Tag: lunar period of anomaly

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Almagest Book IV: Correction of the Mean Motions of the Moon in Longitude and Anomaly

Towards the beginning of Book IV, Ptolemy went through the methodology by which the various motions in the lunar mean motion table could be calculated. But if you were paying extra close attention, you may have noticed that the values that ended up in the mean motion table didn’t actually match what we derived. Specifically, for the daily increment in anomaly, we derived $13;3,53,56,29,38,38^{\frac{º}{day}}$. But in the table, we magically ended up with $13;3,53,56,17,51,59^{\frac{º}{day}}$. Identical until the 4th division.

So what gives? Why did Ptolemy derive one value and report another?

In Chapter 7, he gives the explanation: He found the value needed to be corrected and did so before he put it in the table. But before he could explain to us how, we needed to cover the eclipse triples we did in Chapter 6. So how do we apply them to check the mean motions? Continue reading “Almagest Book IV: Correction of the Mean Motions of the Moon in Longitude and Anomaly”

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Almagest Book IV: Lunar Mean Motion Tables

The fourth chapter of Book IV takes what we worked on in the last post and expands it for convenient reference. As with the solar mean motion tables we created back in Book III, Ptolemy lays this one out in several intervals: 18 year periods, single year periods, months, days, and hours.

These tables essentially answer the question: “If the moon’s mean position was as X, if I waited Y interval of time, where would it be then?” Continue reading “Almagest Book IV: Lunar Mean Motion Tables”

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Almagest Book IV: Favorable Positions for Lunar Eclipse Pairs

Now that we’ve covered the positions the sun needs to be in to avoid its anomaly influencing things, and the positions to avoid for the moon, so its anomaly doesn’t influence things, we’ll look into some positions which would make it the most obvious if the above were. Ptolemy states this saying,

we should select intervals [the ends of which are situated] so as to best indicate [whether the interval is or is not a period of anomaly] by displaying the discrepancy [between two intervals] when they do not contain an integer number of returns in anomaly.

So which are those? Continue reading “Almagest Book IV: Favorable Positions for Lunar Eclipse Pairs”

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Almagest Book IV: The Lunar Anomaly and Eclipses

In the last post, we covered how the sun’s anomaly impacts things, but

we must pay no less attention to the moon’s [varying] speed. For if this is not taken into account, it will be possible for the moon, in many situations, to cover equal arcs in longitude in equal times which do not at all represent a return in lunar anomaly as well.

I’ll preface this section by saying this is, to date, by far the hardest section I’ve grappled with. I believe a large part of the difficulty came from the fact that Ptolemy is exceptionally unclear about what his goal is with this section. My initial belief was that it was to find the full period in which a the position of the sun and moon would “reset” as discussed in the last post. However, that’s something we’re going to have to work up to.

For now, we’re going to concentrate on just one of the various types of months. Namely, the “return in lunar anomaly” which is another way of saying the anomalistic month. Continue reading “Almagest Book IV: The Lunar Anomaly and Eclipses”