so that it can be updated independently with non-contiguous data in the range of each cell over time. A weighted superposition of these piecewise local models across the flight envelope forms a global nonlinear model that also accurately captures the local aerodynamics. The SPLITR approach is demonstrated using both simulation and flight data, and the results are analyzed in terms of model predictive capabilities as well as interpretability. The results show that SPLITR can be used to automatically partition complex nonlinear aerodynamic behavior, produce an accurate model, and provide valuable physical insight into the local and global aerodynamics.
Weinstein, Rose↗
High zonal harmonics of rapidly rotating planets
A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.
Hubbard, W. B.↗
Internal structure of Uranus
An updated study is presented of Uranus interior models using current information about the planet's gravity field and rotation rate. The most plausible model, both from the point of view of recent data and cosmogony, has a central core of iron and magnesium silicates, an outer envelope of liquid water, methane, and ammonia, and a deep 'atmosphere' of almost four earth masses of hydrogen, helium, and methane. The 'atmosphere' contains a gravitationally nonnegligible amount of methane - about 40% by mass. All plausible models are most consistent with a rotation period of 15 to 16 hours.
Macfarlane, J. J.↗
Comparison of model helicopter rotor primary and secondary blade/vortex interaction blade slap
Previously cited in issue 10, p. 1475, Accession no. A83-25934
Hubbard, J. E., Jr.↗
Lunar mare basalts - Conference summary
Compositionally, lunar mare basalts are similar to some very young subalkaline basalts from terrestrial mid-ocean ridges and to very old pods of basaltic material incorporated into ancient metamorphic rocks. Basalt flows in Mare Imbrium are considered, taking into account the results of orbital gamma ray spectroscopic studies. The results of the analyses of lunar samples obtained from the Apollo missions are evaluated and various models are discussed in connection with an interpretation of the observed conditions.
Merrill, B.↗
An expanded set of brown dwarf and very low mass star models
We present in this paper updated and improved theoretical models of brown dwarfs and late M dwarfs. The evolution and characteristics of objects between 0.01 and 0.2 solar mass are exhaustively investigated and special emphasis is placed on their properties at early ages. The dependence on the helium fraction, deuterium fraction, and metallicity of the masses, effective temperature and luminosities at the edge of the hydrogen main sequence are calculated. We derive luminosity functions for representative mass functions and compare our predictions to recent cluster data. We show that there are distinctive features in the theoretical luminosity functions that can serve as diagnostics of brown dwarf physics. A zero-metallicity model is presented as a bound to or approximation of a putative extreme halo population.
Burrows, A.↗
Interior structure of Saturn inferred from Pioneer 11 gravity data
The structure of Saturn is studied via a fourth-order theory for rotating planets and equations of state for the envelope which depend parametrically on the helium abundance, on the starting temperature for the adiabat, and on adopted forms of the pressure-density curve in the region of transition from molecular to metallic hydrogen. Models are constrained by the values of J2 and J4 obtained from the Pioneer-Saturn celestial mechanics experiment. Equations of state are tested by computing Jupiter models, which can now be subjected to a more stringent comparison with observed zonal harmonics. It is found that Saturn has a low-density hydrogen-helium envelope with no evidence for enhancement of H2O, CH4, or other abundant compounds. Such compounds are presumably located near the core. The helium mass abundance for Saturn's envelope appears to be in the range of approximately 0.12 to 0.19, but this result is very model-dependent. The helium abundance in the envelope of Jupiter is apparently very similar to that of Saturn.
Hubbard, W. B.↗
Comparison of measured and modeled radiation, heat and water vapor fluxes: FIFE pilot study
The primary objectives of the 1985 study were to test the feasibility of using radio frequency receivers to collect data from automated weather stations and to evaluate the use of the data collected by the automated weather stations for modeling the fluxes of latent heat, sensible heat, and radiation over wheat. The model Cupid was used to calculate these fluxes which were compared with fluxes of these entities measured using micrometeorological techniques. The primary objectives of the 1986 study were to measure and model reflected and emitted radiation streams at a few locations within the First International Satellite Land-Surface Climatology Project Field Experiment (FIFE) site and to compare modeled and measured latent heat and sensible heat fluxes from the prairie vegetation.
Blad, Blaine L.↗
Optimized Jupiter, Saturn, and Uranus interior models
A method for inverting gravitational data is the basis for the present models of Saturn, Jupiter, and Uranus, which have been computed to the third-order in rotational disturbance to the total potential and yield exact matches for recent, highly-accurate determinations of gravitational harmonics for these planets. These results indicate that a major He depletion has either not occurred in the outer layers of Jupiter or of Saturn, or that such a depletion's effect on the density profile has been masked by the presence of denser components. Considerable uncertainty characterizes Uranian models; the one presently preferred has substantial heavy-element enhancement at depth and little ice-rock separation.
Hubbard, W. B.↗
Theoretical quasar emission-line ratios. VII - Energy-balance models for finite hydrogen slabs
The present energy balance calculations for finite, isobaric, hydrogen-slab quasar emission line clouds incorporate probabilistic radiative transfer (RT) in all lines and bound-free continua of a five-level continuum model hydrogen atom. Attention is given to the line ratios, line formation regions, level populations and model applicability results obtained. H lines and a variety of other considerations suggest the possibility of emission line cloud densities in excess of 10 to the 10th/cu cm. Lyman-beta/Lyman-alpha line ratios that are in agreement with observed values are obtained by the models. The observed Lyman/Balmer ratios can be achieved with clouds whose column depths are about 10 to the 22nd/sq cm.
Hubbard, E. N.↗
Theoretical Thermodynamics of Mixtures at High Pressures
The development of an understanding of the chemistry of mixtures of metallic hydrogen and abundant, higher-z material such as oxygen, carbon, etc., is important for understanding of fundamental processes of energy release, differentiation, and development of atmospheric abundances in the Jovian planets. It provides a significant theoretical base for the interpretation of atmospheric elemental abundances to be provided by atmospheric entry probes in coming years. Significant differences are found when non-perturbative approaches such as Thomas-Fermi-Dirac (TFD) theory are used. Mapping of the phase diagrams of such binary mixtures in the pressure range from approx. 10 Mbar to approx. 1000 Mbar, using results from three-dimensional TFD calculations is undertaken. Derivation of a general and flexible thermodynamic model for such binary mixtures in the relevant pressure range was facilitated by the following breakthrough: there exists an accurate nd fairly simple thermodynamic representation of a liquid two-component plasma (TCP) in which the Helmholtz free energy is represented as a suitable linear combination of terms dependent only on density and terms which depend only on the ion coupling parameter. It is found that the crystal energies of mixtures of H-He, H-C, and H-O can be satisfactorily reproduced by the same type of model, except that an effective, density-dependent ionic charge must be used in place of the actual total ionic charge.
Hubbard, W. B.↗
Observations of electron gyroharmonic waves and the structure of the Io torus
Narrow-banded emissions observed by the planetary radio astronomy experiment on the Voyager 1 spacecraft as it traversed the Io plasma torus are discussed. It is found that the waves occur between harmonics of the electron gyrofrequency; they are Jovian analogue of electrostatic emissions observed and theoretically studied for the terrestrial magnetosphere. It is noted that the observed frequencies always include the component near the upper hybrid resonant frequency but that the distribution of the other observed emissions varies in a systematic way with position in the torus. A detailed discussion of the observations is given. Also included is a refined model of the electron density variation, based on identification of the upper hybrid resonant frequency line.
Birmingham, T. J.↗