Author: VoijaRisa

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The SCAdian Astronomical Epoch – Solar Position

In Book III of the Almagest, Ptolemy developed a methodology by which the solar position could be predicted. This method had a few key components. This included determining the mean motion, the equation of anomaly, and calculating a start date/position to which those could be applied.

Unfortunately, trying to use Ptolemy’s solution would no longer work in the present day. While the mean motion and equation of anomaly are still fine, precession of the equinoxes and other small effects over the past ~1,900 years mean too much has changed. So while we can’t use the exact results of Ptolemy’s it should be possible to recreate his methodology with a more recent starting date again allowing for reasonably accurate predictions of the solar position.

So for my entry to this year’s Virtual Kingdom Arts & Science competition, I did. Continue reading “The SCAdian Astronomical Epoch – Solar Position”

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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: Summer Solstice Observation 6/20/2020

This past weekend was the summer solstice. Since the sun achieves its highest declination on this day, which is related to the obliquity of the ecliptic, this is a fundamental parameter that I try to observe the altitude on the solstice when possible. I did this back in 2018 using the solar angle dial from Book I of the Almagest. This time, I brought out the quadrant as I did for the autumnal equinox in 2018 as well.

Continue reading “Data: Summer Solstice Observation 6/20/2020”

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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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Almagest Book IV: The Babylonian Eclipse Triple – Solar/Lunar Positions & Epicyclic Motion of Anomaly

So far in this book we’ve covered the ancient Greek values for the various motions of the moon. For the most part Ptolemy has accepted them as authoritative, but to demonstrate some of the methodology, Ptolemy wants to walk us through one: The lunar anomaly.

We shall use, first, among the most ancient eclipses available to us, three [which we have selected] as being recorded in an unambiguous fashion, and, secondly, [we shall repeat the procedure] using among contemporary eclipses, three which we ourselves have observed very accurately. In this way our results will be valid over as long a period as possible, and in particular, it will be apparent that approximately the same equation of anomaly results from both demonstrations, and that the increment in the mean motion [between two sets of eclipses] agrees with that computed from the above periods.

Continue reading “Almagest Book IV: The Babylonian Eclipse Triple – Solar/Lunar Positions & Epicyclic Motion of Anomaly”

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Almagest Book IV: Uneven Ratios in Epicyclic and Eccentric Model

In the last post, we explored how the eccentric and epicyclic models could produce the same result even if you didn’t have the same period of anomaly and ecliptic longitude. This was done by allowing the center of the eccentre to rotate around the Earth. In this post, we’ll explore how they can still produce the same result even

if [the members of] the ratios are unequal, and the eccentre is not the same size as the deferent…provided the ratios are similar Continue reading “Almagest Book IV: Uneven Ratios in Epicyclic and Eccentric Model”

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Almagest Book IV: In the Simple Hypothesis of the Moon, the Same Phenomena are Produced by Both the Eccentric and Epicyclic Hypotheses

Our next task is to demonstrate the type and size of the moon’s anomaly.

In chapter 2 of this book, we spent quite a bit of time talking about the moon’s anomaly, describing a method by which Hipparchus could have used periods of eclipses to determine the anomaly’s period. While we never actually completed the method, Ptolemy still gave us the period Hipparchus supposedly derived. Now we’re going to put that to use to start building our first lunar model. Continue reading “Almagest Book IV: In the Simple Hypothesis of the Moon, the Same Phenomena are Produced by Both the Eccentric and Epicyclic Hypotheses”

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Almagest Book IV: Lunar Mean Motion Tables

The fourth chapter of Book IV takes what we worked on in the last post and expands it for convenient reference. As with the solar mean motion tables we created back in Book III, Ptolemy lays this one out in several intervals: 18 year periods, single year periods, months, days, and hours.

These tables essentially answer the question: “If the moon’s mean position was as X, if I waited Y interval of time, where would it be then?” Continue reading “Almagest Book IV: Lunar Mean Motion Tables”

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Almagest Book IV: Favorable Positions for Lunar Eclipse Pairs

Now that we’ve covered the positions the sun needs to be in to avoid its anomaly influencing things, and the positions to avoid for the moon, so its anomaly doesn’t influence things, we’ll look into some positions which would make it the most obvious if the above were. Ptolemy states this saying,

we should select intervals [the ends of which are situated] so as to best indicate [whether the interval is or is not a period of anomaly] by displaying the discrepancy [between two intervals] when they do not contain an integer number of returns in anomaly.

So which are those? Continue reading “Almagest Book IV: Favorable Positions for Lunar Eclipse Pairs”