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Some remarks on the paper by B. G. Marsden “An attempt to reconcile the dynamical and radar determinations of the Astronomical Unit”

Published online by Cambridge University Press:  14 August 2015

Eugene Rabe*
Affiliation:
University of Cincinnati Observatory.

Extract

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While Marsden's solution C leaves residuals with the relatively small [vv] of 13.73, it should be realized that this representation of the observations of Eros does not satisfy the fundamental principle of the least squares method, in so far as the associated value of [vv] is not a minimum with respect to small arbitrary deviations from solution C. As a matter of fact, there is an infinite number of “solutions” with [vv] between the 13.73 of Marsden's solution C and the 8.66 of his solution A, each of these being associated with a certain arbitrarily prescribed value of the mass of Mars and with a related mass of Earth + Moon. Of this infinite series of solutions, only solution A is a least squares solution in the true sense, with a minimum value of [vv]. This can be seen and verified as follows.

Type
Research Article
Copyright
Copyright © CNRS 1965