In the third chapter of Book IV, we’re going to do some more work with the lunar motion. We already did a fair amount of that at the beginning of the last chapter in which Ptolemy essentially quoted some numbers for various lunar periods from his predecessors. Now, we’ll extend those. Continue reading “Almagest Book IV: On the Individual Mean Motions of the Moon”
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”
Almagest Book IV: The Lunar Anomaly and Eclipses
In the last post, we covered how the sun’s anomaly impacts things, but
we must pay no less attention to the moon’s [varying] speed. For if this is not taken into account, it will be possible for the moon, in many situations, to cover equal arcs in longitude in equal times which do not at all represent a return in lunar anomaly as well.
I’ll preface this section by saying this is, to date, by far the hardest section I’ve grappled with. I believe a large part of the difficulty came from the fact that Ptolemy is exceptionally unclear about what his goal is with this section. My initial belief was that it was to find the full period in which a the position of the sun and moon would “reset” as discussed in the last post. However, that’s something we’re going to have to work up to.
For now, we’re going to concentrate on just one of the various types of months. Namely, the “return in lunar anomaly” which is another way of saying the anomalistic month. Continue reading “Almagest Book IV: The Lunar Anomaly and Eclipses”
Data: Stellar Quadrant Observations – 4/21/20
I managed to get out and do a bit of observing last night. It’s been 4 months to do the day since my last opportunity to do so and I started off by making a rather large blunder. The location I usually observe at has several pads for observing and I have one I usually use. It’s straight down a path that points generally north which makes finding the north star fairly easy, even without looking for the big dipper to verify which star it is.
Well, last night I looked for the star over where the path met the parking lot, but because I was on a pad a bit to the west of where I normally am, I accidentally aligned on Kochab, the second brightest star in Ursa Minor, and ended up making three observations over the course of a half hour before I realized the error. Fortunately, we still got in 11 observations, and all of them were new stars! Continue reading “Data: Stellar Quadrant Observations – 4/21/20”
Almagest Book IV: The Solar Anomaly and Lunar Periods
In the last post, we explored various lunar cycles from astronomers predating Ptolemy in which the moon reset its ecliptic longitude and anomalistic motion to define a full lunar period. These ancient astronomers did this by studying pairs of lunar eclipses1but Ptolemy notes that this method
is not simple or easy to carry out, but demands a great deal of extraordinary care
The reason for this difficulty is that, without careful consideration there can essentially be false positives of eclipses separated equally in time, but do not in fact, result in the moon returning to the same ecliptic longitude or same speed.
One of the reasons is that the conditions necessary to produce a lunar eclipse are also dependent on the sun, which has anomalistic motion. As such, it could be entirely possible that the moon could not have yet returned to the same ecliptic longitude as a previous eclipse, but the sun’s anomaly could cause an eclipse anyway. Thus, a pair of eclipses may be equally separated in time, but
this is no use to us unless the sun too exhibits no effect due to anomaly, or exhibits the same [anomaly] over both intervals: for if this is not the case, but instead, as I have said, the equation of anomaly has some effect, the sun will not have travelled equal distances over [the two] equal time intervals, nor, obviously, will the moon.
To illustrate this, Ptolemy starts with an example. Continue reading “Almagest Book IV: The Solar Anomaly and Lunar Periods”
2019 in Review
What a year it’s been.
2019 has seen a great deal of progress in this project and many other aspects of my SCA life, so I wanted to take a bit of time to recap as there’s some things I don’t think have yet made it into the blog. Continue reading “2019 in Review”
Almagest Book IV: Mean Periods of the Moon
When we developed the model for sun, one of the first things we did was to determine the rate of mean motion for the sun to which the anomalistic motion could be added. However, the moon is going to be more complicated for several reasons. As such, before going further, we’ll need to spend some time examining the various lunar periods. Continue reading “Almagest Book IV: Mean Periods of the Moon”
Data: Stellar Quadrant Observations – 12/21/19
Happy Winter Solstice to all. Despite wanting to get out at solar noon today to get an observation of the sun, I was asleep at that time as I have a cold that’s sucking all my energy despite not making me feel all that bad.
However, tonight was also a late moon phase so doing stellar observations was on the schedule. Quieteria helped me with these observations, but as it was very cold tonight, we called it quits fairly early. And because we’re in a rather blank patch of sky with mostly stars well past 4th magnitude, that only led to a fistfull of observations. Continue reading “Data: Stellar Quadrant Observations – 12/21/19”
Almagest Book IV: Observations Necessary to Examine Lunar Phenomena
So far, Books I & II covered the motions of the sky and how to find the rising times of various points along the ecliptic. This was a good start because, in Book III, we explored the motion of the Sun which is confined to that ecliptic. So while the sun was somewhat complex because of its anomaly, it was still relatively simple. In Book IV, we’ll work on deriving a model for the motion of the moon.
Unfortunately, this is going to be a more complex model. Initially we could be concerned about the complexity of the model because the moon is not confined to the ecliptic – it bobbles above and below it by about 5º, but aside from discussing this briefly, we’ll safely ignore this for now and instead only worry about the moon’s motion in ecliptic longitude, that is to say, its projection onto the ecliptic.
However, what will complicate things is that one of the main things we consider regarding the moon, its phase, is also dependent on the sun. Thus, to consider the moon’s phases, we’ll need to be taking into consideration the sun’s anomalies at the same time we consider those of the moon. In addition, the points at which the moon is at apogee and perigee is not consistent as it was for the sun1.
The good news is that we’ve already explored the two models that Ptolemy uses to explain anomalies from the mean motion. As such, there will be far less exposition in this book and we’ll be able to dive in much more quickly. Continue reading “Almagest Book IV: Observations Necessary to Examine Lunar Phenomena”
Almagest Book III: On the Inequality of Solar Days
Finally, we’ve arrived at the end of Book III where we’ve arrived at a well developed model of the solar motion. But before closing out, Ptolemy has one last chapter to discuss the inequality of the solar day. Ptolemy states the problem as follows:
the mean motions which we tabulate for each body are all arranged on the simple system of equal increments, as if all solar days were of equal length. However, it can be seen that this is not so.
What Ptolemy is really getting at here is that the term “day” is somewhat ambiguous. As such, the different ways by which we might measure a “day” are explored in this chapter. Continue reading “Almagest Book III: On the Inequality of Solar Days”