Chapter $11$ of this book is simply the Planetary Equation Tables. I have transcribed them and make them available as a Google Sheet. Continue reading “Almagest Book XI: Planetary Tables of Anomaly”
Almagest Book XI: Saturn’s Epoch Position
Our next step is to determine the epoch position for Saturn. Continue reading “Almagest Book XI: Saturn’s Epoch Position”
Almagest Book XI: Saturn’s Periodic Motion
Ptolemy now walks us through his supposed method for determining the periodic motions of Saturn. I say “supposed” because, again, Ptolemy’s final result doesn’t quite match what he tells us here. But we’ll follow along anyway.
As usual, he begins with an observation from the Babylonian astronomers: Continue reading “Almagest Book XI: Saturn’s Periodic Motion”
Almagest Book XI: Determining the Size of Saturn’s Epicycle
Next, we’ll turn our attention to determining the size of Saturn’s epicycle. As he did for Jupiter, Ptolemy introduces a new observation. Continue reading “Almagest Book XI: Determining the Size of Saturn’s Epicycle”
Almagest Book XI: Checking the Eccentricity and Apogee of Saturn
Our next step in calibrating Saturn’s model, is to verify that the steps we’ve taken so far is able to reproduce the original observations. Continue reading “Almagest Book XI: Checking the Eccentricity and Apogee of Saturn”
Almagest Book XI: Second Iteration for Saturn
With our corrections for the intervals from Saturn’s oppositions in hand, we’re ready to repeat the calculation. As with before, I’m doing this in a Google Sheet to speed things along. This means that I’ll be using modern trig and that the figures I give her may be subject to some rounding as we go since the Sheet is saving higher precision behind the curtain.
We’ll begin with the same diagram as before:
Continue reading “Almagest Book XI: Second Iteration for Saturn”
Almagest Book XI: Corrections for the Equant
Now that we’ve done our initial determination of the eccentricity for Saturn, and the position of its line of apsides, we’ll work on making the first, and only, iterative correction to these. We’ll again start by finding corrections to the angles for each opposition beginning with a diagram that should look familiar. Continue reading “Almagest Book XI: Corrections for the Equant”
Almagest Book XI: Saturn’s Eccentricity
The last planet we’ll need to determine the eccentricity and line of apsides for is Saturn. To do so, we’ll follow exactly the procedures we developed previously. And again, we’ll begin with three observations. Continue reading “Almagest Book XI: Saturn’s Eccentricity”
Almagest Book X: Preliminary Comments Regarding the Models for Superior Planets
Having completed the preliminary models for the inferior planets, Mercury and Venus, Ptolemy now turns his attention towards the superior ones: Mars, Jupiter, and Saturn. Continue reading “Almagest Book X: Preliminary Comments Regarding the Models for Superior Planets”
Almagest Book IX: On the Order of the Spheres
Having laid out “the sum total of the chief topics one may mention as having to do with the fixed stars, in so far as the phenomena [observed] up to now provide the means of progress in our understanding” Ptolemy now moves on to “the treatment of the five planets”. While you might expect that, since we have five books left and five planets, that each would be covered separately. However, that’s not the case. This is because the general model of the planets are largely similar. Mercury will be an exception1, but all of the other planets share a basic model. What is different is how we will derive those orbital elements as the observations necessary to do so differ between the inferior and superior planets.
And, since the models are similar, Ptolemy first proposes that we “avoid repetition” by “explain[ing] the theory of the [planets] by means of an exposition common [to all five], treating each of the methods [for all planets] together.”
Beginning this discussion, Ptolemy introduces us to the order of the spheres for these planets, the sun, and moon. Continue reading “Almagest Book IX: On the Order of the Spheres”