How believable is it that a planet's MOON has an Earth-like, oxygen atmosphere?
Saturn's moon Titan has a thick, nitrogen-based atmosphere, quite possibly like Earth's primordial one. Despite its small size and gravity considerably weaker than that of Earth, Titan is able to retain its atmosphere because it is farther away from the sun than Earth, and consequently colder. But it wouldn't be much of a stretch to postulate a gas giant planet orbiting at a distance from its parent star to be in the right place to have a moon of proper size and gravity and temperature conditions to have an "earth-like" atmosphere. We now know that gas giant planets can orbit quite far closer to their parent stars than Mercury is to the Sun.
The sticker is the oxygen. The free oxygen in Earth's atmosphere is there
only as a consequence of organic life. Oxygen is highly reactive, and is constantly being resupplied on Earth via photosynthetic reactions of plants. It would simply not be found in a free state in a planetary atmosphere
unless there existed some form of biotic production of it. You're just not going to find a lifeless planet with oxygen in its atmosphere.
Another significant matter is the probable necessity of having a nitrogen-dominated atmosphere. Nitrogen and oxygen are close enough in molecular weight that they mix well to form the dominant gases in the atmosphere of Earth. Earth's gravity is too weak to hold free hydrogen or helium, or even significant amounts of methane and ammonia, long-term, because these gases are all considerably lighter than oxygen and nitrogen. Argon, the third most common gas in Earth's atmosphere, is somewhat heavier, and is constantly replenished by way of radioactive decay of potassium-40, the most abundant radioactive isotope in the Earth's crustal rocks. Carbon dioxide, on the other hand, is significantly heavier than nitrogen and oxygen, and Mars is a good example of the consequence of this factor. Its atmosphere is almost entirely CO2, which with it's 1/4 G gravitational pull, it is able to retain, but only in a very attenuated form. The lighter gases like nitrogen and oxygen (if such ever was produced by a Martian biota) probably escaped into space.
Some approximate figures on the molecular weights of common gases (at earth-like temperatures) in the universe:
H2 (diatomic hydrogen) = 2
He (helium) = 4
CH4 (methane) = 16
NH3 (ammonia) = 17
Ne (neon) = 20
HCN (hydrogen cyanide) = 27
N2 (diatomic nitrogen) = 28
C2H6 (ethane) = 30
O2 (diatomic oxygen) = 32
H2S (hydrogen sulfide) = 34
Ar (argon) = 40
CO2 (carbon dioxide) = 44
C3H8 (propane) = 44
The heaviest known substance that exists in a gaseous state at normal atmospheric temperatures and pressures on Earth is OsO4, osmium tetroxide, with an atomic weight of 254. It is also deadly poisonous, but thankfully only exists via laboratory production.
My invoice for this 50-cent lecture will be available via PM on request.
caw