Astronomy and Astrophysics – Astronomy
Scientific paper
May 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006ahes...60..269m&link_type=abstract
Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 60, No. 3, p. 269 - 283 (2006)
Astronomy and Astrophysics
Astronomy
History Of Astronomy, Moon: Angular Velocities, Lunar Tables
Scientific paper
The problem addressed in this paper is an accurate determination of the apparent extreme angular velocities of the Moon as observed from the Earth. For the historical analysis of lunar motion in general an exact knowledge of the extreme lunar velocities seems indispensable. Though the need is selfevident, only crude numerical estimates are to be found even in modern times and the general problem does not seem to have ever been studied using advanced mathematical procedures. We shall demonstrate below our determination following Goldstine's computational procedures, limiting however our mathematical descriptions to a minimum. And thus it may be said that all the lunar velocities to be obtained from the Goldstine Tables, as well as from those of P. V. Neugebauer, Tuckerman, Hunger/Dvorak and Gingerich/Welther and others, are bounded by our three sets of two extreme quantities, instantaneous but expressed in (°/d), which we will determine firstly in the orbit, secondly in the ecliptic, and thirdly for the variation of the lunar elongation from the Sun. We shall then give a simple computational formula for deriving the basic structure of the lunar velocities as well as a practical demonstration of the agreement of our computations with the Goldstine and Tuckerman Tables.
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