Astronomisches Rechen-Institut Heidelberg

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ARI-Heidelberg Veröffentlichungen, No. 21

Author(s): Zech, G.
Title: The Determination of the Mass of the Earth + Moon System by the Dynamical Method from Observations of Eros
Source: Veröffentlichungen des Astronomischen Rechen-Instituts Heidelberg, Nr. 21, Verlag G. Braun, Karlsruhe, 36 Seiten
Year: 1968
Abstract: Doubt about the reliability of previous determinations of the mass of the earth+moon system by the dynamical method has arisen from determinations of the astronomical unit with the help of radar echos from the planet Venus. The results of the radar method have led to the adoption of a new value of the astronomical unit in the I.A.U. System of Astronomical Constants: 1 a. u. = 149 600 000 km. This value corresponds to a mass of the earth+moon system of 1/mE+M = 328 912, while the determination carried out by RABE (1950) from the motion of the minor planet(433) Eros yielded the value 1/mE+M = 328 452 +/- 64(m.e.). The object of this work, begun in 1965, is to clear up the considerable discrepancy between these mass values. Examinations of RABE's (1950) least squares solution have led to the following conclusions: (1) The right-hand sides of the system of normal equations, as published, are incorrect. (2) The solutions for the unknowns are not rigorously reproducible; the occuring differences are small. (3) The mean errors of the unknowns are not correct. Analysis of the influence of the masses of Mercury, Venus, and Mars and of the earth's orbital elements on the determination of the mass of the earth+moon system shows that the value yielded for the mass of earth+moon is not essentially different if various plausible values for the earth's orbital elements are prescribed. Different values for the mass of Mars that were introduced show that the resulting earth+moon mass depends sensitively on the adopted mass of Mars. An independent new determination of the mass of the earth+moon system in connection with an improvement of the orbit of Eros has been carried out by numerical integration with the Heidel- berg N-Body program, and has yielded 1/mE+M = 328 894 +/- 30(m.e.). This value agrees very well with the result obtained from the radar echos. The earlier incorrect result of the dynamical method is explained as a consequence of an incorrect calculation of the coefficients for the corrections to the planetary masses in RABE's (1950) equations of condition. The newest determination by the radar method by ASH et al. (1967) confirms the reliability of the dynamical method in the determination of the mass of the earth+moon system.
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