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NASA NTRS1987

Tidal influences on vertical diffusion and diurnal variability of ozone in the mesosphere

Possible dynamical influences on the diurnal behavior of ozone are investigated. A time dependent one-dimensional photochemical model is developed for this purpose; all model calculations are made at 70 deg N during summer. It is shown that the vertical diffusion can vary as much as 1 order of magnitude within a day as a result of large changes in the zonal wind induced by atmospheric thermal tides. It is found that by introducing a dissipation time scale for turbulence produced by breaking gravity waves, the agreement with Poker Flat echo data is improved. Comparisons of results from photochemical model calculations, where the vertical diffusion is a function of height only, with those in which the vertical diffusion coefficient is changing in time show large differences in the diurnal behavior of ozone between 70 and 90 km. By including the dynamical effect, much better agreement with the Solar Mesosphere Explorers data is obtained. The results are, however, sensitive to the background zonally averaged wind. The influence of including time-varying vertical diffusion coefficient on the OH densities is also large, especially between 80 and 90 km. This suggests that dynamical effects are important in determining the diurnal behavior of the airglow emission from the Meinel bands.

Bjarnason, Gudmundur G.↗
NASA NTRS2002

Hawaii Ocean Mixing Experiment: Program Summary

It is becoming apparent that insufficient mixing occurs in the pelagic ocean to maintain the large scale thermohaline circulation. Observed mixing rates fall a factor of ten short of classical indices such as Munk's "Abyssal Recipe." The growing suspicion is that most of the mixing in the sea occurs near topography. Exciting recent observations by Polzin et al., among others, fuel this speculation. If topographic mixing is indeed important, it must be acknowledged that its geographic distribution, both laterally and vertically, is presently unknown. The vertical distribution of mixing plays a critical role in the Stommel Arons model of the ocean interior circulation. In recent numerical studies, Samelson demonstrates the extreme sensitivity of flow in the abyssal ocean to the spatial distribution of mixing. We propose to study the topographic mixing problem through an integrated program of modeling and observation. We focus on tidally forced mixing as the global energetics of this process have received (and are receiving) considerable study. Also, the well defined frequency of the forcing and the unique geometry of tidal scattering serve to focus the experiment design. The Hawaiian Ridge is selected as a study site. Strong interaction between the barotropic tide and the Ridge is known to take place. The goals of the Hawaiian Ocean Mixing Experiment (HOME) are to quantify the rate of tidal energy loss to mixing at the Ridge and to identify the mechanisms by which energy is lost and mixing generated. We are challenged to develop a sufficiently comprehensive picture that results can be generalized from Hawaii to the global ocean. To achieve these goals, investigators from five institutions have designed HOME, a program of historic data analysis, modeling and field observation. The Analysis and Modeling efforts support the design of the field experiments. As the program progresses, a global model of the barotropic (depth independent) tide, and two models of the baroclinic (depth varying) tide, all validated with near-Ridge data, will be applied, to reveal the mechanisms of tidal energy conversion along the Ridge, and allow spatial and temporal integration of the rate of conversion. Field experiments include a survey to identify "hot spots" of enhanced mixing and barotropic to baroclinic conversion, a Nearfield study identifying the dominant mechanisms responsible for topographic mixing, and a Farfield program which quantifies the barotropic energy flux convergence at the Ridge and the flux divergence associated with low mode baroclinic waves radiation. The difference is a measure of the tidal power available for mixing at the Ridge. Field work is planned from years 2000 through 2002, with analysis and modeling efforts extending through early 2006. If successful, HOME will yield an understanding of the dominant topographic mixing processes applicable throughout the global ocean. It will advance understanding of two central problems in ocean science, the maintenance of the abyssal stratification, and the dissipation of the tides. HOME data will be used to improve the parameterization of dissipation in models which presently assimilate TOPEX-POSEIDON observations. The improved understanding of the dynamics and spatial distribution of mixing processes will benefit future long-term programs such as CLIVAR.

