Engineering topics

Hubbard, W. B.

Publications and source records attributed to Hubbard, W. B..

At least 55 records · Page 3

NASA NTRS1984

Interior structure of Uranus

Key measurements are discussed which are diagnostic of Uranus' interior structure and evolutionary history, and reviews their present status. Typical interior models have chondritic cores, but have the bulk of their mass in an envelope consisting of ice component, principally H2O. The total amount of free H2 in the planet cannot exceed approximately 1 to 2 earth masses. Measurements of the gravitational moments of Uranus are beginning to be accurate enough to constrain models, but are limited in utility by uncertainty in the rotation period. Discussed is evidence that the outermost planetary layers have a gravitationally significant quantity of denser material (ice component?) in addition to H2 and He. The He/H ratio and the deuterium abundance in the atmosphere may be diagnostic of the planet's previous evolutionary history. It is argued that the planet's interior is likely to now be at a temperature approximately 10(3) deg K. Uranus' interior with Neptune's in a number of ways, considering heat flow, degree of internal differentiation, and possible magnetic field.

Hubbard, W. B.↗

NASA NTRS1984

Interior structure of Saturn

The principal observational data that constrain interior models of Saturn are summarized, and why they are relevant is explained. The behavior of hydrogen, Saturn's major constituent, at pressures on the order of 0.1 to 10 Mbar and temperatures on the order of 10,000 K, is discussed. Possible behavior and distributions of minor constituents are also considered, along with processes for their transport. Saturn's external gravitational and magnetic fields are interpreted in terms of interior structure, and the relationship between atmospheric zonal flows and the deep interior is discussed. The constraint imposed by tidal evolution considerations is evaluated. Calculations for the thermal evolution of Saturn are presented, both with and without consideration of possible gravitational unmixing. Possible scenarios for Saturn's mode of origin and their implications for presently observed atmospheric abundances are discussed.

Hubbard, W. B.↗

NASA NTRS1983

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.↗

NASA NTRS1983

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

Macfarlane, J. J.↗

NASA NTRS1983

Computation of Jupiter interior models from gravitational inversion theory

Spacecraft measurements of Jupiter have provided the mass, standard pressure level radius, rotation law, internal mass distribution multipole moments, and internal composition and temperature distribution constraints, for the present implementation of a method for deriving planetary interior models that exactly satisfy a set of N gravitational constraints by means of appropriate iteration. The models are not forced to fit the more indirectly derived constraints, which are instead used as conistency checks. In the case of an He mass fraction in the envelope Y of 0.2, the inferred pressure at a mass density of about 0.2 g/cu cm is about a factor of 2 higher than would be indicated by experimental H compression data in the relevant pressure range of 100,000 to one million bar. The inferred pressure distribution is in better agreement with the shock data for a nominal Y value of 0.3 + or - 0.05.

Hubbard, W. B.↗

NASA NTRS1982

Effects of differential rotation on the gravitational figures of Jupiter and Saturn

It is assumed that observed zonal currents in the atmospheres of Jupiter and Saturn correspond to a state of permanent rotation, and that the angular velocity is constant on cylindrical surfaces parallel to the rotation axis. The equation of hydrostatic equilibrium for a rotating planet is solved under these restrictive assumptions, and the effect of the hypothesized rotation state on the planet's gravity harmonics and external shape is investigated. Spacecraft data on zonal currents are used to derive nearly model-independent corrections to the first four zonal gravity harmonic coefficients, which can be used to correct observed gravity harmonics to values appropriate for solid-body rotation. If the assumed rotation state is applicable, then zonal currents lead to measurable topography of isopycnic surfaces with respect to the reference figure defined by the magnetospheric rotation period and the gravity harmonics. The amplitude of the topography is on the order of 5 km for Jupiter and 60 km for Saturn.

Hubbard, W. B.↗

NASA NTRS1982

Occultation by a possible third satellite of Neptune

The 24 May 1981 close approach of Neptune to an uncataloged star was photoelectrically monitored from two observatories separated by 6 kilometers parallel to the occultation track. An 8.1-second drop in signal, recorded simultaneously at both sites, is interpreted as resulting from the passage of a third satellite of Neptune in front of the star. From the duration of the event, the derived minimum diameter for an object sharing Neptune's motion is 180 kilometers. If the object was in Neptune's equatorial plane and there are no significant errors in the prediction ephemeris, the object was located at a distance of 3 Neptune radii from Neptune's center.

Reitsema, H. J.↗

NASA NTRS1982

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.↗

NASA NTRS1982

Structure of the Martian atmosphere from Epsilon Gem occultation observations

Information about Martian atmospheric scale heights derived from observations of the occultation of Epsilon Gem by Mars on April 8, 1976 has been collected. The observations give data in the altitude range of about 50 to 80 km. A rough, unweighted average of results so far available yields a temperatue of approximately 165 K. Excursions of about + or - 4 K about this mean may be present as a function of both altitude and areographic coordinates.

Hubbard, W. B.↗

NASA NTRS1981

Constraints on the origin and interior structure of the major planets

Fitting models to the external gravity field of the major planets (Uranus, Neptune, Jupiter, and Saturn), it is found that certain interior characteristics may be common to all four. For Uranus and Neptune, a model with a central iron-silicate core of approximately four earth masses, an 'ice' layer of H2O, CH4, and NH3 in solar proportions of about 10 earth masses, and an H2-He atmosphere of about 1-2 earth masses gives a good fit to available constraints, including heat flow measurements. Models of Jupiter and Saturn have cores very similar to those of Uranus and Neptune; the H2-He layer, however, is markedly more extensive. Modes of origin that are consistent with these features are discussed. Models of this type predict a considerable enrichment of deuterium relative to primordial solar abundances in Uranus and Neptune. Such enrichment is not observed in Uranus; implications are discussed for interior structure and origin.

