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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Geometric field-line calculations

Procedure for calculating three components of vector field from spherical harmonic using either geocentric or geodetic coordinates as input and output is described. Three subroutines of computer program are explained. Program is written in FORTRAN for IBM 360 computer.

Stassinopoulos, E. G.↗
NASA NTRS1971

Preliminary Goddard geopotential using optical tracking data and a comparison with SAO models

A preliminary Goddard Space Flight Center (GSFC) geopotential and center of mass station coordinate solution was obtained from satellite orbital data using numerical integration theory. This geodetic solution is a prelude to a more general solution which will combine the 1971 International Satellite Geodesy Experiment (ISAGEX) laser data with the present data being employed. The present GSFC geopotential solution consists of the spherical harmonic coefficients through degree and order eight with higher order satellite resonant coefficients. The solution represents a first iteration result from 17 satellites with approximately 150 weekly orbital arcs containing some 40,000 optical observations. The GSFC preliminary result is compared with final results from the Smithsonian Astrophysical Observatory (SAO) solutions including the 1969 SAO Standard Earth II solution. One aspect of interest for the comparison is that SAO uses an analytic theory for the orbital solution whereas GSFC uses a numerical integration theory. The comparison of geopotential results shows that good agreement exists in general but that there are some areas of minor differences.

Lerch, F. J.↗
NASA NTRS1971

Lunar gravity derived from long-period satellite motion, a proposed method

A method was devised to determine the spherical harmonic coefficients of the lunar gravity field. The method consists of a two-step data reduction and estimation process. Pseudo-Doppler data were generated simulating two different lunar orbits. The analysis included the perturbing effects of the L1 lunar gravity field, the earth, the sun, and solar radiation pressure. Orbit determinations were performed on these data and long-period orbital elements were obtained. The Kepler element rates from these solutions were used to recover L1 lunar gravity coefficients. Overall results of the experiment show that lunar gravity coefficients can be accurately determined and that the method is dynamically consistent with long-period perturbation theory.

Ferrari, A. J.↗
NASA NTRS1971

An Empirical Method for Determining the Lunar Gravity Field

A method has been devised to determine the spherical harmonic coefficients of the lunar gravity field. This method consists of a two-step data reduction and estimation process. In the first step, a weighted least-squares empirical orbit determination scheme is applied to Doppler tracking data from lunar orbits to estimate long-period Kepler elements and rates. Each of the Kepler elements is represented by an independent function of time. The long-period perturbing effects of the earth, sun, and solar radiation are explicitly modeled in this scheme. Kepler element variations estimated by this empirical processor are ascribed to the non-central lunar gravitation features. Doppler data are reduced in this manner for as many orbits as are available. In the second step, the Kepler element rates are used as input to a second least-squares processor that estimates lunar gravity coefficients using the long-period Lagrange perturbation equations.

Ferrari, A. J.↗
NASA NTRS1972

On the determination of the long period tidal perturbations in the elements of artificial earth satellites

The magnitude of the tidal effects depends upon the elastic properties of the earth as described by Love numbers. The Love numbers appear as the coefficients in the expansion of the exterior tidal potential in terms of spherical harmonics (in Maxwellian form). A single averaging process was performed only along the parallels of latitude. This process preserves additional long period tidal effects (with periods of a few days or more). It also eliminates the short period effects with periods of one day or less.

Musen, P.↗
NASA NTRS1972

Gravitational field models for the earth (GEM 1 and 2)

Two models of the earth's gravitational field have been computed at Goddard Space Flight Center. The first, Goddard Earth Model 1 (GEM 1), has been derived from satellite tracking data. The second, Goddard Earth Model 2 (GEM 2), has been derived from a combination of satellite tracking and surface gravimetric data. The geopotential models are represented in spherical harmonics complete to degree and order 16 for the combined solution and complete to degree and order 12 for the satellite solution. Both solutions include zonal terms to degree 21 and related satellite resonant coefficients to degree 22. The satellite data consisted primarily of optical data processed on 300 weekly orbital arcs for 25 close earth satellites. Surface gravity data were employed in the form of 5 deg x 5 deg mean free-air gravity anomalies providing about 70% world coverage. Station locations were obtained for 46 tracking sites by combining electronic, laser, and additional optical tracking data with the above satellite data. Analysis of the radial positions of these stations and a value of mean gravity on the geoid indicated a mean equatorial radius for the earth of about 6378145 meters. Results of geopotential tests on satellite data not used in the solution show that better agreement was obtained with the GEM 1 and GEM 2 models than with the 1969 Smithsonian Standard Earth 2 model.

