Tracing the history of medieval astronomy
Having computed the lunar parallax,
the sun’s parallax for a similar situation [i.e., as measured along an altitude circle] is immediately determined, in a simple fashion (for solar eclipses) from the number in the second column corresponding to the size of the arc from the zenith [to the sun].
Well that sure sounds easy. Let’s look at a quick example. Continue reading “Almagest Book V: Calculating Solar Parallax Along a Great Circle Through the Zenith”
Now that we’ve completed the parallax table, we should discuss how to use it. As usual, Ptolemy will now walk us through the steps, but does not provide an explicit example so I’ll follow an example from Neugebauer1, to help illustrate the procedure.
As our goal, Ptolemy states that our goal is to find
the moon’s parallax at any given position, (first) with respect to the great circle drawn through the moon and zenith
Continue reading “Almagest Book V: Calculating Lunar Parallax Along Great Circle Through Zenith”
As usual, the weather in January and February of this year hasn’t cooperated. Nights were consistently cloudy during good moon phases or the temperatures well below freezing.
But as March has rolled around, temperatures have begun to warm, and the forecast called for a clear night with a good moon phase so Yseult and I headed out to Danville Conservation Area to do some observing. Continue reading “Data: Stellar Quadrant Observations – 3/6/2021”
Upcoming Classes
In the previous chapter, we worked out the parallax for the sun and the moon at 4 different positions. Next, we determined how we might make some corrections for the moon if it were between the positions we described, breaking the corrections into ones for the epicycle and for the eccentre. From that work, Chapter $18$ presents the results in tabular format. Since this one is pretty wide, I’ve again made the decision to put it into a Google Sheet.
It’s been a few weeks since I’ve posted anything but it’s not because I haven’t been busy on astronomy. My recent activity just hasn’t been in the Almagest or observing. Rather, I’ve been working on some classes.
So far in this chapter, we’ve reviewed how to calculate the lunar parallax for certain limits of the lunar position and looked at what’s necessary to estimate the effects for lunar positions away from those limits due to the epicycle. Now, we need to discuss the impact of the eccentre and how that we can estimate the effect on parallax due to it bringing the moon closer and further.
So let’s set up a generic diagram of our eccentric model, ignoring the epicycle and only concerning ourselves with the mean moon:
Continue reading “Almagest Book V: Lunar Distance Adjustments for Eccentre”
In the last post, we explored how to calculate parallax if the distance to an object is known and its distance from the zenith. This was done for the sun and the moon at four different distances. However, because the moon varies so widely in distance in Ptolemy’s model, we need a way to estimate between those positions and we’ll begin by looking at the effect the epicycle has on distance for various points throughout its cycle. To help us, we’ll start with a new diagram:
Continue reading “Almagest Book V: Lunar Distance Adjustments for Epicycle”
Now that Ptolemy has worked out his model for the sun and moon in earth radii, we can use this result to calculate parallax for any position in our model. To begin, we will calculate
the parallaxes with respect to the great circle drawn through the zenith and body.
This is essentially the reverse calculation of what we did in this post, so we can reuse the same diagram:
Continue reading “Almagest Book V: Parallaxes of the Sun and Moon”
Now that we’ve worked out a distance to the sun and moon, as well as the angular diameter, we can put these together to determine the sizes which is what Ptolemy seeks to do in this chapter. Fortunately, we don’t need a new diagram and can simply make reference to the one we used in the last post:
Continue reading “Almagest Book V: Size of the Sun, Moon, and Earth”
