Tag: lunar eclipse

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Almagest Book VI: Predicting Lunar Eclipses

Having set out the above as a preliminary, we can predict lunar eclipses in the following manner.

As Ptolemy states in opening this chapter, we’re finally done with the preliminary work and we’re ready to start diving into how to actually use everything we’ve done to predict eclipses. As usual, Ptolemy walks us through the steps, but does not provide an example, so I will follow my usual procedure of using example $11$ in Appendix A of Toomer’s translation1.In that example, Toomer invites us to examine lunar eclipses around Nabonassar 28, in the month of Thoth (the first month of the Egyptian year). Continue reading “Almagest Book VI: Predicting Lunar Eclipses”

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Almagest Book VI: Eclipse Tables

Having spent five posts building eclipse tables, here’s the full tables. As usual, I’ve placed them in a Google Doc for easy access.

Do note that this table is broken up into four tabs.

Toomer notes that there are a number of errors in the table, but it’s not clear whether they originate with Ptolemy’s calculations or are a result of later transcription errors. Ones that can be confirmed as scribal errors he notes were corrected in the translation.

 

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Almagest Book VI: Table for Magnitudes of Solar and Lunar Eclipses – Lunar Eclipse Example

Having  completed an example calculation for converting linear digits to area digits in the previous post, we’ll now do the same calculation for a lunar eclipse. The good news is the setup is the same. While I don’t strictly need to redraw the diagram, I’m going to anyway because the earth’s shadow is so much larger than the moon and drawing it as such helps me visualize things mentally although the respective position of the points doesn’t change at all.

Continue reading “Almagest Book VI: Table for Magnitudes of Solar and Lunar Eclipses – Lunar Eclipse Example”

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Almagest Book VI: Lunar Eclipses Separated by Seven Months

So far in this chapter, we’ve demonstrated that it’s quite possible that, if either a solar or lunar eclipse occurs, there will be another one six months later. Then, in the last post we showed that, if a lunar eclipse happens, it’s possible (although unlikely) that there can be another one five months later. In this post, we’ll explore whether or not, for lunar eclipses, you can have two separated by seven months.

The procedure will be the same as in the last post. First we’ll determine the motion of the luminaries, taking into account the discrepancies due to the anomalies, as well as the differences between mean and true syzygy, and then compare those to the eclipse windows which we’ll again recalculate for this situation. Continue reading “Almagest Book VI: Lunar Eclipses Separated by Seven Months”

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Almagest Book VI: Lunar Eclipses Separated by Five Months

In the previous post, we showed that , if a solar or lunar eclipse occurs, it is possible that another may occur six months later. Now, we’ll turn to ask whether or not another lunar eclipse can happen five months after a previous one. To answer this question, we’ll first work out how much the moon would have moved in that time period and then compare that to the eclipse window.. Continue reading “Almagest Book VI: Lunar Eclipses Separated by Five Months”

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Almagest Book VI: Solar and Lunar Eclipses Separated by Six Months

Continuing in the theme of checking as few as possible syzygies for eclipses, Ptolemy now turns his attention towards

the problem of intervals at which, in general, it is possible for ecliptic syzygies to occur, so that, once we have determined a single example of of an ecliptic syzygy, we need not apply our examination to the [ecliptic] limits to every succeeding syzygy in turn, but only to those which are separated [from the first] by an interval of months at which it is possible for an eclipse to recur.

Continue reading “Almagest Book VI: Solar and Lunar Eclipses Separated by Six Months”

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Almagest Book VI – Lunar Eclipse Limits

Way back in Book V we determined the angular diameter of the moon as well as earth’s shadow at apogee. In the last post, we repeated the procedure for perigee. In the Almagest, Ptolemy doesn’t actually say what those calculations are for and instead, starts working out some figures for the sun. However, to try to keep things in a more reasonable flow (in my opinion), I’m going to skip to the end of this chapter and discuss why we care about the moon’s diameter and earth’s shadow.

In short, lunar eclipses can only happen near the lunar nodes. But, it doesn’t have to be exactly at a node. First off, the earth’s shadow has some width to it. In addition, the anomalies of the sun and moon play a role, which means the actual range the eclipse could occur in is surprisingly wide. So in this post, we’ll work on that. Continue reading “Almagest Book VI – Lunar Eclipse Limits”