Abstract
In order to obtain accurate computed values of Earth-based range and Doppler observables of a beep space probe, an expression is required for the time differencet−τ, wheret is coordinate time in the solar system barycentric space-time frame of reference and τ is proper time recorded on a fixed atomic clock on earth. This paper is part 1 of a two-part article which obtains an expression fort−τ which is suitable for use in obtaining computed values of observations of a spacecraft or celestial body located anywhere in the solar system. The expression can also be used in the computation of Very Long Baseline Interferometry data types. Part 1 obtains an expression fort−τ which is a function of position and velocity vectors of the major celestial bodies of the solar system and the atomic clock on Earth which reads τ. In Part 2, this expression will be transformed to a function of time and the Earth-fixed coordinates of the atomic clock.
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References
Aoki, S.: 1964, ‘Note on Variability of the Time Standard due to the Relativistic Effect’,Astron. J. 69, 221–223.
Clemence, G. M. and Szebehely, V.: 1967, ‘Annual Variation of an Atomic Clock’,Astron. J. 72, 1324–1326.
de Sitter, W.: 1916, ‘On Einstein's Theory of Gravitation and its Astronomical Consequences’,Monthly Notices Roy. Astron. Soc. 76, 699–728 and77, 155–184.
Eddington, A. and Clark, G. L.: 1938, ‘The Problem ofn Bodies in General Relativity Theory’,Proc. Roy. Soc. London, Ser. A. 166, 465–475.
H.M. Stationery Office: 1961,Explanatory Supplement to the Ephemeris, London.
Infeld, L. and Plebański, J.: 1960,Motion and Relativity, Pergamon Press, Oxford, New York.
Mechtly, E. A.: 1969,The International System of Units, Physical Constants and Conversion Factors, Revised, NASA SP-7012, p. 4.
Misner, C. W., Thorne, K. S. and Wheeler, J. A.: 1973,Gravitation, W. H. Freeman and Co., San Francisco.
Moyer, T. D.: 1965, ‘Relativistic equations of motion’, M.S. Thesis, University of California, Los Angeles, p. 66.
Moyer, T. D.: 1971,Mathematical Formulation of the Double Precision Orbit Determination Program (DPODP), Jet Propulsion Laboratory, Technical Report 32-1527.
Newcomb, S.: 1898, ‘Tables of the four inner planets’,Astron. Papers Am. Ephem. 6, 13–16.
Robertson, D. S.: 1975,Geodetic and Astrometric Measurements with Very-Long-Baseline Interferometry, Goddard Space Flight Center, X-922-77-228.
Seidelmann, P. K., Doggett, L. E. and De Luccia, M. R.: 1974, ‘Mean Elements of the Principal Planets’,Astron. J. 79, 57–60.
Standish, E. M. Jr., Keesey, M. S. W., and Newhall, X X.: 1976,JPL Development Ephemeris Number 96, Jet Propulsion Laboratory, TR 32-1603, p. 30.
Thomas, J. B.: 1975, ‘Reformulation of the Relativistic Conversion between Coordinate Time and Atomic Time’,Astron. J. 80, 405–411.
Winkler, G. M. R. and Van Flandern T. C.: 1977, ‘Ephemeris Time, Relativity, and the Problem of Uniform Time in Astronomy’,Astron. J. 82, 84–92.
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Moyer, T.D. Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference. Celestial Mechanics 23, 33–56 (1981). https://doi.org/10.1007/BF01228543
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DOI: https://doi.org/10.1007/BF01228543