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Almagest Book XI: Jupiter’s Eccentricity

Now that we have established the periodic motion, anomalies, and epochs of the planet Mars, we shall next deal with those of Jupiter in the same way.

It certainly strikes me that splitting up the planets between books is an odd choice on Ptolemy’s part, but at least the methods will be familiar. As Ptolemy tells us:

Once again, we first take, to demonstrate [the position on] the apogee and [the ratio of] the eccentricity, three oppositions [in which Jupiter is] directly opposite the mean sun.

This will be directly paralleling the work we did in X.7-10 for Mars. So bring on the observations! Continue reading “Almagest Book XI: Jupiter’s Eccentricity”

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Almagest Book X: Correction to the Periodic Motions

Back in IX.3, Ptolemy noted that the planetary periods

have been corrected by us, on the basis of the comparison of their positions which became possible after we had demonstrated their anomalies, as we shall explain at that point.

As a reminder, what he was telling us then, was that he had made corrections to the periods provided to him by Hipparchus. We’ll now go over those corrections for Mars. Continue reading “Almagest Book X: Correction to the Periodic Motions”

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Almagest Book X: Second Iteration Correction for Equant – Third Opposition

We’re now ready to make the correction for the third opposition in this second iteration. And the good news is that this is the last time we’ll need to calculate a correction.

Ptolemy still does a third iteration which relies on these corrections, but since he won’t be doing a fourth iteration, further corrections aren’t necessary. So let’s get to it. Continue reading “Almagest Book X: Second Iteration Correction for Equant – Third Opposition”

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Almagest Book X: Second Iteration for Mars – Part 2

Continuing on with our second iteration in which we calculate the revised line of apsides and eccentricity of Mars’ model.

As with before, I’m doing my calculations in a Google Sheet to make it easier to correct should I make an error. This also means that the Sheet will be keeping much higher precision to prevent rounding errors. However, as I’m only showing rounded values, things may look a bit off. So if something seems funny, I encourage checking out the aforementioned Sheet. Continue reading “Almagest Book X: Second Iteration for Mars – Part 2”