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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 VII: On the Rate of Precession from Other Greek Astronomer’s Observations

In the last post, we showed how we can determine the rate of precession if we know how much a star has changed its declination over a long period. In it, we used a baseline of $265$ years, corresponding to the time between Hipparchus and Ptolemy.

Next, Ptolemy wants to increase that baseline further and turns to the observations of three other Greek Astronomers: Timocharis, Agrippa1, and Menelaus. However, these astronomers did not give the position of the stars in equatorial coordinates. Rather, they described occultations of various stars by the moon. Thus, Ptolemy turns to the lunar model to determine the positions of these stars and instead of finding a change in declination, is able to directly compare the ecliptic longitude of them over time. Continue reading “Almagest Book VII: On the Rate of Precession from Other Greek Astronomer’s Observations”

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Almagest Book VII: On the Rate of Precession from Hipparchus’ Observations

In the last post, Ptolemy concluded that the motion of the fixed stars over time, known as precession, happens about the poles of the ecliptic. He determined this by stating that the longitude of stars with relation to the ecliptic remained consistent over a long interval of time but varied with respect to the celestial equator. That post concluded with Ptolemy’s promise that we would be able to determine rate of that precession using the same data he presented previously.

It is particularly [easy to demonstrate] from the differences in declination found for those stars near the equinoctial points.

Continue reading “Almagest Book VII: On the Rate of Precession from Hipparchus’ Observations”

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Almagest Book VII: On the Poles of Precession

From the above, it has become clear to us that the sphere of the fixed stars, too, performs a rearward motion along the ecliptic, of approximately the amount indicated. Our next task is to determine the type of this motion, that is to say, whether it takes place about the poles of the equator or about the poles of the inclined circle of the ecliptic.

Now that Ptolemy has determined that precession does indeed happen at a rate that agrees with Hipparchus, he now asks whether that precession is happening in the same direction as the ecliptic or the celestial equator.

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Data: Stellar Quadrant Observations – 9/16/2022 (Gryphon’s Fest)

Gryphon’s Fest was this past weekend and since I was in charge of the event I wasn’t really focused on observing. However, Jupiter was nearing opposition Friday night, so I wanted to make sure I got some observations there. While that went well, there’s still something much bigger that happened there. Continue reading “Data: Stellar Quadrant Observations – 9/16/2022 (Gryphon’s Fest)”

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Data: Stellar Quadrant Observations – Lilies War (6/19-21/2022) & Saturn Opposition (8/22/2022)

Oof. I haven’t been posting much. This year has been busy. With the SCA starting up again, a lot of time and emotional energy has been spent on prepping for wars, new classes, competitions, and planning an event I’m running next month. Not much time for astronomy.

However, there has been some recent observing. Details below the fold. Continue reading “Data: Stellar Quadrant Observations – Lilies War (6/19-21/2022) & Saturn Opposition (8/22/2022)”

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Data: Stellar Quadrant Observations – 5/27/2022

The weather this year has been frustrating. Winter held on far longer than normal. While temperatures weren’t freezing in March and April, they stubbornly refused to get into a temperature range that would allow me to open the windows. Then, after a few nice days, it immediately jumped into the early summer. Needless to say, such turbulent weather is not good for observing and I’ve only been out twice this year1

However, temperatures have cooled back off and, should a clear night occur, it would be a quite pleasant night to observe. This past Friday, despite solid cloud cover all day, the weather reports said it should clear by around $8$pm, so I headed out to Danville with the quadrant to do some observing. Although there was some high humidity, an adjustment in how I select what objects to observe made this likely one of the most productive observing sessions I’ve yet had. Continue reading “Data: Stellar Quadrant Observations – 5/27/2022”

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Queen’s Prize 2022 – The Astronomical Epoch for Solar and (First) Lunar Models

Thanks to Corona, it’s been quite awhile since we’ve really had an Arts & Sciences competition here in Calontir. While we had a virtual Kingdom A&S in $2020$ the last one we had in person was Queen’s Prize in $2019$.

However, this past weekend we finally had another in person Queen’s Prize and I entered my latest paper revising Ptolemy’s models for use in the present day. My previous entry attempted to update the solar model but contained critical errors1. This was revealed when I started attempting to update the lunar model. Realizing that it was predicting solar positions that would have made the eclipses necessary to calibrate the lunar model impossible, I revisited the solar model and made the necessary corrections.

That, plus the first lunar model were included in this year’s entry which was rewritten using LaTeX for a smoother editing and reading experience as Google’s equation editor was rather poor. The paper ended up being $62$ pages (although roughly $45\%$ of that was front material and appendices) which was a lot to expect anyone to read. As such, I also created a TL;DR version for passerbys.

Continue reading “Queen’s Prize 2022 – The Astronomical Epoch for Solar and (First) Lunar Models”