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 moon1. 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”

Data: Stellar Quadrant Observations – 4/3/21

With the weather finally warming up, last night1 was was one of the nicest nights of observing one could really ask for. The daily high was in the low 70’s and the overnight lows were supposed to be in the mid-50’s. Humidity and winds were both low.

But with nicer weather happening and Easter today, everyone seemed to have plans already so I ended up heading out to Danville by myself. I’ve been wanting to capture some time lapse video of this so I took my GoPro out and tried the night lapse setting.


Continue reading “Data: Stellar Quadrant Observations – 4/3/21”

Almagest Book V: Components of Parallax – A First Approximation

So far in this chapter, we’ve explored how to use the table of parallax to calculate the parallax of the moon and sun by knowing its distance from the zenith. But this in and of itself isn’t particularly useful. For example, when we did a sample lunar parallax calculation, we determined in that situation, the moon was about $1;10º$ off from its true position. But $1;10º$ in which direction?

Thus, the next step will be to break that down into its components, determining how far off in both ecliptic latitude and longitude the parallax makes the moon appear. Ptolemy again gives steps, but no example, so we’ll continue the previous example we did for the moon, following Neugebauer1. Continue reading “Almagest Book V: Components of Parallax – A First Approximation”

Almagest Book V: Calculating Solar Parallax Along a Great Circle Through the Zenith

Having computed the lunar parallax,

the sun’s parallax for a similar situation [i.e., as measured along an altitude circle] is immediately determined, in a simple fashion (for solar eclipses) from the number in the second column corresponding to the size of the arc from the zenith [to the sun].

Well that sure sounds easy. Let’s look at a quick example. Continue reading “Almagest Book V: Calculating Solar Parallax Along a Great Circle Through the Zenith”