Caption: A cartoon of our understanding of the atomist cosmology (see David Furley (1922--2010), The Greek Cosmologists, 1987, p. 139--151 (hereafter Fu)).
Our understanding is imperfect because the writings of the early atomists are lost, except for text fragments and imperfect summaries.
The atomist cosmology seems to be mostly due to Democritus (c.460--c.370 BCE), but his predecessor Leucippus (first half of 5th century BCE) contributed ideas (Fu-139).
Note the cartoon is NOT definitive since we do NOT have a precise understanding and maybe neither did the atomists.
The later atomists, the Epicureans (as evidenced by Epicurus (341--271 BCE) and Lucretius (c.99--c.55 BCE)) made slight variations from the original atomist cosmology. The Epicureans had very little interest in natural philosophy, except as a background for their ethics---live, drink, and be merry.
Here we just describe the original atomist cosmology keeping in mind that the atomists created a rational myth from first principles and NOT a derivation from first principles.
Features:
The atomists called the universe το παν (to pan = the all) which is distinct from cosmos in their terminology: see below.
Note the atomists had only a qualitative understanding of mass and motion. They were a long way from Newton's 3 laws of motion.
The atomists certainly got this idea from the rotation of the celestial sphere plus what they probably identified as miniature versions in fluid motion: eddies, whirlpools, and whirlwinds.
There are as many cosmoi formed from the vortices.
We live in our cosmos and can't see out.
By the by, the word cosmos was reputedly introduced into cosmology by Pythagoras (c.570--c.495 BCE) meaning ordered and beautiful system (see Fu-58--60).
They are indeed correct who use cosmology and cosmetology as synonyms.
At some level in the membrane solid land and ocean form a disk. Above is air and maybe below is air too (see Fu-143).
The vortex is still swirling the cosmos around. In the cosmos, the axis of rotation (the celestial axis) has become titled to the north and is ∼ 40° above due north as viewed from Greece. The disk of land and ocean may have been thought of as a bit curved to allow for variations in the altitude of the celestial axis, but this is unclear (see Fu-145). The atomist cosmology was essentially a flat-Earth one.
The fact that it was a flat-Earth cosmology shows that the atomists were obtuse about astronomy and geodesy as understood already in the 5th century BCE when the spherical-Earth theory was already well known with probably with solid evidence.
The membrane like the celestial sphere of the stars was finally ruled out by the Copernican revolution.
The planets, Sun, and Moon were probably closer and swirled in a more complicated way. Democritus did believe the Moon was closest and shone by reflected light from the Sun The atomists seem to have thought of the astronomical objects hot condensations from the formation of the cosmos (see Fu-145).
It is clear that the atomists, both the early and later ones, took very little account of even qualitative astronomy perhaps because astronomy evidenced the spherical-Earth theory and a very large celestial sphere/membrane.
Yours truly thinks that the atomists could have accommodated astronomy if they had tried.