Tracing the history of medieval astronomy
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”
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”
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”
This past week, I started a new job which allows me to sleep in a few hours later. This has meant that doing a bit of observing on work nights suddenly became a possibility. So when Yseult messaged me noting that the weather would be ideal for observing and it was a new moon, I was happy to observe on a Sunday night. Continue reading “Data: Stellar Quadrant Observations – 4/11/21”
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”
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 Neugebauer2. Continue reading “Almagest Book V: Components of Parallax – A First Approximation”
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”
Now that we’ve completed the parallax table, we should discuss how to use it. As usual, Ptolemy will now walk us through the steps, but does not provide an explicit example so I’ll follow an example from Neugebauer3, to help illustrate the procedure.
As our goal, Ptolemy states that our goal is to find
the moon’s parallax at any given position, (first) with respect to the great circle drawn through the moon and zenith
Continue reading “Almagest Book V: Calculating Lunar Parallax Along Great Circle Through Zenith”
As usual, the weather in January and February of this year hasn’t cooperated. Nights were consistently cloudy during good moon phases or the temperatures well below freezing.
But as March has rolled around, temperatures have begun to warm, and the forecast called for a clear night with a good moon phase so Yseult and I headed out to Danville Conservation Area to do some observing. Continue reading “Data: Stellar Quadrant Observations – 3/6/2021”
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