I am currently re-reading Les Epicuriens on the train on my way to/from work, and in the process of trying to imagine or re-construct what these lectures or discussions consisted of as far as possible, so that we can create modern dialogues around these issues to replace the literature that is missing.
Book 10
Discusses a bit about the nature of Time, how to measure it (mentions days and nights), the use of conventional language for it and the fact that time is real.
Book 11
Discusses objects that float in the air, says "certain people conceive Earth circled by walls … and suppose that Earth is in the center of everything".
Discusses where the sun rises and sets and distance; various models to interpret this. The commentators categorize this book as a polemic against the ancient astronomers who were using certain tools or machines (alluded to in this book) to evaluate the movements of celestial objects, and against Eudoxus' geocentric model. I looked this up and found this about Eudoxus of Cnidus:
http://cmb.physics.wisc.edu/pub/tutorial/briefhist.html
An astronomer named Eudoxus created the first model of a geocentric universe around 380 B.C. Eudoxus designed his model of the universe as a series of cosmic spheres containing the stars, the sun, and the moon all built around the Earth at its center. Unfortunately, as the Greeks continued to explore the motion of the sun, the moon, and the other planets, it became increasingly apparent that their geocentric models could not accurately nor easily predict the motion of the other planets.
The next section of the 11th book is on what sustains Earth from below and seeks to explain its stability. Epicurus argued that densities below and above provide counter-balance to each other, to maintain the "appropriate analogical model" for the immobility of Earth. He said that the Earth was "equidistant to all the sides", and so it didn't fall in any direction because it had similar pressure from all sides.
Now, since Epicurus believed the universe was infinite, we know that he would have rejected the Earth-centered model because an infinite model of cosmos would not have a center and all things would be relative to each other, there would be multiple centers. He is, in essence, explaining what an orbit is--an organized dance that acquires a certain balance of pushing and pulling and falling--without really having the word "orbit" for it.
Here, from his use of "appropriate analogical model" which he presumably was trying to create, it is clear that he is using the Epicurean method of looking at things that can be observed and reasoning by analogy. This means that he appealed to how we can see that things of similar weight balance each other's forces, and he's applying that logic to the orbit of the Earth.
Book 12
Eclipses.
I've noticed that E is addressing in each of these books phenomena that caused superstitious fear and panic in the ancients, or mythical explanations. Obviously, the orbit of the sun was a huge mystery and inspired the entire mythos of the Egyptian god Ra, while the phases of the moon inspired the Osiris mythical cycle. These were the common explanations in antiquity.
I also surmise that some ancients, particularly those who rejected the myths and observed nature, would have observed that eclipses and phases of the moon apparently showed the shadow of the Earth against the moon, and would have reasoned that the Earth was round from the observation of its shadow against the moon. This is not mentioned in this book, but it would have been consistent with the Epicurean method to conclude the Earth was round.
According to Philodemus, in book 12 (not extant portion) Epicurus said that humans had the idea of "certain imperishable natures" and this book appears to address theology also.
Book 13
Philodemus says that here, E addressed the "rapports of affinity, and also of hostility, that gods have with certain persons".
So this seems to continue the conversations about gods in the previous book.
