For Christmas this year, I have received a few items for use with this project. This has prompted me to think back to Christmas last year and how far I’ve come overall.
Almagest Book II: Applications of Rising-Time Tables
At this point we’ve spent some considerable time doing the work to develop our rising time tables. Now Ptolemy answers the question: What can we do with them?
Ptolemy provides several algorithms:
Seasonal Hours (Alternative Method)
Seasonal Hours to Equinoctial Hours
Upper Culmination (Alternative Method)
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Almagest Book II: Rising Time of the Ecliptic Tables
Over the past several posts we have worked towards an understanding of the rising times of arcs of the ecliptic at various latitudes. With this work complete, Ptolemy presents a table of these rising times in 10º intervals for select latitudes. Continue reading “Almagest Book II: Rising Time of the Ecliptic Tables”
Almagest Book II: Calculation of Rising Times at Sphaera Obliqua for 10º Arcs
With the previous theorem about the ascensional differences complete, it’s time to move on to determine how to figure out the rising time of arcs of the ecliptic for 10º segments at various latitudes using what Ptolemy promises to be a shortcut in the math. In the modern sense it really doesn’t seem to be much of a shortcut, but that’s because with the assistance of calculator’s, the equations we were using previously seem much less daunting. If it had to be done by hand, I’m sure it would be far more tedious.
Instead, Ptolemy reduces the number of calculations by going through the proof regarding ascensional differences as well as making use of some previously calculated values to avoid having to do other calculations.
To get started, Ptolemy revises the previous drawing, making it a bit simpler by removing the ecliptic and renaming a few of the points, as well as changing a few definitions.
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Almagest Book II: Ascensional Difference
Not content to simply figure out how long it would take a zodiacal constellation to rise at latitudes other than the equator, Ptolemy sets out to further divide the ecliptic into 10º arcs and he’s promised an easier method than what we’ve done previously. But before we can get there, Ptolemy gives a brief proof which he’ll make use of later.
To start, we begin with the vernal equinox on the horizon:
Data: Stellar Quadrant Observations – 12/23/18
It’s been almost three months since I’ve been able to get out and observe. It’s been a combination of assistants being sick, bad weather, bad moonphases, and starting a new job. But just before the holiday this year, we had a nice clear night. There was a near full moon, but as Padraig is planning on moving to Boston in the next year, I’m in need of someone else that wants to help. Fortunately, another member of my barony, Auga, volunteered to assist, so this night was mostly meant to get her trained on how things work and the moon was actually somewhat helpful as it made seeing what we were doing with setup and learning the instrument all the easier.
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