Ray, Richard D.↗
NASA NTRS1977

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Volland, H.↗
NASA NTRS1972

A numerical study of a three dimensional spherical thermospheric density and wind model

Numerical calculations of the generation and propagation of the two important fundamental symmetric tidal wave modes - the diurnal mode (1, 1, 1,) and the semidiurnal mode (2, 2, 2) - were performed applying a realistic model thermosphere and taking into account heat conduction and the temporally and spatially varying ion-neutral collision number. Both wave modes are predominantly generated by the solar EUV heat input. It is shown that the latitude structure of the (1, 1, 1)-mode which is identical with the Hough function(1, -1) within the lower non-dissipative atmosphere degenerates into the spherical function P sub 1, 1 at thermospheric heights. The pressure field of this mode constitutes the observed pressure bulge of the thermosphere, the diurnal component of which peaks at 15 h L. T. The electric polarization field of the geomagnetic Sq current generates a significant fraction of this wave mode at F layer heights. This wave component shifts the total horizontal wind system to earlier times by about 1 hour in agreement with ionospheric observations. The latitude structure of the (2, 2, 2) mode is identical with the Hough function (2, 2) within the lower non-dissipative atmosphere. It degenerates to the spherical function P sub 2, 2 at thermospheric heights.

Volland, H.↗
NASA NTRS1994

Double-core evolution. 5: Three-dimensional effects in the merger of a red giant with a dwarf companion

The evolution of the common envelope phase of a binary system consisting of a 4.67 solar mass red giant and a 0.94 solar mass dwarf is studied using smoothed particle hydrodynamics. We demonstrate that the three-dimensional effects associated with the gravitational tidal torques lead to a rapid decay of the orbit on timescales approximately less than 1 yr. The relative orbit of the two cores in the common envelope is initally eccentric and tends to circularize as the orbital separation of the two cores decreases. The angular momentum lost from the orbital motion is distributed throughout the common envelope, and the double core does not evolve to a state of co-rotation for the evolutionary time followed. The energy dissipated from the relative orbit and deposited in the common envelope results in the ejection of approximately 13% of the mass of the envelope. The mass is ejected in all directions, but there is a preference for mass ejection in the orbital plane of the binary system. For example, approximately 80% of the ejected mass lies within 30 deg of the binary orbital plane. Because gravitational forces are long range, most of the energy and angular momentum is imparted to a small fraction of the common envelope resulting in an efficiency of the mass ejection process of approximately 15%. The core of the red giant executes significant displacement with respect to the center of mass of the system and contributes nearly equally to the total energy dissipation rate during the latter phases of the evolution. The degree of departure from synchronism of the initial binary system can be an important property of the system which can affect the outcome of the common envelope phase.

Terman, James L.↗
NASA NTRS1977

Phobos and Deimos

Ground-based and spacecraft observations of Phobos and Deimos are reviewed and the satellites' origin is discussed. The crater densities of both bodies are close to the saturation level. The largest impact events may have caused extensive fracturing of their surfaces. The surfaces are at least 1.5 billion years old and may date back to the early history of the solar system. The Martian satellites display large deviations from sphericity. As a result of tidal processes, they are in synchronous rotation. Several independent lines of evidence show that they have regoliths. Despite some provocative arguments, their internal strengths and the nature of their interior are poorly known at present. Photometric measurements suggest that they are made of either carbonaceous chondritic material or a basalt. Sinclair (1972), Born and Duxbury (1975) and Shor (1975) apparently have successfully determined Phobos' secular acceleration. Their value of approximately .001 deg/year/year implies that the interior of Mars has a low specific dissipation factor (about 100), may indicate that a portion of the Martian interior is experiencing partial melting. The low inclination of the satellites' orbits indicates that they were formed as part of the same process that resulted in Mars.

Pollack, J. B.↗
NASA NTRS1994

Ultraluminous starbursts in major mergers

We use numerical simulation to investigate the triggering of starbursts in merging disk galaxies. The properties of the merger-driven starbursts are sensitive to the structure of the progenitor galaxies; specifically, to the amount of material in a dense central bulge. Galaxies without bulges develop bars shortly after their first close passage, driving significant gas inflow and subsequent starbursts in the centers of the galaxies. These starbursts significantly deplete the star-forming gas, so that only relatively weak starbursts arise during the final merger. By contrast, models of galaxies with central bulges show that a bulge acts to stabilize the galaxies against inflow and starbursts until the galaxies actually merge. At this time, strong dissipation leads to the formation of a massive central gas mass and an ensuing star-formation rate two orders of magnitude greater than that in our isolated disk models. These starbursts are very short in duration, typically approximately 50 Myr, suggesting that the rarity of ultraluminous infrared galaxies is a result of their being in a very short evolutionary phase, rather than special and rare formation conditions. The fact that these mergers display many of the properties of ultraluminous infrared galaxies--tidal features, double nuclei, massive compact gas concentrations, and extreme levels of starburst activity--suggets that merger-driven starbursts can explain the emission from many ultraluminous infrared galaxies without an active nucleus.

