NDLI: Mean Motions in Ptolemy’s Planetary Hypotheses

Content Provider	Springer Nature Link
Author	Duke, Dennis
Copyright Year	2009
Abstract	In the Planetary Hypotheses, Ptolemy summarizes the planetary models that he discusses in great detail in the Almagest, but he changes the mean motions to account for more prolonged comparison of observations. He gives the mean motions in two different forms: first, in terms of ‘simple, unmixed’ periods and next, in terms of ‘particular, complex’ periods, which are approximations to linear combinations of the simple periods. As a consequence, all of the epoch values for the Moon and the planets are different at era Philip. This is in part a consequence of the changes in the mean motions and in part due to changes in Ptolemy’s time in the anomaly, but not the longitude or latitude, of the Moon, the mean longitude of Saturn and Jupiter, but not Mars, and the anomaly of Venus and Mercury, the former a large change, the latter a small one. The pattern of parameter changes we see suggests that the analyses that yielded the Planetary Hypotheses parameters were not the elegant trio analyses of the Almagest but some sort of serial determinations of the parameters based on sequences of independent observations.
Starting Page	635
Ending Page	654
Page Count	20
File Format	PDF
ISSN	00039519
Journal	Archive for History of Exact Sciences
Volume Number	63
Issue Number	6
e-ISSN	14320657
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-07-04
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Astronomy, Observations and Techniques Physics Mathematics History of Science Philosophy of Science History of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics History and Philosophy of Science

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