The best material I've come across regarding this is an article titled "Symbolism of the Sphere" by Michael R. Molnar in the June 1998 Celator. In short, it's not a globe representing the Earch that's depicted, a common falacy, but a sphere, or
orb, symbolizing the Cosmos.
This is clear on well-engraved, struck, and preserved coins such as the one
Pat just shared with us. There you see not land or oceans depicted but astronomical/astrological markings. Most of these orbs are smooth from die wear or circulation wear, thus the common misunderstanding that this is a globe representing the Earth.
It's believed, as you said, that orbs used on
Roman coins symbolized a god, most commonly
Sol or
Jupiter, conferring power to an emperor, handing him the Cosmos. There are other depictions too, including but not limited to
Italia sitting on top of the
orb, which symbolized her presiding over the cosmic sphere, or everything.
Just took a look again at this article, and it describes the X on Pat's coin, mine, and others as an equinoctial
cross, representing the
spring and autumnal equinoxes, symbolizing the belief in the cosmic cycles of birth, death, and rebirth, rooted in Greek philosophy, and discussed by
Plato, Pliny, Aratus, and Manilius.
Another common marking on these orbs, on other coins, is a grid system originated by Greek astronomers to locate stars and planets.