# Browsing by Subject "Gravitational fields"

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Item A comparison of range and range-rate based GRACE gravity field solutions(2011-05) Pasupathy, Muthukumar; Tapley, Byron D.; Poole, Steven Ross, 1954-Show more In the generation of the standard GRACE gravity fields, the K-Band Ranging (KBR) system data is used in its range-rate mode. Because time derivatives attenuate the gravity signal relative to the data noise at the lower frequencies, it is thought that solutions using range data might have better low-degree (low-frequency) characteristics. The purpose of this work is to detail the methods required to generate range-based solutions, to determine some of the properties of these solutions and then to compare them to range-rate based solutions. It is demonstrated that the range-based solutions are feasible. Different subarc lengths and parameterizations were considered. Although, the most effective combination of subarc lengths and parameterizations are not picked, it is concluded that estimating the mixed periodic term along with bias, bias-rate, bias-acceleration and periodic terms degrades the quality of the range based solution and therefore should not be used. Further study is necessary to pick the optimal combination of subarc length and parameterization which would be used in the time-series analysis.Show more Item Computational methods and processing strategies for estimating Earth's gravity field(2004) Gunter, Brian Christopher; Tapley, Byron D.Show more The focus of this study was to observe and characterize the behavior of certain types of errors present in the gravity field model estimation process, as they relate to fields created from the recently launched Gravity Recovery and Climate Experiment (GRACE). The instruments and configuration of the GRACE satellites are different from any other previously flown gravity mission, so the impact that these error sources have on the GRACE gravity solutions is not fully understood. The high resolution gravity perturbations detectable by GRACE also mean that many of these errors can only be fully explored through the use of high spherical harmonic degree and order solutions. When this study first began, a software estimation tool did not exist that was capable of handling the extremely large problem sizes that the GRACE mission can create. To address this issue, a parallel application called the Advanced Equation Solver for Parallel Systems (AESoP) was developed that was designed to accommodate the computational requirements of GRACE. An outline of the functionality and methodologies employed by AESoP is provided, as well as detailed descriptions of the parallel algorithms created as part of its development. Using this new software tool, several types of errors inherent to the GRACE gravity field estimation process were analyzed. Investigations into the errors of omission and commission were performed using both real and simulated GRACE data. Additional studies into the combination of the GPS and inter-satellite ranging measurements were also conducted in an attempt to maximize the contribution of each data type as well as to improve processing efficiency. The results of these studies outline several processing strategies by which many of the error sources investigated can be significantly reduced while simultaneously decreasing the processing time and disk storage requirements by roughly 75% for an average GRACE solution.Show more Item Light deflection and time delay in the solar gravitational field(1983) Richter, Gary William; Matzner, Richard A. (Richard Alfred), 1942-Show more The second nonvanishing order of contribution to light deflection and time delay in the solar gravitational field is studied for a realistic solar model and for a wide range of metric theories of gravity. It is shown that the second-order effects arise at order (GM/c²R)² = ε⁴. To calculate these effects, every component of the solar metric must be known to order ε⁴. The parametrized post Newtonian (PPN) metric provides most of those components. However, some extension of the PPN metric is required. This extension leads to the parametrized post-linear (PPL) metric, which is used in all calculations. To study light deflection to order ε⁴ requires that the orbits of scattered photons be known to that order. These orbits are solved for, first in the equatorial plane and then in general, and are used to determine the deflection as measured by an observer at rest with respect to the sun. In the equatorial plane there is only a radial component to this deflection. In general, there is another component orthogonal to the radial plane, but knowledge of this component is not necessary to determine the total deflection to order ε⁴. The total second-order deflection can be as large as 300 μ arcsec (for deflection by Jupiter). Measurements of some second-order terms are within the astrometric capabilities of experiments proposed for the 1990's. The time delay in the round-trip travel time of a radar beam reflected from a planet is due to the variable coordinate speed of the light signal and to the bending of the beam path. The delay is calculated to order ε⁴ . It is shown that the beam-bending gives a second-order contribution as large as the present-day uncertainties in time delay experiments with the Viking spacecraft. Polarization changes in light waves propagating through the solar gravitational field are also studied to order ε⁴Show more Item A numerical study of relativistic fluid collapse(2003) Noble, Scott Charles; Morrison, Philip J.; Choptuik, Matthew WilliamShow more We investigate the dynamics of self-gravitating, spherically-symmetric distributions of fluid through numerical means. In particular, systems involving neutron star models driven far from equilibrium in the strong-field regime of general relativity are studied. Hydrostatic solutions of Einstein’s equations using a stiff, polytropic equation of state are used for the stellar models. Even though the assumption of spherical symmetry simplifies Einstein’s equations a great deal, the hydrodynamic equations of motion coupled to the time-dependent geometry still represent a set of highly-coupled, nonlinear partial differential equations that can only be solved with computational methods. Further, many of the scenarios we examine involve highly-relativistic flows that require improvements upon previously published methods to simulate. Most importantly, with techniques such as those used and developed in this thesis, there is still considerable physics to be extracted from simulations of perfect fluid collapse, even in spherical symmetry. Here our particular focus is on the physical behavior of the coupled fluid-gravitational system at the threshold of black hole formation—so-called black hole critical phenomena. To investigate such phenomena starting from conditions representing stable stars, we must drive the star far from its initial stable configuration. We use one of two different mechanisms to do this: setting the initial velocity profile of the star to be in-going, or collapsing a shell of massless scalar field onto the star. Both of these approaches give rise to a large range of dynamical scenarios that the star may follow. These scenarios have been extensively surveyed by using different initial star solutions, and by varying either the magnitude of the velocity profile or the amplitude of the scalar field pulse. In addition to illuminating the critical phenomena associated with the fluid collapse, the resulting phase diagram of possible outcomes provides an approximate picture of the stability of neutron stars to large, external perturbations that may occur in nature. Black hole threshold, or critical, solutions, occur in in two varieties: Type I and Type II. Generically, a Type I solution is either static or periodic and exhibits a finite black hole mass at threshold, whereas a Type II solution is generally either discretely or continuously self-similar and characterized by infinitesimal black hole mass at threshold. We find both types of critical behavior in our space of star solutions. The Type I critical solutions we find are perturbed equilibrium solutions with masses slightly larger than their progenitors. In contrast, the Type II solutions are continuously self-similar solutions that strongly resemble those found previously in ultra-relativistic perfect fluids. The boundary between these two types of critical solutions is also discussed.Show more Item On the application of quantum perturbation theory to gravitational interactions(1950) DeWitt, Bryce S. (Bryce Seligman), 1923-2004Show more Part 1: The formalism preliminary to a quantum perturbation treatment of the interaction of wave fields with gravitation is here developed. Since spinor fields are of importance, a resumé is given of Pauli’s treatment of spinors in general coordinates, involving the introduction of generalized Dirac operators. The essential points of the Einstein-Mie theory are outlined, and spin angular momentum is discussed from the general coordinate viewpoint with the aid of the generalized orthogonal group. The commutation law for covariant differentiation is obtained for arbitrary fields. The symmetric stress tensor can be constructed either from the canonical energy-momentum tensor together with the spin angular momentum tensor or directly through variation of the metric tensor. The concepts of energy, momentum and spin angular momentum, and hence the Hamiltonian formalism itself, can be introduced for the gravitational field only with respect to a "background space" which has a flat metric of no physical geometrical significance. In the background space only Lorentz transformations have immediate invariant significance, and general coordinate transformations appear as "gauge transformations" in the gravitational and accompanying matter fields. Only the total integrated energy, momentum and spin angular momentum quantities are invariant under these “gauge transformations.”Show more