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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.
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.
Metric theories of gravity are presented, including the definition of metric theory, evidence for its existence, and response of matter to gravity with test body trajectories, gravitational red shift, and stressed matter responses. Parametrized post-Newtonian framework and interpretations are reviewed. Gamma, beta and gamma, and varied other parameters were measured. Deflection of electromagnetic waves, radar time delay, geodetic gyroscope precession, perihelion shifts, and periodic effects in orbits are among various studies carried out for metric theory experimentation.
Gyroscopes in motion about a massive body are found to have two main effects: (1) geodetic effect, solely due to motion of the gyroscope about the earth and (2) motional effect, due to earth rotation. An experiment is proposed to measure the precession rate of one or more gyroscopes, mounted either on earth or in a satellite, with respect to the axis of a telescope pointing at a suitable fixed star. The procedures and apparatus to be used in this experiment are outlined; the error analysis is summarized. The relation of error to size, speed, and mechanical properties of rotor is presented, along with the design requirements for accuracy of 10 to the -16th power rad/s.
A brief discussion of the actual laser tracking performance of geodetic satellites is followed by a discussion of the errors inherent in the laser system. An estimate is made of the capability expected within the next few years for the tracking of a heliocentric probe. The GEOS 1, GRARR, and GEOS 2 systems are considered. Errors in the tracking of a heliocentric probe are noted. These include errors due to the earth's atmosphere, (beam bending, atmospheric absorption, atmospheric turbulence, and atmospheric distortion of short laser pulses), and errors due to coronal effects.
An experiment is proposed to test a first generation spacecraft-borne radar altimeter's capability to measure the topography of the sea surface. The initial radar altimeter will have an instrumental error of one meter and an overall accuracy to two to five meters. This instrument will thus improve the accuracy of the geoid from the present 10 to 20 meters to better than 5 meters. In order to detect storm surges, tidal forces, and ocean currents, an altimeter with an overall accuracy of at least ?1 meter will be required. The overall accuracy of the initial radar altimeter will thus primarily provide geodetic information and possible oceanographic information such as sea state.
The analytic formulations at different elevation angles and at a frequency of 2-GHz for the ionospheric refraction corrections used on the GEOS satellite tracking data are compared. The formulas and ray trace results for elevations greater than 10 deg, where most satellite tracking is done, differ in elevation, range, and range rate by less than 0.4 millidegrees (1.4 arc-seconds), 12 meters, and 12 cm/sec, respectively. In comparison to most operational requirements, this is insignificant. However, for the GEOS Observation Systems Intercomparison Investigation, these differences are equivalent in size to observed differences in system biases for some of the best electronic geodetic tracking systems and are probably contributing to the observed biases. The ray trace results and most of the more detailed analytic correction formulas show that the ionospheric refraction correction for range rate on an overhead pass is a maximum for elevation angles between 15 deg and 30 deg and falls off rapidly for both higher and lower elevation angles, contrary to the effect of the troposphere and to some reports in the literature.
Radio astronomy programs comprise three very-long-baseline interferometer projects, ten spectral line investigations, one continuum mapping in the 0.8 cm region, and one monitoring of variable sources. A low-noise mixer was used in mapping observations of 3C273 at 31 GHz and in detecting of a new methyl alcohol line at 36,169 MHz in Sgr B2. The new Mark 2 VLBI recording terminal was used in galactic H2O source observations using Haystack and the Crimean Observatory, USSR. One feature in W29 appears to have a diameter of 0.3 millisec of arc and a brightness temperature of 1.4 x 10 to the 15th power K. Geodetic baseline measurements via VLBI between Green Bank and Haystack are mutually consistent within a few meters. Radar investigations of Mercury, Venus, Mars, and the Moon have continued. The favorable opposition of Mars and improvements in the radar permit measurements on a number of topographic features with unprecedented accuracy, including scarps and crater walls. The floor of Mare Serenitatis slopes upward towards the northeast and is also the location of a strong gravitational anomaly.
Experimental investigations of the percent polarization of sunlight reflected from the surfaces of each of the Echo 2 Satellite and PAGEOS (Passive Geodetic Earth Orbiting Satellite) were performed to determine the stability of their surfaces in the space environment. The Echo 2 surface material was amorphous phosphate chemically bonded to a rolled aluminum substrate while the PAGEOS 1 surface material is vapor deposited aluminum on a poly (ethylene terephthalate) film. The stability of the satellites' surfaces was analyzed by comparing the light polarizing properties of the satellites, to those of test surfaces representative of the satellites' surfaces. The properties of flat test surfaces were measured experimentally in the laboratory, and the effects of surface strain, surface geometry, and vacuum upon these properties were examined. The laboratory analyses revealed that the polarization properties of the Echo 2 surface were significantly affected by surface geometry and vacuum, and that the properties of the PAGEOS 1 surface were not significantly altered by any of the above mechanisms.
