Tracing the history of medieval astronomy
First off, what’s a gnomon?
Apparently it’s the part of a sundial that casts shadows. Now you know.
To start this next chapter, Ptolemy dives straight into a new figure, but I want to take a moment to justify it first. To begin, let’s start with a simple diagram. Just a side view of the meridian, the horizon, and the north celestial pole. The zenith is also marked (A).
Continue reading “Almagest Book II: Ratio of Gnomon Equinoctial and Solsticial Shadows”
The fourth chapter in book two is a very short one. In fact, it’s a single paragraph so I almost didn’t dedicate an entire post to it but ultimately decided to as it didn’t really fit with either the previous or next chapter.
In this, Ptolemy says,
it is a straighforward computation to determine for what regions, when, and how often the sun reaches the zenith. For it is immediately obvious that for those beneath a parallel which is farther away from the equator than the 23;51,20º (approximately), which represents the distance of the summer solstice, the sun never reaches the zenith at all, while for those beneath the parallel which is exactly that distance, it reaches the zenith once a year, precisely at the summer solstice.
For the past few Almagest posts, we’ve been working on the following diagram:
As a refresher, AEG is the celestial equator and BED is the horizon of an observer. Z is south. H is the point of the winter solstice as it crosses the horizon (or rises).
In the first post we determined $arc \; EH$. In the second post, we used that to determine $arc \; BZ$. In the third, we’ve determined $arc \; E \Theta$ and then came full circle and showed another way to get $arc \; EH$.
Now, Ptolemy wants to generalize. Continue reading “Almagest Book II: Symmetries of Arcs and Day/Night Lengths”
So far I’ve had two nights of observing with the quadrant. The first was a test run and trying to determine an organization to the logistics of observing. The second was the Mars opposition which had a nearly full moon. In both cases, the amount of actual observing was somewhat limited as a result.
As such, we’ve been waiting for a nice moon-free night to really concentrate on observations. As last night was the new moon, it seemed like a good night, and I was able to tempt a few people into helping out as it’s also very near the peak of the annual Perseid meteor shower. Continue reading “Data: Stellar Quadrant Observations – 8/12/18 (Perseid Meteor Shower)”
The next demonstration Ptolemy does is actually a reverse of what we did in the past 2 posts. Now, given latitude Ptolemy asks what the difference in length between the longest (or shortest) day and the daylight on the equinox would be. Again, Ptolemy has actually already given us the answer for the case we’re considering of the Greek city of Rhodes which is at 36º N latitude for which the longest day (the summer solstice) is 14.5 hours. Since the length of the day on the equinox is 12 hours, the answer will be 2.5, but Ptolemy simply wants to demonstrate that this can be achieved mathematically.
Again, we’ll use Menelaus’ Theorem II.
In our last post, we explored how to find the angular distance around the horizon from the ecliptic and celestial equator. In this chapter, we explore another value that can be derived from knowing the length of the longest day (i.e. on the summer solstice): the elevation (or altitude) of the celestial pole (which is also the latitude).
Once again, we’ll start with the same diagram we’ve been using for awhile now:
Continue reading “Almagest Book II: From Length of Longest Day Finding Elevation of the Pole”
Let us take as a general basis for our examples the parallel circle to the equator through Rhodes, where the elevation of the pole is 36º, and the longest day $14 \frac{1}{2}$ equinoctial hours.
Immediately starting the second chapter, we’re given a lot to unpack. First off, Ptolemy chooses to work through this problem by means of an example, selecting Rhodes, a city in Greece as the exemplar. I’m assuming that the “elevation of the pole” is the latitude, as Rhodes’ latitude is 36.2º. But what of these equinoctial hours? Continue reading “Almagest Book II: Arcs of the Horizon between Equator and Ecliptic”
One of the long term goals of this project is to collect enough data to derive the orbit of Mars. However, because Kepler didn’t know the orbit of Earth, he couldn’t use the observation on any given night. Instead, he only used observations from when Mars was at opposition1. This happened to be last night, so we packed up the quadrant and headed out.
Continue reading “Data: Stellar Quadrant Observations – 7/27/18 (Mars Opposition)”
It’s been awhile since I’ve posted anything on the Almagest. That’s mostly because I was at a nice stopping point and with the quadrant getting finished up and observations beginning, that stole my focus for awhile. But it’s finally time to jump into Book II. The first chapter in this book is just text. No math. So what does Ptolemy have to say? Continue reading “Almagest Book II: Introduction”
Having finished the quadrant this past weekend, I was finally able to take it out for it’s first light1. A special thanks to Her Excellency Slaine for helping me transport parts that wouldn’t fit in my car as well as Padrig for being my chief observer.
So how’d it go? Continue reading “Data: Stellar Quadrant Observations – 7/20/18 (First Light)”