Author: VoijaRisa

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Mean to True Conjunction Alternate Method

In our last post, we walked through Ptolemy’s method for finding the angular distance between the mean and true conjunction.

When I initially wrote the post, I followed Neugebauer’s explanation as Ptolemy’s was quite difficult to parse and although they contain a lot of the same key elements, one important piece is left out of Neugebauer’s solution. Specifically, the part where Ptolemy’s iterative method leads naturally to the increase over the anomaly of $\frac{1}{12}$. Writing a later post, I realized that this was an important piece of information since it pops up later and thus made the effort to more completely understand Ptolemy’s method and rewrote the post to explain it. However, I didn’t want to lose the original work, following Neugebauer since readers may appreciate some explanation of Neugebauer’s work as it too is quite dense. Thus, I’ve included that original text beneath the fold as a separate post. Continue reading “Mean to True Conjunction Alternate Method”

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Almagest Book VI – Lunar Eclipse Limits

Way back in Book V we determined the angular diameter of the moon as well as earth’s shadow at apogee. In the last post, we repeated the procedure for perigee. In the Almagest, Ptolemy doesn’t actually say what those calculations are for and instead, starts working out some figures for the sun. However, to try to keep things in a more reasonable flow (in my opinion), I’m going to skip to the end of this chapter and discuss why we care about the moon’s diameter and earth’s shadow.

In short, lunar eclipses can only happen near the lunar nodes. But, it doesn’t have to be exactly at a node. First off, the earth’s shadow has some width to it. In addition, the anomalies of the sun and moon play a role, which means the actual range the eclipse could occur in is surprisingly wide. So in this post, we’ll work on that. Continue reading “Almagest Book VI – Lunar Eclipse Limits”

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Data: Stellar Quadrant Observations – 11/6/21

It has been seven months since I have done any observing. Between unfortunate weather during good moon phases this summer, being exhausted from mundane life things, running an event… it just didn’t happen.

But now that a lot of that is behind me, we had a crisp fall night with daytime temps in the 60’s and lows in the 40’s. Chilly, but entirely manageable. Especially since I purchased a heated vest last winter. I’ve been looking for a pair of heated pants to go with it, but haven’t found any with sufficiently good reviews at a decent price just yet.

Yseult joined me again, and we got through 60 observations. Continue reading “Data: Stellar Quadrant Observations – 11/6/21”

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Almagest Book VI: Lunar Diameter and Earth’s Shadow at Perigee During Syzygy

In the last post, we explored how to make use of the table of mean syzygies to calculate the true syzygies. However, that chapter focused mostly on finding the time when the moon and sun would have either the same or exactly opposite ecliptic latitude. But what got left by the wayside was the lunar ecliptic latitude. We did a bit of work on calculating the argument of it but, aside from my mention of it in the afterword of the post, we never really completed that calculation. And eclipses of either type cannot truly occur unless the lunar ecliptic latitude is reasonably close to zero.

So we could calculate the ecliptic latitude of the moon for every conjunction and opposition but instead, Ptolemy decides we should first do a bit of a sanity check before getting any more involved. To do so, Ptolemy wants to examine how far from a node is it even possible for the ecliptic longitude of the syzygy to occur and still have an eclipse. If it’s outside of these limits, then no further calculation is necessary. To do this, Ptolemy is going to need to know some additional values. In this post, we’ll explore the angular diameter when the moon is at the perigee of its epicycle at syzygy1 as well as determining the width of Earth’s shadow at that distance. Continue reading “Almagest Book VI: Lunar Diameter and Earth’s Shadow at Perigee During Syzygy”

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Almagest Book VI: How to Determine the Mean and True Syzygies

Now that we’ve created our table of conjunctions and oppositions, how do we go about using it? As usual, Ptolemy walks through the process in a vacuum, so to help, I’ll follow along with the example Neugebauer does in History of Ancient Mathematical Astronomy on pages $123-124$, although somewhat slimmed down. In particular, I’ll walk through finding the true opposition from the year $718$ in the epoch for the first opposition in the year. Continue reading “Almagest Book VI: How to Determine the Mean and True Syzygies”

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Almagest Book VI: Construction of the Table of Mean Syzygies

As promised in the last chapter, Ptolemy’s first task in eclipse prediction is going to be laying out a table of mean syzygies around which eclipses might be possible, so we can check those to see if an eclipse might occur instead of performing useless calculations where the sun and moon are nowhere near a syzygy. In this post, we’ll go over the construction of that table! Continue reading “Almagest Book VI: Construction of the Table of Mean Syzygies”

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Upcoming Class: Christianity and Astronomy in the Medieval Period

Popping in briefly to say that I’ll be teaching my Christianity and Astronomy in the Medieval Period class this coming Saturday at 7pm CST for the Canton of Whyt Whey. If you’re interested in attending, it will be held on Google Meets. Here’s the link to the meet.

This is one of my favorite classes because it really challenges some of the traditional narratives – both those that try to depict Christianity as an enemy of science as well as the counter narrative that Christianity inspired or made possible modern science.

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Almagest Book VI: On Conjunctions and Oppositions of Sun and Moon

Finally we’re on Book VI. So far in the Almagest, we’ve had a few books which laid out some preliminary tables and concepts, a book on the sun, and two on the moon2. Now it’s time to put the sun and the moon together to start looking at some of the most dramatic astronomical phenomena: eclipses. To introduce this topic, Ptolemy begins with an uncharacteristically short chapter which is a single paragraph. Continue reading “Almagest Book VI: On Conjunctions and Oppositions of Sun and Moon”