Mihos, J. Christopher↗
NASA NTRS1994

Hydrodynamics of rotating stars and close binary interactions: Compressible ellipsoid models

We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids, and the hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. Both viscous dissipation and the gravitational radiation reaction are incorporated. We establish the validity of our approximations and demonstrate the simplicity and power of the method by rederiving a number of known results concerning the stability and dynamical oscillations of rapidly rotating polytropes. In particular, we present a generalization to compressible fluids of Chandrasekhar's classical results for the secular and dynamical instabilities of incompressible Maclaurin spheroids. We also present several applications of our method to astrophysical problems of great current interest, such as the tidal disruption of a star by a massive black hole, the coalescence of compact binaries driven by the emission of gravitational waves, and the development of instabilities in close binary systems.

Lai, Dong↗
NASA NTRS1997

Numerical Modeling of Tidal Effects in Polytropic Accretion Disks

A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m = 1 eccentric instability in the disk. While the m = 2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m = 2 azimuthal mode), with an elliptic pattern rotating at about a fraction (approx. = 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r(Omega)/c(sub s) = M approx. = 40) we also find a critical value of the viscosity parameter (alpha approx. = 0.01), below which shock dissipation dominates and is balanced by the wave amplification due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number M(sub s) approx. = 1.3.

Godon, Patrick↗
NASA NTRS1990

Tidal evolution of the Uranian satellites. III - Evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities

Numerical experiments have been conducted which indicate that the orbital eccentricity of Miranda may have reached a value sufficiently large to have affected its thermal evolution. There is a large chaotic zone associated with the Miranda-Ariel 5:3 mean-motion commensurability, even in the planar approximation; the orbital eccentricities of both satellites may vary chaotically for a considerable period. Since the anomalously high orbital inclination of Miranda is a consequence of passage through the 3:1 commensurability with Umbriel, the requirement that the satellites encountered this resonance places a lower limit on the Uranian specific dissipation function of 39,000.

Tittemore, William C.↗
NASA NTRS2010

Ocean Turbulence, III: New GISS Vertical Mixing Scheme

We have found a new way to express the solutions of the RSM (Reynolds Stress Model) equations that allows us to present the turbulent diffusivities for heat, salt and momentum in a way that is considerably simpler and thus easier to implement than in previous work. The RSM provides the dimensionless mixing efficiencies Gamma-alpha (alpha stands for heat, salt and momentum). However, to compute the diffusivities, one needs additional information, specifically, the dissipation Epsilon. Since a dynamic equation for the latter that includes the physical processes relevant to the ocean is still not available, one must resort to different sources of information outside the RSM to obtain a complete Mixing Scheme usable in OGCMs. As for the RSM results, we show that the Gamma-alpha s are functions of both Ri and Rq (Richardson number and density ratio representing double diffusion, DD); the Gamma-alpha are different for heat, salt and momentum; in the case of heat, the traditional value Gamma-h = 0.2 is valid only in the presence of strong shear (when DD is inoperative) while when shear subsides, NATRE data show that Gamma-h can be three times as large, a result that we reproduce. The salt Gamma-s is given in terms of Gamma-h. The momentum Gamma-m has thus far been guessed with different prescriptions while the RSM provides a well defined expression for Gamma-m(Ri,R-rho). Having tested Gamma-h, we then test the momentum Gamma-m by showing that the turbulent Prandtl number Gamma-m/Gamma-h vs. Ri reproduces the available data quite well. As for the dissipation epsilon, we use different representations, one for the mixed layer (ML), one for the thermocline and one for the ocean;s bottom. For the ML, we adopt a procedure analogous to the one successfully used in PB (planetary boundary layer) studies; for the thermocline, we employ an expression for the variable epsilon/N(exp 2) from studies of the internal gravity waves spectra which includes a latitude dependence; for the ocean bottom, we adopt the enhanced bottom diffusivity expression used by previous authors but with a state of the art internal tidal energy formulation and replace the fixed Gamma-alpha = 0.2 with the RSM result that brings into the problem the Ri, R-rho dependence of the Gamma-alpha; the unresolved bottom drag, which has thus far been either ignored or modeled with heuristic relations, is modeled using a formalism we previously developed and tested in PBL studies. We carried out several tests without an OGCM. Prandtl and flux Richardson numbers vs. Ri. The RSM model reproduces both types of data satisfactorily. DD and Mixing efficiency Gamma-h(Ri,Rq). The RSM model reproduces well the NATRE data. Bimodal epsilon-distribution. NATRE data show that epsilon (Ri < 1) approximately equals 10epsilon(Ri > 1), which our model reproduces. Heat to salt flux ratio. In the Ri much greater than 1 regime, the RSM predictions reproduce the data satisfactorily. NATRE mass diffusivity. The z-profile of the mass diffusivity reproduces well the measurements at NATRE. The local form of the mixing scheme is algebraic with one cubic equation to solve.

