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”
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 5ยบ, 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”