Yikes. It’s been nearly two months since I made any sort of post here! Here’s a quick update on what’s been going on and there’s a little bit of astronomy in there. Continue reading “Apologies for Recent Absence”
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”
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”
Almagest Book VI: Table of Mean Syzygies
Now that we’ve walked through how it’s calculated, here is Ptolemy’s Table of Mean Syzygies. As with previous tables, I’ve made this into a Google Sheet. I’ve also broken it into tabs to make the formatting easier since the first section has two tables and gives actual positions whereas the ones for years and months gives increments.
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”
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.
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”
Almagest Book V: Components of Parallax – Correction Example
Now that Ptolemy has straightened us out regarding which angle we need to be using, Ptolemy sets out
a convention method for making the above kind of correction of the angles and arcs, if anyone wants to make it when the [differences] involved are so small.
Fortunately, we can use the same diagram we ended with last time which was the generic case:
Ptolemy lays his method on us in his familiar brick of text: Continue reading “Almagest Book V: Components of Parallax – Correction Example”
Almagest Book V: Components of Parallax – Corrections
At the end of the last post, we noted that Ptolemy wasn’t quite satisfied with what we did previously because we used some rather faulty assumptions.
As Ptolemy states it:
For lunar parallaxes, we considered it sufficient to use the arcs and angles formed by the great circle through the poles of the horizon [i.e., an altitude circle] at the ecliptic, instead of those at the moon’s inclined circle. For we saw that the difference which would result at syzygies in which eclipses occur is imperceptible, and to set out the latter would have been complicated to demonstrate and laborious to calculate; for the distance of the moon from the node is not fixed for a given position of the moon on the ecliptic, but undergoes multiple changes in both the amount and relative position.
The key phrase here is the “at the ecliptic, instead of the moon’s inclined circle.” This got swept under the rug in that post because Ptolemy didn’t really explain why the algorithm he gave us should work. So to understand, let’s start by taking a harder look at what’s actually going on.
Continue reading “Almagest Book V: Components of Parallax – Corrections”
Welcome to Sky & Telescope Readers
Greetings to any of you who have found me as a result of the Astronomer’s Workbench article in Sky & Telescope. As the article in question was limited in length, I wanted to take this opportunity to expound more on my project as the quadrant is only a small portion of a much larger project as well as answer some questions I expect you may have. Continue reading “Welcome to Sky & Telescope Readers”