Canuto, V. M.↗
NASA NTRS2021

Kozai–Lidov Oscillations Triggered by a Tilt Instability of Detached Circumplanetary Discs

Circumplanetary discs can be linearly unstable to the growth of disc tilt in the tidal potential of the star–planet system. We use3D hydrodynamical simulations to characterize the disc conditions needed for instability, together with its long-term evolution.Tilt growth occurs for disc aspect ratios, evaluated near the disc outer edge, ofH/r0.05, with a weak dependence on viscosityin the wave-like regime of warp propagation. Lower mass giant planets are more likely to have circumplanetary discs thatsatisfy the conditions for instability. We show that the tilt instability can excite the inclination to above the threshold where thecircumplanetary disc becomes unstable to Kozai–Lidov (KL) oscillations. Dissipation in the KL unstable regime caps furthertilt growth, but the disc experiences large oscillations in both inclination and eccentricity. Planetary accretion occurs in episodicaccretion events. We discuss implications of the joint tilt–KL instability for the detectability of circumplanetary discs, for theobliquity evolution of forming giant planets, and for the formation of satellite systems.

Rebecca G Martin↗
NASA NTRS1986

Tidal coupling with the lower atmosphere (invited review)

The various ways are reviewed in which propagating tidal components excited in the mesophere and below affect the structure of the thermosphere and ionosphere above 100 km. Dynamo effects are not treated here. The physical processes affecting the propagation of upward propagating tides are examined and how they are interrelated in the context of a numerical model. Propagating diurnal and semidiurnal tides which reach thermospheric heights are excited primarily by insolation absorption by tropospheric water vapor (0 to 5 km) and stratospheric/mesospheric ozone (40 to 60 km), respectively. Simulation of these oscillations requires consideration of mean zonal winds and meridional temperature gradients, and the damping effects of turbulent and molecular dissipation, radiative cooling, and ion drag. These effects must be considered on a spherical rotating atmosphere extending from the ground to above 300 km, as they are in the model developed by Forbes depicted schematically.

Forbes, J. M.↗
NASA NTRS1997

The General Circulation of the Venus Atmosphere: An Assessment

The overall spin or "superrotation" of the Venus atmosphere is a striking phenomenon. In the 15 years since the NASA Pioneer Venus mission, a first-order understanding has been reached of the dynamics of the atmospheric region near and just above the Venus cloud tops. Tidal motions induced by solar heating produce a traveling disturbance whose vertical momentum transports are balanced by mean flow advection. The balance explains the strength of the mean flow above the clouds, and partially explains the strength of the mean flow at the cloud level where the strongest superrotation of the atmosphere occurs. But the fundamental cause of the global superrotation remains a mystery in spite of data from Earth-based observatories, from Pioneer Venus, from several Russian probes, from a Russian/French balloon experiment, and from the NASA Galileo flyby. The key missing knowledge is of momentum transfer processing the deep atmosphere, between the surface and the cloud deck. Neither the forcing nor the drag and dissipation mechanisms are known. The existing data are reviewed here and theoretical suggestions are listed. It is concluded that further measurements, in conjunction with numerical modeling, will be required to resolve this puzzling and challenging question. New data must improve by an order of magnitude on the accuracies achieved by the Pioneer Venus probes. Velocities in the deep atmosphere must be measured to better than 0.1 m/s and relative temperatures to beter than 0.1 K near the surface.

Gierasch, P. J.↗
NASA NTRS2001

Gravitational Core-Mantle Coupling and the Acceleration of the Earth

Gravitational core-mantle coupling may be the cause of the observed variable acceleration of the Earth's rotation on the 1000 year timescale. The idea is that density inhomogeneities which randomly come and go in the liquid outer core gravitationally attract density inhomogeneities in the mantle and crust, torquing the mantle and changing its rotation state. The corresponding torque by the mantle on the core may also explain the westward drift of the magnetic field of 0.2 deg per year. Gravitational core-mantle coupling would stochastically affect the rate of change of the Earth's obliquity by just a few per cent. Its contribution to polar wander would only be about 0.5% the presently observed rate. Tidal friction is slowing down the rotation of the Earth, overwhelming a smaller positive acceleration from postglacial rebound. Coupling between the liquid outer core of the Earth and the mantle has long been a suspected reason for changes in the length-of-day. The present investigation focuses on the gravitational coupling between the density anomalies in the convecting liquid outer core and those in the mantle and crust as a possible cause for the observed nonsecular acceleration on the millenial timescale. The basic idea is as follows. There are density inhomogeneities caused by blobs circulating in the outer core like the blobs in a lava lamp; thus the outer core's gravitational field is not featureless. Moreover, these blobs will form and dissipate somewhat randomly. Thus there will be a time variability to the fields. These density inhomogeneities will gravitationally attract the density anomalies in the mantle.

