As we saw for the sun, to be able to use the tables of mean motion to predict the position of the moon, we’ll need to know where the moon was at a specific point in time. Ptolemy chooses as that point in time as the beginning of the first year of the Nabonassar reign. To determine the position of the moon on this date, Ptolemy starts with the second eclipse of the Babylonian triple we discussed in the last chapter and then calculates backwards.
As a reminder, that eclipse took place
in the second year of Mardokempad, Thoth 18/19 in the Egyptian calendar, 50 minutes before midnight.
Ptolemy calculates the interval between the epoch and that date as
27 Egyptian years, 17 days, 11 hours, and 10 minutes.
If we then take that interval and add up the corresponding motion in the lunar mean motion table we would find that the moon advanced $123;22º$ in longitude and $103;35º$ in anomaly1. So to undo that motion to get back to the epoch date, we’ll need to subtract those values from the positions found for the eclipse in question which we covered in this post.
We had determined the position of the mean moon to be $14;44º$ into Virgo which is $164;44º$ ecliptic longitude. So subtracting $123;22º$ leaves us with $41;22º$ ecliptic longitude which is $11;22º$ into Taurus.
We also found that the moon was $12;24º$ in after apogee2. Subtracting the change in anomaly, we determine that it was $268;49º$ after the apogee at the beginning of the epoch.
Lastly, we can also determine the position of the moon’s elongation. We’ve only touched on this briefly when we talked about the motions of the moon, but elongation is just how far from the sun along the ecliptic an object3 is. So while we could reverse calculate this like we did4 above. But we don’t really need to since we just calculated the position of the moon, and have already calculated the sun’s position at the beginning of the epoch as well.
So the sun was at $330;45º$ ecliptic longitude, and the moon was at $41;22º$. This means that the sun isn’t quite back around to apogee yet, but the moon is already past it. So taking that difference, we get that the moon is $70;37º$ ahead of the sun5.
Thus, we have calculated three of the four initial positions for the beginning of the epoch. We haven’t covered the motion in latitude yet. As with the anomaly, Ptolemy wants to make a correction to it as well which will be the subject of the next chapter!
- Around the epicycle.
- This would be $12;24º$ clockwise on the epicycle from apogee since that’s how Ptolemy has the model set up. However, since this is opposite the direction of motion for the mean moon on the deferent, it would produce a negative equation of anomaly.
- Often a planet.
- Or more accurately, didn’t. Because we’ve seen how to do use the motion tables enough times now.
- Which is to say, $70;37º$ elongation.