Earth's gravity field to the sixteenth degree and station coordinates from satellite and terrestrial data
Earth gravity field and satellite tracking stations positions geodetic parameters in geocentric reference frame
Gaposchkin, E. M.↗
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Resonance spectra of a paramagnetic probe dissolved in a viscous medium
A model is presented for calculating the paramagnetic resonance (EPR) spectrum of vanadyl acetylacetonate (VAAC) dissolved in either a liquid crystal or isotropic solvent. It employs density matrix formulation in the rotating reference frame. The molecules occupy several discrete angles with respect to the magnetic field and can relax to neighboring positions in a characteristic time tau(theta). The form of tau(theta) is found from a diffusion approach, and the magnitude of tau(theta) is a measure of how freely the VAAC probe tumbles in the solvent. Spectra are predicted for values of tau between 10 to the minus 11th power sec and 10 to the minus 7th power sec. The EPR spectrum, in the isotropic case, is obtained be summing the contributions from the allowed angles weighted by the polar volume element, sin theta. When applying the model to the nematic liquid crystal case it is also necessary to multiply by the Saupe distribution function. For this case tau(theta) is obtained from the diffusion approach in which two diffusion constants are employed to reflect the difference in the parallel and perpendicular components of the viscosity.
Kaplan, J. I.↗
Resonance spectra of a paramagnetic probe dissolved in a viscous medium.
The paramagnetic resonance spectrum of Vanadyl acetylacetonate (VAAC) dissolved in either a liquid crystal or isotropic solvent is calculated with the aid of a presented model. Density matrix formulation is employed in the rotating reference frame. The molecules occupy several discrete angles with respect to the magnetic field and can relax to neighboring positions in a characteristic time. The form of this characteristic time is found from a diffusion approach, and the magnitude of this time is a measure of how freely the VAAC probe tumbles in the solvent. Spectra are predicted for time values ranging from 10 picoseconds to 10 microseconds.
Kaplan, J. I.↗
A method for calculating laminar viscous, compressible flows with small pressure gradients
A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.
Martin, E. D.↗
Space shuttle guidance, navigation and control equation document no. 19: Prelaunch alignment and platform compensation
The prelaunch-alignment program which aligns the stable platform to some desired orientation with respect to the local navigation reference frame is discussed. The alignment progresses in three distinct phases: coarse aligning, leveling, and gyrocompassing. While the program is in the leveling or gyrocompassing phase, a new launch azimuth may be specified without reinitiating the program. At liftoff, control is passed to a navigation monitor/control program. A description of the stable-platform-compensation program is included. The programs and equations given are similar to those used for Apollo.
Gallagher, J. L.↗
Interplanetary gas. XVIII - Models and the mean free path of protons at 1 astronomical unit.
Velocity distribution functions of solar-wind protons obtained by the Vela 3 satellites have been analyzed to obtain a microscopic determination of the momentum flux along magnetic field lines with respect to a reference frame moving at the bulk speed. The determination from macroscopic parameters allows the calculation of an effective mean free path for protons at 1 AU which averages 0.06 AU and is relatively independent of solar-wind velocity w. For quiet times when w is from 300 to 400 km/sec, the experimental mean free path is 2 to 3 times smaller than the value from plasma theory. For w greater than 400 km/sec, the experimental value is 10 to 100 times smaller than the theoretical value.
Brandt, J. C.↗
A method for determining the preferred orientation of crystallites normal to a surface
Techniques representing the angular distribution of a particular direction in a crystallographic reference frame or analytical methods were developed. The data required by these techniques for displaying preferred orientation is obtained by measuring the orientation of a large number of crystallites. This may be done visually using etch-pit or Laue techniques which, experimentally, are both tedious and difficult. The intensities of X ray diffraction maxima are proportional to the number of crystallites whose crystallographic plane normals bisect the incident and diffracted beams. Parameters used in calculating powder patterns are also presented.
Snyder, R. L.↗
Earth's gravity field to the eighteenth degree and geocentric coordinates for 104 stations from satellite and terrestrial data
Geodetic parameters describing the earth's gravity field and the positions of satellite-tracking stations in a geocentric reference frame were computed. These parameters were estimated by means of a combination of five different types of data: routine and simultaneous satellite observations, observations of deep-space probes, measurements of terrestrial gravity, and surface-triangulation data. The combination gives better parameters than does any subset of data types. The dynamic solution used precision-reduced Baker-Nunn observations and laser range data of 25 satellites. Data from the 49-station National Oceanic and Atmospheric Administration BC-4 network, the 19-station Smithsonian Astrophysical Observatory Baker-Nunn network, and independent camera stations were employed in the geometrical solution. Data from the tracking of deep-space probes were converted to relative longitudes and distances to the earth's axis of rotation of the tracking stations. Surface-gravity data in the form of 550-km squares were derived from 19,328 1 deg X 1 deg mean gravity anomalies.
Gaposchkin, E. M.↗
A finite element solution algorithm for the Navier-Stokes equations
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.
