Ptolemy gives the interval of time between the beginning of his epoch and the ancient observation from our last post as $518$ Egyptian years, $133 \\frac{1}{4}$ days.<\/p>\n
Taking this to the Planetary mean motion tables, I find an increase in longitude of 216;08,26\u00ba. Toomer notes that Ptolemy’s value has some uncertainty to it. Many of the Greek manuscripts have $216\u00ba$ or $216;00\u00ba$. However, some have $216;09\u00ba$ which would be consistent with how Ptolemy tends to round. However, Toomer takes Ptolemy to have meant $216;10\u00ba$ as this is the value implied by a calculation we’ll do shortly.<\/p>\n
Turning to the anomaly, I find an increase of $149;15,26\u00ba$ which is consistent with Ptolemy’s value of $149;15\u00ba.$<\/p>\n
These now get subtracted from the positions from the Babylonian astronomers observation. As a reminder, in the last post, we determined that Saturn was $2;53\u00ba$ into Virgo, and $183;17\u00ba$ about its epicycle from the apogee of the epicycle.<\/p>\n
Thus, for longitude, if we subtract using the value of $216;10\u00ba$ that Toomer proposes, I find that Saturn would have been $26;43\u00ba$ into Capricorn which is the value Ptolemy gives and is found in all manuscripts, affirming that Toomer’s value for the increase in longitude over this interval is likely what Ptolemy intended, even if it is a bit rounded.<\/p>\n
For the anomaly, I find that Saturn would have been $34;02\u00ba$ about its epicycle from apogee.<\/p>\n
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