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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

Shebalin, John V.↗
NASA NTRS1980

Equivalent source modeling of the main field using MAGSAT data

The software was considerably enhanced to accommodate a more comprehensive examination of data available for field modeling using the equivalent sources method by (1) implementing a dynamic core allocation capability into the software system for the automatic dimensioning of the normal matrix; (2) implementing a time dependent model for the dipoles; (3) incorporating the capability to input specialized data formats in a fashion similar to models in spherical harmonics; and (4) implementing the optional ability to simultaneously estimate observatory anomaly biases where annual means data is utilized. The time dependence capability was demonstrated by estimating a component model of 21 deg resolution using the 14 day MAGSAT data set of Goddard's MGST (12/80). The equivalent source model reproduced both the constant and the secular variation found in MGST (12/80).

Source record↗
NASA NTRS1973

Mars gravity derived from the long-period motion of Mariner 9

The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-

Ferrari, A. J.↗
NASA NTRS2013

Covariance Analysis Tool (G-CAT) for Computing Ascent, Descent, and Landing Errors

G-CAT is a covariance analysis tool that enables fast and accurate computation of error ellipses for descent, landing, ascent, and rendezvous scenarios, and quantifies knowledge error contributions needed for error budgeting purposes. Because GCAT supports hardware/system trade studies in spacecraft and mission design, it is useful in both early and late mission/ proposal phases where Monte Carlo simulation capability is not mature, Monte Carlo simulation takes too long to run, and/or there is a need to perform multiple parametric system design trades that would require an unwieldy number of Monte Carlo runs. G-CAT is formulated as a variable-order square-root linearized Kalman filter (LKF), typically using over 120 filter states. An important property of G-CAT is that it is based on a 6-DOF (degrees of freedom) formulation that completely captures the combined effects of both attitude and translation errors on the propagated trajectories. This ensures its accuracy for guidance, navigation, and control (GN&C) analysis. G-CAT provides the desired fast turnaround analysis needed for error budgeting in support of mission concept formulations, design trade studies, and proposal development efforts. The main usefulness of a covariance analysis tool such as G-CAT is its ability to calculate the performance envelope directly from a single run. This is in sharp contrast to running thousands of simulations to obtain similar information using Monte Carlo methods. It does this by propagating the "statistics" of the overall design, rather than simulating individual trajectories. G-CAT supports applications to lunar, planetary, and small body missions. It characterizes onboard knowledge propagation errors associated with inertial measurement unit (IMU) errors (gyro and accelerometer), gravity errors/dispersions (spherical harmonics, masscons), and radar errors (multiple altimeter beams, multiple Doppler velocimeter beams). G-CAT is a standalone MATLAB- based tool intended to run on any engineer's desktop computer.

Boussalis, Dhemetrios↗
NASA NTRS1989

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction: An attempt of global numerical computations

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.

Wang, Y. M.↗
NASA NTRS1981

Some new methods in geomagnetic field modeling applied to the 1960 - 1980 epoch

The utilization of satellite and surface data together permitted the incorporation of a solution for the anomaly field at each observatory. The residuals of the observatory measurements to such models is commensurate with the actual measurment accuracy. Incorporation of the anomaly estimation enabled the inclusion of stable time derivatives of the spherical harmonic coefficients up to the third derivative. A spherical harmonic model is derived with degree and order 13 in its constant and first time derivative terms, six in its second derivative terms and four in its third derivative terms.

Langel, R. A.↗
NASA NTRS1994

Venus spherical harmonic gravity model to degree and order 60

The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.

Konopliv, Alex S.↗
NASA NTRS1963

The World Magnetic Survey

The mathematical and graphical description of the earth's main field has been, and is, a "data limited" problem. The World Magnetic Survey (WMS) is an endeavor to minimize this limitation by rapidly and comprehensively blanketing the earth with magnetic field measurements. Satellite surveys, which will play a key role in the W MS, are the principal topic of this paper. Existing magnetic field descriptions, the expected results from new surveys, and the methods of obtaining these results with the POGO satellite are emphasized. It is anticipated on the basis of extrapolation from Vanguard 3 results and other considerations that a factor of 10 improvement will be obtained. This means that the average errors of 1 to 3 percent now present in field charts and spherical harmonic descriptions should be reduced to 0.1 to 0.3 percent as a result of the survey.

MATHEMATICS↗
NASA NTRS1973

Geodesic synchrotron radiation

This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.

