The gravitational influence of Jupiter on the Ptolemaic value for the eccentricity of Saturn

Archive for History of Exact Sciences 75 (4):439-454 (2021)
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Abstract

The gravitational influence of Jupiter on Saturn produces, among other things, non-negligible changes in the eccentricity of Saturn that affect the magnitude of error of Ptolemaic astronomy. The value that Ptolemy obtained for the eccentricity of Saturn is a good approximation of the real eccentricity—including the perturbation of Jupiter—that Saturn had during the time of Ptolemy's planetary observations or a bit earlier. Therefore, it seems more probable that the observations used for obtaining the eccentricity of Saturn were done near Ptolemy’s time, and rather unlikely earlier than the first century AD. Even if this is not quite a demonstration that Ptolemy used observations of his own, my argument increases its probability and practically discards the idea that Ptolemy borrowed values or observations from astronomers further back than the first century AD, such as Hipparchus or the Babylonians.

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References found in this work

The Arabic Version of Ptolemy's Planetary Hypotheses.G. J. Toomer & Bernard R. Goldstein - 1970 - Journal of the American Oriental Society 90 (2):296.
Ptolemaic planetary models and Kepler’s laws.Gonzalo L. Recio & Christián C. Carman - 2019 - Archive for History of Exact Sciences 73 (1):39-124.
Ptolemy.J. Feke & A. Jones - 2010 - In Lloyd Gerson (ed.), The Cambridge History of Philosophy in Late Antiquity. Cambridge, UK: Cambridge University Press. pp. 197-209.
Ptolemy’s Treatment of the Outer Planets.Dennis Duke - 2005 - Archive for History of Exact Sciences 59 (2):169-187.
Mean Motions in Ptolemy’s Planetary Hypotheses.Dennis Duke - 2009 - Archive for History of Exact Sciences 63 (6).

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