Hubbard, W. B.↗

NASA NTRS1981

Interiors of the giant planets

Unlike the terrestrial planets, the giant planets - Jupiter, Saturn, Uranus, and Neptune - have retained large amounts of the carbon, nitrogen, and oxygen compounds that were present in their zone of formation. A smaller fraction of the available hydrogen and helium was retained. The distribution and relative amounts of these components in the interiors of the Jovian planets can be inferred from theoretical and experimental data on equations of state and from the planets' hydrostatic equilibrium response to rotation.

Hubbard, W. B.↗

NASA NTRS1981

High-speed photometry of the 11 December 1979 Juno occultation

The occultation of SAO 115946 by Juno on 11 December 1979 was observed from two sites in southern California with portable two-color, high-speed photometers. A composite light curve was constructed from the data by suitable scaling of individual observations, using an astrometric solution for the location of the contact points on Juno's limb. The preliminary astrometric solution used here has a semiminor axis of 118 km and a semimajor axis of 145 km at position angle 75.5 deg. The composite light curve is compatible with a stellar radius of (1.6 + or - 0.8) x 10 to the -4th arcsec, consistent with the radius estimated from the color and visual magnitude. There is no evidence for any companions to SAO 115946 or Juno. The prospects for use of asteroid occultations to determine stellar radii and asteroid surface slopes are discussed as compared with the lunar occultation technique.

Reitsema, H. J.↗

NASA NTRS1980

Results from the 10 March 1977 occultation by the Uranus system

Timings of occultation events observed at Perth, Australia during the appulse of Uranus to SAO 158687 are presented. In addition to pre- and post-appulse observations of the alpha ring, a search of the data confirms events by the '4', '5', and '6' rings on the pre-appulse side of Venus, and the '5' and beta rings on the post-appulse side. A table of other suspected events obtained from a statistical search of the data down to the same level of significance as the '4', '5', and '6' events is presented. A fairly strong 'event', so far unconfirmed, is noted near the 5:1 Miranda resonance orbit. Examination of the light curves at high time resolution indicates that the alpha ring was, during this aspect, about 10 km in radial extent and about 50% transparent.

Hubbard, W. B.↗

NASA NTRS1980

Theoretical predictions of deuterium abundances in the Jovian planets

Current concepts for the origin of the Jovian planets and current constraints on their interior structure are used to support the argument that the presence of large amounts of 'ice' (H2O, CH4, and NH3) in Uranus and Neptune indicates temperature low enough to condense these species at the time Uranus and Neptune formed. Such low temperatures, however, imply orders-of-magnitude fractionation effects for deuterium into the 'ice' component if isotopic equilibration can occur. The present models thus imply that Uranus and Neptune should have D/H ratio at least four times primordial, contrary to observation for Uranus. It is found that the Jovian and Saturnian D/H should be close to primordial regardless of formation scenario.

Hubbard, W. B.↗

NASA NTRS1980

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.↗

NASA NTRS1980

Intrinsic luminosities of the Jovian planets

Available data and theories on the size and nature of interior power sources in the four Jovian planets are reviewed. These four planets are Jupiter, Saturn, Uranus and Neptune. Various models, ranging from simple cooling to gravitational layering to radioactivity, are discussed. The evidence and interpretations presented in the discussion seem to indicate that (1) all four Jovian planets were once more luminous and are presently cooling to a state of equilibrium with sunlight; and (2) the thermal evolution of the Jovian planets is predominantly controlled by their photospheres and does not depend on interior conductivity. Both conclusions are consistent with either the simple adiabatic cooling model or with more complicated gravitational unmixing models of the type discussed by Stevenson and Salpeter (1977).

Hubbard, W. B.↗

NASA NTRS1980

Pioneer Saturn celestial mechanics experiment

The paper investigates a continuous round-trip radio link at S band (2.2 GHz) that was maintained during the Pioneer Saturn encounter between stations of the Deep Space Network and the spacecraft. From an analysis of the Doppler shift in the radio carrier frequency, a number of gravitational effects on the trajectory were determined. Gravitational moments for Saturn were found from a preliminary analysis, as well as mass values for the Saturn satellites Rhea, Iapetus, and Titan. It was determined that the densities of all three satellites are low and consistent with the compositions of ices. Theoretical calculations for the Saturn interior are described which use the latest observational data, including Pioneer Saturn and state-of-the-art physics for the internal composition.

Anderson, J. D.↗

NASA NTRS1980

Structure and evolution of Uranus and Neptune

Three-layer interior models of Uranus and Neptune with central rocky cores, mantles of water, methane, and ammonia (the 'ices'), and outer envelopes primarily composed of hydrogen and helium are presented. The models incorporate a new H2O equation of state based on experimental data which is considerably 'softer' than previous H2O equations of state. Corrections for interior temperatures approximately 5000 K are included in the models, and the thermal evolution of both planets is investigated using recent heat flow measurements. It is found that the evolutionary considerations are consistent with gravitational field data in supporting models with approximately solar abundances of 'ice' and 'rock'. Evolutionary considerations indicate that initial temperatures and luminosities for Uranus and Neptune were not substantially higher than the present value. Both planets apparently have relatively small approximately 1-2 earth masses) hydrogen-helium envelopes, with Neptune's envelope smaller than Uranus'. A monotonic trend is evident among the Jovian planets: all have central rock-ice cores of approximately 15 earth masses, but with hydrogen-helium envelopes which decrease in mass from Jupiter to Saturn to Uranus to Neptune.

Hubbard, W. B.↗