Baker, A. J.↗
Theory of a ring laser
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Menegozzi, L. N.↗
Satellite attitude control simulations
Work was conducted to develop an extremely low drift rate gyroscope and a very precise star tracker. A proposed relativity satellite will measure very accurately the theoretically predicted 'relativistic' precession of the gyroscope relative to an inertial reference frame provided by the star tracker. Aspects of precision spinning attitude control are discussed together with questions of gyro operation, and the hopping mode for lunar transportation. For the attitude control system of the lunar hopper, a number of control laws were investigated. The studies indicated that some suboptimal controls should be adequate for the system.
Debra, D. B.↗
Finite elasto-plastic deformation. I - Theory and numerical examples
It is demonstrated that the problem of elasto-plastic finite deformation is governed by a quasi-linear model irrespective of deformation magnitude. This feature follows from the adoption of a rate viewpoint toward finite deformation analysis in an Eulerian reference frame. Objectivity of the formulation is preserved by introduction of a frame-invariant stress rate. Equations for piece-wise linear incremental finite element analysis are developed by application of the Galerkin method to the instantaneously linear governing differential equations of the quasi-linear model. Numerical solution capability has been established for problems of plane strain and plane stress. The accuracy of the numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation admitting comparative analytic solution. It is shown that accurate, objective numerical solutions can be obtained for problems involving dimensional changes of an order of magnitude and rotations of a full radian.
Osias, J. R.↗
Earth's gravity field to the eighteenth degree and geocentric coordinates for 104 stations from satellite and terrestrial data
Geodetic parameters describing the earth's gravity field and the positions of satellite-tracking stations in a geocentric reference frame have been computed. These parameters were estimated by means of a combination of five different types of data: routine and simultaneous satellite observations, observations of deep space probes, measurements of terrestrial gravity, and surface triangulation data. The combination gives better parameters than does any subset of data types. The dynamic solution used precision-reduced Baker-Nunn observations and laser range data of 25 satellites. Data from the 49-station National Oceanic and Atmospheric Administration BC-4 network, the 19-station Smithsonian Astrophysical Observatory Baker-Nunn network, and independent camera stations were employed in the geometrical solution.
Gaposchkin, E. M.↗
Absolute plate motions by boundary velocity minimizations
The main interaction of the earth's interior with the lithosphere is as a material source and sink. An absolute reference frame defined by minimizing the translational motion of tectonic plate boundaries differs by 0.6 cm/year from a frame defined by hot spot traces and by 0.4 cm/year from the frame defined by the most plausible model of drag forces on the plates. The rms absolute translational velocities are about 2 cm/year for ocean-ocean plate boundaries and 1.5 cm/year for ocean-continent plate boundaries. The close agreement between the source and sink and the drag-dependent definitions suggests that the lithosphere, as a stress guide, to some extent controls the locations of its sources and sinks.
Kaula, W. M.↗
Numerical simulation of interacting, three-dimensional vortex filaments
Unsteady three-dimensional fluid flows which are characterized by low viscosity and the presence of distinct regions of high vorticity embedded in an otherwise irrotational flow are considered, taking into account the case in which an intermingling of vortex filaments appears. Incompressible flows of the considered type are simulated with the aid of an approach in which the vorticity distribution is modeled in terms of continuous closed filaments. It is attempted to track these filaments in a Lagrangian reference frame.
Leonard, A.↗
ALSEP: Quasar differential VLBI
A program of Apollo Lunar Surface Experiments Package (ALSEP)-Quasar Very Long Baseline Interferometry (VLBI) is being reported. These observations primarily employ a 4 antenna technique, whereby simultaneous observations with two antennas at each end of an intercontinental baseline are used to derive the differential interferometric phase between a compact extragalactic radio source (usually a quasar) and a number of ALSEP transmitters on the lunar surface. A continous ALSEP-quasar differential phase history over a few hour period leads to extremely high angular accuracy in measuring the lunar position against the quasar reference frame. This application of the 4 antenna technique has been underway for more than a year and is now producing high quality data utilizing Deep Space Network (DSN) stations in Australia, Spain, and Goldstone, California, as well as the Spaceflight Tracking and Data Network (STDN) Apollo station at Goldstone.
Slade, M. A.↗
Disturbing effects of attitude control maneuvers on the orbital motion of the Helios spacecraft
The position of the spin axis of the Helios A spacecraft has been maintained and updated by a series of attitude control maneuvers, by means of a sequence of unbalanced jet forces which produce an additional disturbed motion of the spacecraft's center of mass. The character of this motion, its magnitude and direction was studied. For practical purposes of the orbit determination of the spacecraft, a computer program is given which shows how the components of the disturbing acceleration in the spacecraft-fixed reference frame can be easily computed.
Georgevic, R. M.↗
A demonstration of an independent-station radio interferometry system with 4-cm precision on a 16-km base line
Radio interferometry promises eventually to measure directly, with accuracies of a few centimeters, both whole earth motions and relative crustal motions with respect to an 'inertial' reference frame. Interferometry measurements of arbitrarily long base lines require, however, the development of new techniques for independent-station observation. In connection with the development of such techniques, a series of short base line demonstration experiments has been conducted between two antennas. The experiments were related to a program involving the design of independent-station instrumentation capable of making three-dimensional earth-fixed base line measurements with an accuracy of a few centimeters. Attention is given to the instrumentation used in the experiments, aspects of data analysis, and the experimental results.
Thomas, J. B.↗