Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-18T19:26:21.863Z Has data issue: false hasContentIssue false

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

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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