The objective of the program is to collect a set of homogeneous and well distributed precise laser and camera satellite observations for the purpose of dynamic and geometric geodesy. The data gathering portion of the experiment extended from December 15, 1970 to August 31, 1971 and consisted of seven three-week saturation tracking periods. The seven geodetic satellites tracked were BE-B, BE-C, GEOS-1, GEOS-2, DI-C, DI-D, and PEOLE. The techniques employed to generate acquisition data for the two lasers are described. Analyses of the quick-look Astrosoviet NAFA-25 camera data indicated that the accuracy of these data was on the order of a few minutes of arc. These data were useful in definitive orbit determination.
Laser and minitrack observational data from GEOS-2 collected during the period April 23, 1971 to May 1971, have been used for the purpose of assessing the influence of tracking station location on the accuracy of orbit determination. These data were processed using a unified set of coordinates for the tracking station locations. Concurrently, these data were processed using nonunified station locations referred to a variety of geodetic datums. The resultant orbits based on the two different sets of station locations were compared and relative differences in the position of the satellite were determined. Differences between the two groups of orbits fitted over four-day data spans ranged from 250 meters to 500 meters for orbits derived from laser data only. For orbits observed from Minitrack data alone the relative differences in GEOS-2 spacecraft position ranged from 50 meters to 190 meters. Utilizing the laser data alone in each arc, definitive orbits were computed using the unified and nonunified station location coordinates. The differences in the satellite position in the overlap region when using the unified laser station coordinates ranged from 25 meters to 150 meters, whereas when using the nonunified laser station coordinates the differences in position ranges from 180 to 650 meters.
A satellite time synchronization technique has been used for synchronization of remotely separated clocks during the past several years. The NASA network has been successfully synchronized to an accuracy of tens of microseconds via the NASA Geodetic Earth Orbiting Satellite GEOS-11. The results indicate that a polar orbit satellite having an onboard clock can effectively be used to synchronize clocks on a global basis.
Current work related to geodetic altimetry is summarized. Special emphasis is placed on the effects of pulse length on both altimetry and sea-state estimation. Some discussion is also given of system tradeoff parameters and sea truth requirements to support scattering studies. The problem of analyzing signal characteristics and altimeter waveforms arising from rough surface backscattering is also considered.
Basic features of sea surface topography are reviewed, to show those oceanographic results which may be of value to a geodetic satellite program: (1) the shape and magnitude of the large scale features of the mean sea surface, relative to a level surface; (2) the position and magnitude of the slopes across the western boundary currents, from a variety of data; (3) an estimate of the position of the geoid, tied into the U.S. leveling network; and (4) a documented change of 60 to 70 cm in mean sea level, with respect to the geoid, between the U.S. east and west coasts.
The effect of omitting the parallactic refraction correction for satellite optical observations in the determination of station coordinates is analyzed for a large satellite data distribution. A significant error effect is seen in station heights. A geodetic satellite data distribution of 23 close earth satellites, containing 30,000 optical observations obtained by 13 principal Baker-Nunn camera sites, is employed. This distribution was used in a preliminary Goddard Earth Model (GEM 1) for the determination of the gravity field of the earth and geocentric tracking station locations. The parallactic refraction correction is modeled as an error on the above satellite data and a least squares adjustment for station locations is obtained for each of the 13 Baker-Nunn sites. Results show an average station height shift of +8 meters with a dispersion of plus or minus 0.7 meters for individual sites. Station latitude and longitude shifts amounted to less than a meter. Similar results are obtained from a theoretical method employing a probability distribution for the satellite optical observations.
The basic purpose of this experiment was to compute reduced normal equations from the observational data of several different systems described below to combine them eventually with the normal equations of the Wild BC-4 observations taken in the DOD/DOC cooperative worldwide geodetic satellite program and provide station coordinates from a single least squares adjustment. The solution described is a partial one obtained without the use of the BC-4 data. The observational systems combined were the Baker-Nunn simultaneous camera observational systems combined were the Baker-Nunn simultaneous camera observations from the SAO worldwide network, the MOTS and PC-1000 optical observations in North America, miscellaneous camera observations in Europe which were included in the SAO69 solution, and, lastly, a group of optical observations where Baker-Nunn cameras observed simultaneously with MOTS and/or PC-1000 cameras in the previously mentioned group.
One of the secondary objectives of the GEOS-2 C-band Systems Project is to study the feasibility of using geodetic satellites to both evaluate shipborne instrumentation and to determine ship positions in broad ocean areas. The purpose of this task is to determine whether shipborne C-band radar tracking, in conjunction with ground based tracking, is sufficiently accurate to provide instrumentation evaluation and ship position estimates. Data from several Apollo tracking ships, in particular the USNS Vanguard, was made available for this effort. A series of tests, using the USNS Vanguard, were carried out in the Port Canaveral and Bahama Acoustic Transponder Array Areas. The major portion of the analyses reported are the result of preliminary investigations using the data from these tests.
The material presented covers the general topic of C-band radars and their use throughout the GEOS-2 C-band Radar System Project and has direct application to the general problem of gathering accurate radar tracking data. The material is hardware oriented and all analyses and evaluations described pertain to the gathering of accurate data rather than to the application of the gathered data. The radar oriented investigations formed a basic and necessary part of the overall C-band experiment. The successful completion of these efforts led to the definition of how the radars were to be operated and calibrated. These hardware decisions directly affected the quality of the radar data and therefore played a large part in the successful application of these data to geodetic research.