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Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 2

In the last post, we began the process of determining Mars’ eccentricity and the position of apogee. The technique is fundamentally similar to the three eclipse method used for the moon, but the presence of the equant is throwing a wrench in things.

Specifically, right at the beginning of the last post we had to make an assumption about $\angle BDG$ that we know was incorrect. We’re not quite ready to address that, but for now we’ll work on finishing finding the line of apsides as well as the eccentricity as if that assumption were correct. Then, in future posts, we’ll go about trying to iteratively correct that assumption. Continue reading “Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 2”

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Almagest Book X: Observations and Introduction to Iterative Calculations for Apogee and Eccentricity

In the last Almagest post, Ptolemy explained that for the models of the superior planets, we’ll be needing to use oppositions. So with that explained, we’ll begin by working to develop the model for Mars by looking at its eccentricity and apogee. However, this isn’t going to be nearly as straightforward as it has been previously. As we’ll see, we’re missing some of the angles and arcs that would be needed for this. Thus, Ptolemy is going to use an iterative method to close in on them. Continue reading “Almagest Book X: Observations and Introduction to Iterative Calculations for Apogee and Eccentricity”