Abstract
Until very recently, there has been no identification of the significant gravitational constraints on the many common artificial earth satellite orbits in shallow resonance. Without them it is difficult to compare results derived for different sets of harmonics from different orbits. With them it is possible to extend these results to any degree without reintegration of the orbits. All such constraints are shown to be harmonic in the argument of perigee with constants determinable from tracking data:
The constants are simple linear combinations of geopotential harmonics. Five such constants (lumped harmonics) have been derived for the GEOS-2 orbit (order 13, to 30th degree) whose principal resonant period is 6 days. These five lumped harmonics are shown to account for almost all (>98%) of the resonant information in the tracking. They agree well with recent gravitational models which include substantial amounts of GEOS-2 data.
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References
Allan, R. R.: (1973),Planetary Space Sci.,21, 205–225.
Douglas, B. C. and Marsh, J. G.: 1970,Celest. Mech. 1, 479–490.
Gaposchkin, E. M. and Lambeck, K.: 1970, ‘1969 Smithsonian Standard Earth II’, SAO Special Report 315.
Gaposchkin, E. M.: 1973, ‘1973 Smithsonian Standard Earth III’, SAO Special Report 353.
Garfinkel, B.: (1965),Astron. J. 70, 784–786.
Gedeon, G. S.: 1969,Celest. Mech. 1, 167–189.
Kaula, W. M.: 1966,Theory of Satellite Geodesy, Blaisdell Press, Waltham, Mass.
Klosko, S. M. and Krabill, W. B.: Bulletin Geodesique, No. 114, 387–408.
Koch, K. R. and Witte, B. U.: 1971,JGR,76, 8471–8479.
Lerch, F. J.et al.: 1972, ‘Gravitational Field Models of the Earth (GEM-1 and 2)’, GSFC Document X-553-72-146.
Lerch, F. J., Wagner, C. A., Putney, B. H., Sandson, M. L., Brownd, J. E., Richardson, J. A., and Taylor, W. A.: 1972, ‘Gravitational Field Models GEM-3 and 4’, GSFC Document X592-72-476.
Lerch, F. J., Wagner, C. A., Richardson, J. A., and Brownd, J. E.; 1974, ‘Goddard Earth Models (5 and 6)’, NASA-GSFC Document X-921-74-145, Greenbelt, Md.
Lerch, F. J.: 1974, private communication for PGS62.
Marsh, J. G., Douglas, B. C., and Klosko, S. M.: 1975, ‘A Global Station Coordinate Solution Based Upon Camera and Laser Data: GSFC 1973’, The Use of Artificial Satellites for Geodesy and Geodynamics, Athens, Greece.
Martin, C. F.: 1970, ‘Mathematical Description of the Error Analysis of Satellite to Satellite Tracking Program’, WOLF Contract Report to NASA/GSFC for Contract NAS 5-11736 MOD 3.
Martin, C. F. and Roy, N. A.: 1972, ‘Error Model for the SAO 1969 Standard Earth’, The uses of Artificial Satellites for Geodesy, AGU Monograph.
Martin, T. V.: 1972, ‘GEODYN Systems Operation Description’, WOLF Final Report on Contract NAS 5-11736-129.
Rapp, R. H.: 1967, ‘The Geopotential to (14, 14) from a Combination of Satellite and Gravimetrle Data’, Presented at the XIV General Assembly International Union of Geodesy and Geophysics, Lucerne, Switzerland.
Riegber, C. H.: 1973,Space Res. 13, 3–10.
Riegler, C. H.: 1974, ‘Bestimmungsgleichungen für Resonanzparameter der Ordnung 13 aus der Analyse Von Bahnen der Satelliten GEOS-B, BEC und D10’, Deutsche Geodatische Kommission, Reihe C, Haft 198.
Reigber, C. H. and Ilk, K. N.: 1975, ‘Vergleich von Resonanzparameterbestimmungen mitteis Ausgbeichung und Kollokation’, Mittellung Nr. 119 des Instituts für Astronomische und Physikahsche Geodasle der Technischen Universität München, Munich, West Germany.
Smith, D. E., Lerch, F. J., and Wagner, C. A.: 1973,Space Res. 13, 11–20.
Wagner, C. A. and Douglas, B. C.: 1969,Planetary Space Sci. 17, 1505–1517.
Wagner, C. A., Lerch, F. J., Brownd, J. E. and Richardson, J. A.: 1977, ‘Improvement in the Geopotential Derived from Satellite and Surface Data (GEM-7 and 8)’, JGR,82, 901–914.
Yionoulis, S. M.: 1968, ‘Improved Coefficients of the Thirteenth-Order Harmonics of the Geopotential Derived from Satellite Doppler Data at Three Different Orbital Inclinations’, APL Report TG-1003.
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Wagner, C.A., Klosko, S.M. Gravitational harmonics from shallow resonant orbits. Celestial Mechanics 16, 143–163 (1977). https://doi.org/10.1007/BF01228597
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DOI: https://doi.org/10.1007/BF01228597