Having determined the eccentricity of Mars’ model as well as the line of apsides,
Our next task is to demonstrate the ratio of the size of the epicycle.
Continue reading “Almagest Book X: The Size of Mars’ Epicycle”
Almagest Book X: Checking the Eccentricity and Apogee
Now that we’ve sorted out the angles around the circle of mean motion, Ptolemy sets about checking to ensure that they return the observed angles from apogee from the point of view of the observer. Continue reading “Almagest Book X: Checking the Eccentricity and Apogee”
Almagest Book X: Third Iteration for Mars
Finally we’re ready to calculate our final eccentricities and line of apsides. And instead of breaking it into two posts, I’m going to do it all at once so we can be done with it1.
Here we go! Continue reading “Almagest Book X: Third Iteration for Mars”
Almagest Book X: Second Iteration Correction for Equant – Third Opposition
We’re now ready to make the correction for the third opposition in this second iteration. And the good news is that this is the last time we’ll need to calculate a correction.
Ptolemy still does a third iteration which relies on these corrections, but since he won’t be doing a fourth iteration, further corrections aren’t necessary. So let’s get to it. Continue reading “Almagest Book X: Second Iteration Correction for Equant – Third Opposition”
Almagest Book X: Second Iteration Correction for Equant – Second Opposition
Next, we’ll work on the correction for the second opposition in our second iteration. Continue reading “Almagest Book X: Second Iteration Correction for Equant – Second Opposition”
Almagest Book X: Second Iteration Correction for Equant – First Opposition
Now it’s time to determine the small angles that get applied as corrections. As with before, we’ll start with the first opposition, again using the same diagram. Continue reading “Almagest Book X: Second Iteration Correction for Equant – First Opposition”
Almagest Book X: Second Iteration for Mars – Part 2
Continuing on with our second iteration in which we calculate the revised line of apsides and eccentricity of Mars’ model.
As with before, I’m doing my calculations in a Google Sheet to make it easier to correct should I make an error. This also means that the Sheet will be keeping much higher precision to prevent rounding errors. However, as I’m only showing rounded values, things may look a bit off. So if something seems funny, I encourage checking out the aforementioned Sheet. Continue reading “Almagest Book X: Second Iteration for Mars – Part 2”
Almagest Book X: Second Iteration for Mars – Part 1
Chapter $7$ of Book X has been a lengthy one. We already have six posts behind us and we’re really just getting started because now we have to repeat all of those posts again, iterating through to better approximate an angle we didn’t know at the outset.
To do a quick review, in the first post in this chapter, we needed $\angle ZNH$, the apparent change along the equant circle from the point of view of the observer in the diagram below.
However, what we had was $\angle LNG$ which was the apparent change along the ecliptic from the point of view of the observer.
As you can tell, they’re close, but not quite the same. However, we could get to what we needed from what we had by subtracting $\angle LNT$ and $\angle YNM$.
We found both of these angles to be $0;33º$ in this post and $0;50º$ in this post, respectively.
Unfortunately, both of those values were calculated starting from an incorrect value for $\angle ZNH$. But, the good news is that applying them anyway will (Ptolemy hopes) still get us closer to the correct value! And then we’ll be able to iterate through again to reduce the discrepancy even further.
So let’s get started. Continue reading “Almagest Book X: Second Iteration for Mars – Part 1”
Pseudo-Ptolemy’s Treatise on the 9 Types of Comets
Starting around the 13th century, various astronomical texts began making their way into Christian Europe. These texts were largely translated from Arabic.
Among them, was a text that was originally attributed to Ptolemy which discussed the character and astrological implications of comets. Scholars have since concluded that this text is not by Ptolemy, but it was still widely distributed.
This text is one of many that is under investigation for the Ptolemaeus Arabus et Latinus project. There they provide a scan of a manuscript in the collection of the British Library (Sloane 2030) as well as a transcription of the text.
However, there was no translation. As such, I have attempted my own which is placed below the fold.
Continue reading “Pseudo-Ptolemy’s Treatise on the 9 Types of Comets”Class Schedule for Pennsic 2024
Pennsic is only a few short weeks away and as usual, I’m teaching a whole host of astronomy classes.
This will include my previous classes but will also be introducing a new class on comets in the SCA period.
Full schedule beneath the fold.
Continue reading “Class Schedule for Pennsic 2024”