Category: Instrumentation

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Almagest Book VII: On the Method Used to Record [the Positions of] the Fixed Stars

Having established that the sphere of fixed stars has a rearwards motion, Ptolemy turns now to

making our observations and records of each of the above fixed stars, and of the others too, to give their positions, as observed in our time, in terms of longitude and latitude, not with respect to the equator, but with respect to the ecliptic, [i.e.,] as determined by the great circle drawn through the poles of the ecliptic and each individual star. In this way, in accordance with the hypothesis of their motion established above, their positions in latitude with respect to the ecliptic must necessarily remain the same, while their positions in longitude must always traverse equal arcs towards the rear in equal times.

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Almagest Book V: The Parallactic Instrument

The primary instrument I’ve used for my observing is an astronomical quadrant. That instrument is designed primarily to measure the angular distance of an object above the horizon1, otherwise known as its altitude. However, this isn’t the only instrument good for this sort of thing. Brahe’s Astronomiae Instauratae Mechanica is filled with instruments that essentially fill this same purpose, but in different ways.

One design, he describes as a “parallactic instrument” but it was also known as a triquetrum in period. This design dates back to Ptolemy and is described in Chapter $12$. Here’s a drawing of it from Toomer:

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Data: Stellar Quadrant Observations – 12/21/2020 (Great Conjunction)

Last night was the much hyped Great Conjunction of Jupiter and Saturn. I was asked if this had any meaning for my project. It really doesn’t have any special astronomical meaning, but it was fun to look at through a telescope. However, I decided that this would be an interesting stress test for the quadrant. After all, Jupiter and Saturn were only $6$ minutes of arc apart. This is a single division on the quadrant’s scale. So could I actually tell them apart? Continue reading “Data: Stellar Quadrant Observations – 12/21/2020 (Great Conjunction)”

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Almagest Book V: On the Use of an Astrolabe

Now that Ptolemy has described how to construct an astrolabe, he covers its usage. Specifically, Ptolemy begins when

both sun and moon could be observed above the earth at the same time.

As a brief reminder, what Ptolemy is really discussing here is what was necessary for him to make the observations that revealed the moon’s second anomaly. So what is given here is really in that context. As such, neither the sun nor moon is actually required for use of this instrument. In this case, Ptolemy is using the sun to align the instrument for use, and considering the moon to be the target, hence why the sun and moon are required. But, as we’ll see, a star can be used for alignment and there’s no reason one couldn’t be used as a target either.

Continue reading “Almagest Book V: On the Use of an Astrolabe”

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Almagest Book V: On the Construction of an Astrolabe

Book IV was all about setting up a preliminary lunar model with a single anomaly which Ptolemy modeled using the epicyclic model. But throughout, Ptolemy kept referencing a second anomaly he discovered, without ever saying how. In his introduction to Book V, Ptolemy finally gives the answer:

We were led to awareness of and belief in this [second anomaly] by the observations of lunar positions recorded by Hipparchus, and also by our own observations, which were made by means of an instrument which we constructed for this purpose.

That instrument was, at the time, called an “astrolabe” which simply means “for taking the [position of] stars,”2 but today we would call it an armillary sphere. Ptolemy describes how one should be constructed which is what we’ll be exploring in this post. To help us, here’s the image of one labeled from Toomer’s translation3.

Continue reading “Almagest Book V: On the Construction of an Astrolabe”

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Data: Stellar Quadrant Observations – 7/13/20

In my last post on observing, I introduced the recent upgrades to the quadrant. Unfortunately, the initial tests weren’t good. There was a significant error in the azimuth averaging $~2º$ at $180º$ azimuth. I’ve since determined the reason behind this and implemented what I hoped was a correction. And this recent observing session tested it. Continue reading “Data: Stellar Quadrant Observations – 7/13/20”

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Data: Stellar Quadrant Observations – 6/13/20 & 6/17/2020

NOTE: This post is actually being posted in December $2020$, as when I was writing my year end post, I was reminded I’d never posted this. This was largely due to having not decided what to actually do with the data for reasons you’ll see. Ultimately, I’ve decided to exclude the data completely.

In addition, since I hadn’t posted this, the discussion of the enhancements to the quadrant was actually featured in a post from July. But for readers who may read this in chronological order, I have instead moved that portion to this post.

It’s been awhile since I’ve posted about observing. Due to COVID, it’s been extra challenging to do any observations given the quarantine I’ve been doing my best to observe. I do still have a few friends that I see in a very small social circle, but between that and the weather last month, there hasn’t been a lot of opportunity. So when the weather called for a near-perfect night for observing and one of the people I trust was willing to assist, there was no way I was going to miss observing.

In addition, this night was extra special because it was going to allow me to test two new upgrades to the quadrant which I’ll start by introducing. Continue reading “Data: Stellar Quadrant Observations – 6/13/20 & 6/17/2020”

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Statistical Review of the Great Quadrant

Kingdom A&S is in just over a month and coincidentally falls on the one year anniversary of first light of the quadrant. Originally, I’d planned to do a deep dive statistical review of the quadrant, looking at sources of error, but this would be a modern mathematical review of an instrument that isn’t entirely period. Discussing it with friends, we decided it was a little too meta/degrees of separation.

Instead, I’ll do a blog post! So if you really want to get into the accuracy on the quadrant, hold on because I’m about to get mathy. Continue reading “Statistical Review of the Great Quadrant”