Breuer, R. A.↗
NASA NTRS2010

Seismic Constraints on Interior Solar Convection

We constrain the velocity spectral distribution of global-scale solar convective cells at depth using techniques of local helioseismology. We calibrate the sensitivity of helioseismic waves to large-scale convective cells in the interior by analyzing simulations of waves propagating through a velocity snapshot of global solar convection via methods of time-distance helioseismology. Applying identical analysis techniques to observations of the Sun, we are able to bound from above the magnitudes of solar convective cells as a function of spatial convective scale. We find that convection at a depth of r/R(solar) = 0.95 with spatial extent l < 30, where l is the spherical harmonic degree, comprise weak flow systems, on the order of 15 m/s or less. Convective features deeper than r/R(solar) = 0.95 are more difficult to image due to the rapidly decreasing sensitivity of helioseismic waves.

Hanasoge, Shravan M.↗
NASA NTRS2023

The Impact of New Accelerometer Transplant Data (ACH) on GRACE Follow-On Along-Orbit Inter-Satellite Laser Ranging Observations and Monthly Time-Variable Gravity and Mascon Solutions

GRACE-D accelerometer data show significant bias jumps since one month after the launch of the GRACE Follow-On (GRACE-FO) satellites in May 2018, making them inapplicable for correcting GRACE-FO products for non-gravitational accelerations. The GRACE-FO Science Data System (SDS) compensated this issue by transplanting the GRACE-C accelerometer data toward that of GRACE-D. Recently, GRACE-FO SDS implemented an updated transplant method, used in the latest release of GRACE-FO data. Here, we examine the impact of updated accelerometer transplant data (ACH) on GRACE-FO measurements at all levels: (a) Level-1B inter-satellite laser ranging residuals measured along satellite orbit, (b) Level-2 time-variable gravity solutions from all SDS centers (JPL, CSR, and GFZ), and (c) Level-3 mascon solutions. We show that inter-satellite laser ranging residuals are modified at low frequencies below 1 mHz, affecting the along-orbit analysis of large-scale time-variable gravity signals. When mapped into monthly Level-2 spherical harmonic coefficients of geopotential, the low-frequency change in inter-satellite ranging residuals leads to substantial improvement of coefficients associated with resonant orders (i.e., 15, 30, 45, etc.) and C 30 . We also present an improved SLR-derived C 30 which significantly improves the agreement with updated GRACE-FO C 30 at seasonal and interannual timescales. Moreover, we demonstrate the noise reduction in mass change estimates from new GRACE-FO Level-2 data over oceans, Greenland, and Antarctica for all SDS solutions. GRACE-FO mascon solutions show a moderate change in the updated release. Our comprehensive analyses demonstrate high-quality estimates of non-gravitational accelerations by the updated transplant method, resulting in more accurate GRACE-FO time-variable gravity and mass change observations.

Laser ranging interferometer↗
NASA NTRS1978

Incompressible fluid ellipsoids in halos. I - The second-harmonic oscillations of the Maclaurin spheroids

The structure and stability of Maclaurin spheroids embedded in rigid uniform-density oblate spheroidal halos are determined by the tensor virial-equation method. These spheroid-halo systems can be thought of as crude fluid analogs of disk galaxies with halos. The halos are assumed to have the same center, the same axis of symmetry, and the same equatorial radius as the Maclaurin spheroids. Only halos with lower eccentricity than the Maclaurin spheroids are considered. The dynamic instability of the toroidal (barlike) modes is suppressed when m, the ratio of the halo mass to Maclaurin spheroid mass, is greater than 3 pi/8 for spherical halos and when m is greater than 1/2 for halos congruent to the Maclaurin spheroids. Intermediate halo flattenings yield intermediate critical m-values. On the other hand, a neutral point of the toroidal modes in the rotating and inertial frames occurs for all m and for all allowed halo flattenings. Growth rates for secular instability beyond the neutral point are calculated, and the eigenfrequencies of all second-harmonic modes are given for select cases. The Ostriker-Peebles (1973) conjecture concerning the stability of disk galaxies against barlike perturbations appears to be incorrect.

Durisen, R. H.↗
NASA NTRS1983

Geomagnetism of earth's core

Instrumentation, analytical methods, and research goals for understanding the behavior and source of geophysical magnetism are reviewed. Magsat, launched in 1979, collected global magnetometer data and identified the main terrestrial magnetic fields. The data has been treated by representing the curl-free field in terms of a scalar potential which is decomposed into a truncated series of spherical harmonics. Solutions to the Laplace equation then extend the field upward or downward from the measurement level through intervening spaces with no source. Further research is necessary on the interaction between harmonics of various spatial scales. Attempts are also being made to analytically model the main field and its secular variation at the core-mantle boundary. Work is also being done on characterizing the core structure, composition, thermodynamics, energetics, and formation, as well as designing a new Magsat or a tethered satellite to be flown on the Shuttle.

