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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, in that previous post we showed that an line extended through the observer from one of the observations did not have a length of $120^p$ which affirmed that the observer was still off center.

So in this post, we’ll use that information to determine how far off center so that we can complete the task we set about. Continue reading “Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 2”

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Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 1

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.

As with many previous posts, we’ll start with a series of observations. He tells us that these observations were taken using the “astrolabe”. However, we need to recall that what Ptolemy called the astrolabe, we would think of as an armillary sphere. Thus, the methodology here was to align the equatorial ring with the celestial equator, and ensure that, when the star was sighted, its position was $180º$ from the calculated position for the mean sun.

So here are the observations: Continue reading “Almagest Book X: Preliminary determination of Mars’ Apogee & Eccentricity – Part 1”