Lerch, F. J.↗
NASA NTRS1971

Cosmic-ray variations and the interplanetary sector structures.

Fifteen passages of interplanetary sector structures that occurred between December 1967 and June 1968 are examined. A spherical harmonic analysis of cosmic ray intensity is performed to obtain cosmic ray intensity variations as a function of asymptotic latitude, longitude, and universal time. A clear north-south asymmetry of cosmic ray intensity, which depends on the sign of the interplanetary sector magnetic fields, is revealed.

Yoshida, S.↗
NASA NTRS1971

New half-range differential approximation for spherically-symmetric radiative transfer.

A new half-range differential approximation for radiative transfer with spherical symmetry is presented. The development is motivated by the various failures of existing differential approximations in determining emissive-power distributions and heat transfer for concentric-spheres problems. The new approach represents a modification of the four-moment double spherical-harmonics method, to which it reduces in the planar limit. The difference is effected by relocating the discontinuity of the assumed directional distribution of radiation intensity. The shift takes the discontinuity from precisely on the division between radially inward and radially outward, to just within the radially-outward directional half range. The method is tested on a variety of concentric spheres problems with and without internal heat sources, reproducing all the important features of the exact results.

Moreno, J. B.↗
NASA NTRS1971

Representation of the earth's gravitational potential.

The paper represents the earth's gravitational potential V, outside a sphere bounding the earth, by means of its difference from the author's spheroidal potential. The difference is in turn represented as arising from a surface density on the sphere bounding the earth. Because of the slow decrease with order n of the normalized coefficients in the spherical harmonic expansion of V, the density anomalies from which the higher coefficients arise must occur in regions close to the earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thickness. Values of surface density are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of surface density and for its contour map. The numerical values obtained for surface density are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cu cm, and occur in the crust alone.

Vinti, J. P.↗
NASA NTRS1972

The configuration of the geomagnetic field.

Spherical harmonic representations of the geomagnetic field based on ground-based and low-altitude spacecraft measurements adequately describe the field within several earth radii of the earth's surface. As the internal field decreases with increasing distance from the earth, external field sources become relatively more important. In the region of 3 to 6 earth radii, magnetospheric plasma inflates the field lines and decreases the field strength by an amount which is typically 10's of gammas and occasionally 100's of gammas. At greater distances on the day side of the earth, the solar wind compresses the field and produces equatorial field strengths of approximately 60 gammas at 10 earth radii. Field lines near the magnetopause intersect the earth at approximately 78 deg latitude in the sunward hemisphere. The solar wind drags high latitude field lines away from the earth in the night hemisphere forming the geomagnetic tail and neutral sheet. Asymmetric field inflation in the magnetosphere occurs during magnetic disturbances with the largest effects concentrated in the evening quadrant. The tail configuration can deviate substantially from the average configuration during magnetic disturbances.

Fairfield, D. H.↗
NASA NTRS1971

Semiannual variations in the neutral composition.

Meteor trail observations of the meridional mesospheric wind field are analyzed in terms of spherical harmonics, showing a predominance in the P3 term for the semiannual component. This suggests two heat sources for the semiannual variations. One that peaks at the equator is associated with the semiannual migration of the sun between the two hemispheres. A second heat input of greater magnitude that peaks at high latitudes is presumably related to auroral heating associated with the semiannual component in the occurrence of magnetic storms. The wind circulation, consistent with these sources, is shown to cause a semiannual redistribution of the minor constituent O in the lower thermosphere with the effects of decreasing the ratios of O/N2 and O/O2 at high latitudes and of enhancing these ratios at mid to low latitudes during equinox.

Mayr, H. G.↗
NASA NTRS1972

Recent results on the mass, gravitational field and moments of inertia of the moon.

Use of Doppler tracking data from the Lunar Orbiter series of spacecraft in an analysis of the spherical harmonic coefficients of the lunar gravitational field through thirteenth degree and order. The value obtained for the mass of the moon, GM = 4902.84 cu km/sec/sec, is in good agreement with previous results and with results obtained by alternate procedures. Acceleration contour plots, derived from the gravitational coefficients, show correlations with surface features on the near side of the moon, but are of questionable validity for the far side because of the lack of direct tracking data on the far side. Based on the most recent gravitational field data, the current estimate for the polar moment of inertia of the moon is C/Ma squared = 0.4019 super + 0.004 sub - 0.002. This value indicates that the interior of the moon can be homogeneous, but some results presented strongly suggest that the moon is differentiated, with an excess of mass in the direction toward the earth.

Michael, W. H., Jr.↗