Benton, E. R.↗
NASA NTRS2004

Narrow Scale Flow and a Weak Field by the Top of Earth's Core: Evidence from Orsted, Magsat and Secular Variation

As Earth's main magnetic field weakens, our magnetic shield against the onslaught of the solar wind thins. And the field strength needed to fend off battering by solar coronal mass ejections is decreasing, just when the delicate complexity of modem, vulnerable, electro-technological systems is increasing at an unprecedented rate. Recently, a working group of distinguished scientist from across the nation has asked NASA's Solid Earth and Natural Hazards program a key question: What are the dynamics of Earth s magnetic field and its interactions with the Earth system? Paleomagnetic studies of crustal rocks magnetized in the geologic past reveal that polarity reversals have occurred many times during Earth s history. Networked super-computer simulations of core field and flow, including effects of gravitational, pressure, rotational Coriolis, magnetic and viscous forces, suggest how this might happen in detail. And space-based measurements of the real, time-varying magnetic field help constrain estimates of the speed and direction of fluid iron flowing near the top of the core and enable tests of some hypotheses about such flow. Now scientists at NASA s Goddard Space Flight Center have developed and applied methods to test the hypotheses of narrow scale flow and of a dynamically weak magnetic field near the top of Earth s core. Using two completely different methods, C. V. Voorhies has shown these hypotheses lead to specific theoretical forms for the "spectrum" of Earth s main magnetic field and the spectrum of its rate of change. Much as solar physicists use a prism to separate sunlight into its spectrum, from long wavelength red to short wavelength blue light, geophysicists use a digital prism, spherical harmonic analysis, to separate the measured geomagnetic field into its spectrum, from long to short wavelength fields. They do this for the rate of change of the field as well.

Voorhies, Coerte V.↗
NASA NTRS1977

Ion sheath effects on RF plasma probes - Experimental results in laboratory plasmas

Laboratory work dealing with the frequency characteristic of the plasma impedance of spherical and cylindrical electrode systems is reported. The influence of the ion sheath on various features of the impedance characteristic is emphasized. Those features are the series and parallel resonance as well as additional resonances due to the excitation of electroacoustic and cyclotron harmonic waves. The dependence of the series and parallel resonances on dc biasing leads to a method of determining the ion sheath capacity for a cylindrical electrode system. The obtained values agree fairly well with those obtained from a theoretical model for the density and potential distribution in the sheath of a cylindrical sensor aligned with a supersonic plasma flow. The amplitude of resonances due to excitation of longitudinal plasma waves (electroacoustic and cyclotron harmonic) is reduced or even vanishes for sufficiently negative dc bias. Positive bias first leads to an increased amplitude up to a certain dc bias value above which, however, the amplitude decreases again due to electron absorption at the sensor surface.

Kist, R.↗
NASA NTRS2000

Retrieving the Balanced Winds on the Globe as a Generalized Inverse Problem

A generalized inverse technique is applied to retrieve two types of balanced winds that characterize the large-scale dynamics of the atmosphere: rotational winds based upon the linear balance equation, and divergent winds based upon the vorticity budget equation. Both balance equations are singular at or near the equator. The balance equations are transformed in spherical harmonic function space to an under-determined system, for which the scale-weighed least-squares solution consists of a sum of principal and singular components. The principal components represent the response to the source function for the regular eigenmodes, while the singular components are determined by the projection of an independent measurement on the singular eigenmodes. The method was tested with the NCEP/NCAR reanalysis data in which a quasi-balance condition exists. A realistic balanced wind field is retrievable when the singular components are computed based upon the reanalyzed wind data.

Lu, Huei-Iin↗
NASA NTRS2013

A T Matrix Method Based upon Scalar Basis Functions

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

wave functions↗
NASA NTRS1981

A method of defining topographic datums of planetary bodies

Since no known planetary bodies in the solar system other than the earth have large bodies of water, a topographical datum other than a sea-level reference must be used as a zero-elevation reference surface. The present paper discusses the definition of the topographic datums of Mars and the moon in terms of a gravity-level surface. Planetary gravitational field potentials were represented by a spherical harmonic expansion in terms of gravity coefficients measured by planetary orbiters, and the topographical datum was taken as the sum of an arbitrarily selected radius of the mean sphere and the radial deviation from the mean sphere. The datum defined for Mars on the basis of Mariner 9 data can be approximated as a triaxial ellipsoid with semimajor axes of 3394.6 and 3393.3 km and semiminor axis of 3376.3 km, based on a mean radius of 3382.9 km. For the moon, Lunar Orbiter IV tracking and ranging data give a datum approximated by a triaxial figure with semimajor axes 1738.30 and 1738.18 km and semiminor axis 1737.65 km, based on a mean radius of 1738 km. A topographic datum of Venus is also planned based on Pioneer-Venus gravity data.

Wu, S. S. C.↗