Can a Mercury sized moon support an atmosphere?

[willstaruss22]

Lets say there is a gas giant similar to Jupiter orbiting a yellow star similar to our Sun. The planet and moon orbit at a distance that would resemble in between Mars and Earth. So the moon would receive 70% the sunlight that Earth receives. Around this planet exists a moon with 0.064 Earth masses and 0.4 Earth radii. This would put it into the rocky moon category. The moon orbits at Europa's distance from the planet with a slightly eccentric orbit and the interior would be pushed and pulled by interactions with other moons. Could the tidal heating from the planet cause geological activity on the moon and create an atmosphere in the process? If so how thick could the atmosphere become?

 

[Simon Bridge]

A light Moon will not be able to hold on to an atmosphere on it's own, but, it is vaguely plausible that it's atmosphere could orbit in resonance with it due to the action of other satellites.
Certainly been used in SF:

A gas torus is the result of a light mass in orbit around a heavy mass, as Titan orbits Saturn. It may be that the light mass is too weak to hold its atmosphere. The faster molecules of air escape-but they go into orbit about the heavy mass. Thus, Titan circles Saturn within a ring of escaped Titanian atmosphere, as lo orbits Jupiter within a ring of sulfur ionized by Jupiter's ferocious magnetic field.
-- Niven L. The Integral Trees​

It is vaguely plausible that gravitational process could heat the moon to give it a gaseous atmosphere - since you have not specified what the other bodies are doing. It can be as thick as you like - adjust other parameters to suit. However, it would be plausibly a heavy-gas atmosphere and very cold (too hot and the gas molecules exceed escape velocity).

The heating process is unlikely to be subtle.

There are lots of plausibility issues with a Mercury-sized object with a livable atmosphere and comfortable temperatures though. The easiest approach to this sort of thing is to look to other bodies in the solar system.

 

[willstaruss22]

There would be 2 other moons orbiting it and these would be outside of it. 1 would be 0.035 Earth masses and orbit 250,000 km away from the 0.064 Earth mass moon. The other moon would be 0.018 Earth masses and orbit 600,000 km away from the 0.064 Earth mass moon. The eccentricity of the 0.064 mass moon would be 0.008 which would be double the amount of Io's. So I was thinking there would likely be more geological activity and volcanic activity. This moon would orbit at a distance of 400,000 km above the host planets surface.

 

[Simon Bridge]

Sounds like it would be pretty inhospitable yes.

 

[willstaruss22]

Yes it would but since it is receiving 70% less sunlight than Earth I would think there could be reasonable temperatures even with the extra tidal heating.

 

[Simon Bridge]

The trouble with reasonable temperatures is how much of the gas ends up in a ring around the planet instead of around the moon ... but it's your setup.

 

[willstaruss22]

Could the moon enter that gas ring and recapture the gas though? I should mention that I wasn't talking about an Earth thickness atmosphere because with a 0.064 Earth mass moon its unlikely I was more in the lines of an atmosphere 0.01 atm.

Interestingly I found a gas retention chart and with this chart I but in a body with 40% Earths radius 2550 km and density 5.5 at 280 K and found that CO2 could remain indefinitely. However other gases such as nitrogen and oxygen would have to be continuously gained or else they would disappear in a few million years and water would remain an even shorter time.

http://astro.unl.edu/naap/atmosphere/animations/gasRetentionPlot.html
I had no idea this link even existed.

 

[Simon Bridge]

The thing is that the gas ring is the gas that has too much kinetic energy for the moon to hold onto ... if you want the moon to plausibly pick it up again, you'll end up with something more like Niven's "Smoke Ring".

Of course, you could say that your system is very young?
This is SF right?

 

[willstaruss22]

Yes it is.

 

[Simon Bridge]

Well there you go.
Anything the characters won't see need not be explained in detail.