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The formalism for studying perturbations of a triaxial rigid body within the Hamilton-Jacobi framework is developed. The motion of a triaxial artificial earth satellite about its center of mass is studied. Variables are found which permit separation, and the Euler angles and associated conjugate momenta are obtained as functions of canonical constants and time.
The effects of earthquakes on the rotational motion of the earth were studied. The connection between the fault parameters and the corresponding changes in the moments and products of inertia were analytically developed. The reciprocal theorem of elasticity and Volterra's formula were applied as well as the displacement and stress fields for the second degree static response of the earth model being used. The numerical results of the investigation yield the magnitude and direction of the pole shift as well as the change in the length of the day. The changes in the second degree coefficients of the geopotential were computed. Source parameters corresponding to the Alaskan earthquake on March 28, 1964 were used to generate numerical results.
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Two Apollo Soyuz experiments designed to detect gravity anomalies from spacecraft motion are described. The geodynamics experiment (MA-128) measured large-scale gravity anomalies by detecting small accelerations of Apollo in the 222 km orbit, using Doppler tracking from the ATS-6 satellite. Experiment MA-089 measured 300 km anomalies on the earth's surface by detecting minute changes in the separation between Apollo and the docking module. Topics discussed in relation to these experiments include the Doppler effect, gravimeters, and the discovery of mascons on the moon.
The interpretation of gravity is valuable for understanding lithospheric plate motion and mantle convection. Postulated models of anomalous mass distributions in the earth and the observed geopotential as expressed in the spherical harmonic expansion are compared. In particular, models of the anomalous density as a function of radius are found which can closely match the average magnitude of the spherical harmonic coefficients of a degree. These models include: (1) a two-component model consisting of an anomalous layer at 200 km depth (below the earth's surface) and at 1500 km depth (2) a two-component model where the upper component is distributed in the region between 1000 and 2800 km depth, and(3) a model with density anomalies which continuously increase with depth more than an order of magnitude.
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Seasonal and latitude dependent corrections to the gravity and height anomalies are developed in order to account for the neglect of the atmospheric masses outside the geoid, when using Stokes' equation. It is shown that the atmospheric correction to gravity at sea level is almost constant, equal to 0.871 mgals with a variation of 2 microgals whereas the height anomaly correction varies between -0.1 cm and -1.3 cm. Further, when the combined latitudinal/seasonal dependence is neglected in the atmospheric corrections, the maximum error introduced is on the order of 40 microgals for the gravity corrections and 0.7 cm for the height anomaly corrections.
The effect of post-Newtonian potentials on the rotation of a nearly rigid body is shown to consist of a precession and a torque. The frequency of the precession can be exactly represented by means of suitable differential operators. The relativistic torques in the quadrupole approximation depend on the instantaneous orientation of the principal axes of one body with respect to the position like the classical torque and velocity of the other. For a relatively low mass body, such as a gyroscope, these velocity-dependent torques have no observable consequences.
The tectonic forces or stresses due to the small scale mantle flow under the South American plate are detected and determined by utilizing the harmonics of the geopotential field model. The high degree harmonics are assumed to describe the small scale mantle convection patterns. The input data used in the derivation of this model is made up of 840,000 optical, electronic, and laser observations and 1,656 5 deg x 5 deg mean free air anomalies. Although there remain some statistically questionable aspects of the high degree harmonics, it seems appropriate now to explore their implications for the tectonic forces or stress field under the crust.
The effect of post-Newtonian potentials on the rotation of a perfect fluid, nearly rigid body is shown to consist of a precession and a torque. The frequency of the precession can be exactly represented by means of suitable differential operators. The relativistic torques, in the quadrupole approximation, depend on the instantaneous orientation of the principal axes of one body with respect to the position - like the classical torque - and velocity of the other. For a relatively low-mass body, such as a gyroscope, these velocity-dependent torques have no observable consequences.
An analytic method is described by means of which the preferred planes into which gas will settle by dissipative differential precession in a slightly nonspherical, nonstatic potential can be determined. Attention is given to the analysis of circular orbit precession in the external potential of a slightly prolate spheroidal mass that is tumbling about a short axis, providing a crude model for barred spiral galaxies as well as for prolate elliptical ones. The results obtained agree with previous work on the existence, orientation, and stability of periodic orbits in triaxial potentials. Depending on the source and injection geometry of the gas and on the nature of dissipation in the gas, the orbital dynamics presented could lead to enhanced, or even catastrophic, radial inflow and to steady state warped structures.
A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modelled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.
A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later Shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modeled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.
The Al-In-Sn alloys were directionally solidified in the NASA KC-135 aircraft which flies a series of parabolas to generate high (high-g) and low (low-g) gravity forces parallel to the longitudinal growth axis. Thus, for a given sample, successive sections can be identified which were solidified in high-g and low-g. Measurements of the electronic properties of the samples reveal that: the resistivity of the low-g sections is larger (about a factor of 10) than that of the high-g sections; the low-g sections behave conductively like a semi-metal, while the high-g sections are essentially metallic; and both high-g and low-g sections are superconducting but the superconducting transition temperature of the low-g sections is 1 K higher than that of the high-g sections.
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The Al-In-Sn alloys were directionally solidified in the NASA KC-135 aircraft which flies a series of parabolas to generate high (high-g) and low (low-g) gravity forces parallel to the longitudinal growth axis. Thus, for a given sample, successive sections can be identified which were solidified in high-g and low-g. Measurements of the electronic properties of the samples reveal that: the resistivity of the low-g sections is larger (about a factor of 10) than that of the high-g sections; the low-g sections behave conductively like a semi-metal, while the high-g sections are essentially metallic; and both high-g and low-g sections are superconducting but the superconducting transition temperature of the low-g sections is 1 K higher than that of the high-g sections.
The evolution of two miscible liquids meeting at an initially sharp interface inside a cavity under microgravity g-jitter conditions is studied numerically. The response of the interface and kinematics of the flowfield to various g-jitter accelerations and aspect ratio variations is shown. The interface region acts like a vortex source sheet, and it can be unstable to Kelvin-Helmholtz and Rayleigh-Taylor instabilities. The vortices produced along the interface can serve as a stirring mechanism to promote local mixing. Below the critical Stokes-Reynolds number, the destabilization of the interface results in deformation into wavy structures. In some parameter regions, these structures oscillate in time; in others, they are quasi-steady. Above the critical Stokes-Reynolds number, 'chaotic' instability results, and the interface breaks into concentration pockets. The morphology of the initial breakup is similar to observed Rayleigh-Taylor instability. Subsequent mixing of the two fluids after the breakup of the interface is then very rapid.
Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.