Rubincam, David Parry↗
DOE OSTI2022

SDSS IV MaNGA - star-formation driven biconical outflows in face-on galaxies

ABSTRACT We find 132 face-on and low inclination galaxies with central star formation driven biconical gas outflows (FSFB) in the SDSS MaNGA (Mapping Nearby Galaxies at APO) survey. The FSFB galaxies show either double peaked or broadened emission line profiles at their centres. The peak and maximum outflow velocities are 58 and 212 km s−1, respectively. The gas velocity dispersion reveals a mild dependence on the central star formation surface density compatible with models of gas dispersion powered by the Jeans instability in gas clumps or by gas turbulence dissipation. We estimate the gas outflow rate and conclude that the central gas depletion time does not depend on galactic mass. In turn, the ratio of the gas outflow rate to the gas consumption rate by the star formation is low in massive galaxies and high in low mass objects, while the star formation is a more rapid process of the gas consumption. We compare properties of the FSFB galaxies with a control sample of 375 comparison galaxies and find that the FSFB objects have high central concentration of star formation and also younger central stellar population with respect to their periphery. We analysed the environment of the galaxies and identified nearby satellites and elements of low surface brightness structure. We see that many tidal-enhanced features that can be assigned to early and intermediate stages of galactic interaction are much more frequent in the FSFB galaxies with respect to the comparison sample. We conclude that the gas should be replenished via the accretion from small satellites.

Bizyaev, D. (ORCID:000000023601133X)↗
NASA NTRS1994

Contributions to the Earth's Obliquity Rate, Precession, and Nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub 2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024 sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The effects have generally been allowed for in past nutation theories and some precession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta(psi) plus out-of-phase contributions of 0.14 mas in Delta(psi) and -0.03 mas in Delta(sub epsilon). The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C =0.003 273 763 4 which, in combination with a satellite-derived J(sub 2), gives a normalized polar moment of inertia C/MR(exp 2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub 2) Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗
NASA NTRS1994

Contributions to the Earth's obliquity rate, precession, and nutation

The precession and nutation of the Earth's equator arise from solar, lunar, and planetary torques on the oblate Earth. The mean lunar orbit plane is nearly coincident with the ecliptic plane. A small tilt out of the ecliptic is caused by planetary perturbations and the Earth's gravitational harmonic J(sub2). These planetary perturbations on the lunar orbit result in torques on the oblate Earth which contribute to precession, obliquity rate, and nutation while the J(sub 2) perturbations contribute to precession and nutation. Small additional contributions to the secular rates arise from tidal effects and planetary torques on the Earth's bulge. The total correction to the obliquity rate is -0.024sec/century, it is an observable motion in space (the much larger conventional obliquity rate is wholly from the motion of the ecliptic, not the equator), and it is not present in the IAU-adopted expressions for the orientation of the Earth's equator. The J(sub2) effects have generally been allowed for in past nutation theories and some procession theories. For the planetary effect, the contributions to the 18.6 yr nutation are -0.03 mas (milliarcseconds) for the in-phase Delta phi plus out-of-phase contributions of 0.14 mas in Delta phi and -0.03 mas in Delta epsilon. The latter terms demonstrate that out-of-phase contributions can arise by means other than dissipation. The sum of the contributions to the precession rate is considered and the inferred value of the moment of inertia combination (C-A)/C, which is used to scale the coefficients in the nutation series, is evaluated. Using an updated value for the precession rate, the rigid body (C-A)/C = 0.003 273 763 4 which, in combination with a satellite-derived J(sub2), gives a normalized polar moment of inertia C/MR(exp2) = 0.330 700 7. The planetary contributions to the precession and obliquity rates are not constant for long times causing accelerations in both quantities. Acceleration in precession also arises from tides and changing J(sub2). Contributions from the improved theory, masses, ecliptic motion, and measured values of the precession rate and obliquity are combined to give expressions (polynomials in time) for precession, obliquity, and Greenwich Mean Sidereal Time.

Williams, James G.↗