Computer Science – Numerical Analysis
Scientific paper
Feb 1966
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1966saosr.200.....l&link_type=abstract
SAO Special Report #200 (1966)
Computer Science
Numerical Analysis
10
Scientific paper
This report was presented as a culmination of the massive effort to determine a set of constants defining the size, shape, and gravitational field of the earth. The first purpose of these three volumes is a comprehensive exposition of the data and techniques used to obtain the adopted standard parameters. The second purpose is the interpretation and elaboration of these data in conventional geodetic format. The primary instrument of the program was the Baker-Nunn satellite tracking camera used by 12 basic tracking stations around the world. This optical system provides an F/1 Schmidt-type instrument with a field of view of some 30° covered by a narrow film that can be changed automatically and rapidly. A dual-shutter system permits the time to be measured by breaks in the trails of either satellites or background stars with an accuracy of 0.001 sec. The first volume deals with theory and methods. It describes how the harmonic coefficients of the earth's gravitational field were evaluated, how a reference system for satellite observations was established, how data were processed, and how results of two different observing techniques were combined for increased accuracy. The second volume proceeds to a numerical analysis of observations; the results of the undertaking are interpreted in the third volume. The principal geodetic parameters adopted at SAO are simply a set of Cartesian coordinates for instrument positions at observing stations and a set of coefficients for a representation of the earth's gravitational potential in spherical harmonics. Both sets are expressed in an orthogonal geocentric coordinate system with its z axis through the mean pole of 1900-1905 as defined by the International Polar Motion Service and with its x axis implicity determined by the defined latitude of the U.S. Naval Observatory, to which tabulations of Universal Time correspond. This coordinate system, fixed in the earth, is related to celestial directions through the expressions and data given by the international services monitoring the motion of the earth. The star positions in the SAO Star Catalog imply the celestial coordinates. Finally, the distance scale comes from the adopted value for GM, the multiplicative constant in the geopotential representation. Results from orbital dynamics are combined with geometrical information in the form of directions between stations. The combination calculation gives a further improved set of station coordinates and harmonic coefficients. These new values go back into the differential orbit improvement program, and new orbital elements subsequently result. This cycle of calculations continues until significant changes cease to occur and the process is judged to have converged. The adopted standard coordinates for the 12 SAO stations were those from the final combination calculation. The standard tesseral harmonic coefficients were derived from a determination of these coefficients alone because the number of unknowns was limited by the computer program and because freezing station positions in the final step allowed a solution for more geopotential coefficients. Volume 3 includes discussions of datum displacement, the deflection of the vertical, and the unification of precise astrogeodetic maps. A comparison of coordinates with the Jet Propulsion Laboratory DSIF stations was another interesting calculation. The agreement between JPL and SAO position data is very satisfying, and because the systems and methods are totally independent, this constitutes a strong verification of the accuracy of both systems. Together, the coordinates of the BakerNunn instruments in their respective survey datum and in the SAO standard system imply relationships between the various datums. The number of station sites in any major datum, is, of course, small, but nevertheless the derived relations between datums appear reasonable. As an indication of the quality of the standard geopotential, a comparison with surface--gravity information is useful. Another test of the geopotential is its value in determining orbits of satellites other than those from which it was derived. Experience with such determinations has been good, and the orbits for new satellites are essentially as accurate as those for corresponding satellites used in the standard solution.
Lundquist Charles A.
Veis George
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