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Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a liquid or solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Ceres is just outside the snow/frost line based upon my calculations.
3. When I could find them I used melting & boiling points for 0.1 atmosphere pressures. When I couldn't find those I used those for 1.0 atmosphere.
4. Tweaking the fudge factor is tricky. Tweak it too high and Mars gets too much atmosphere. Tweak it too low and Titan doesn't get enough. I think I found a happy compromise since Ganymede doesn't get any, Titan has one as long as there's some replenishment, and Mars lost most of its atmosphere.

Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a liquid or solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Ceres is just outside the snow/frost line based upon my calculations.
3. When I could find them I used melting & boiling points for 0.1 atmosphere pressures. When I couldn't find those I used those for 1.0 atmosphere.
4. Tweaking the fudge factor is tricky. Tweak it too high and Mars gets too much atmosphere. Tweak it too low and Titan doesn't get enough. I think I found a happy compromise since Ganymede doesn't get any, Titan has one as long as there's some replenishment, and Mars lost most of its atmosphere.
5. Red background means half-life < 100,000,000 years
6. Yellow background means half-life < 4,500,000,000 years
7. Green background means half-life > 4,500,000,000 years
8. White background means substance isn't a gas at those conditions

Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a liquid or solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Ceres is just outside the snow/frost line based upon my calculations.
3. When I could find them I used melting & boiling points for 0.1 atmosphere pressures. When I couldn't find those I used those for 1.0 atmosphere.
4. Tweaking the fudge factor is tricky. Tweak it too low and Mars too much atmosphere. Tweak it too high and Titan gets too much. I think I found a happy compromise since Ganymede doesn't get any, Titan has one as long as there's some replenishment, and Mars lost most of its.

Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a liquid or solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Ceres is just outside the snow/frost line based upon my calculations.
3. When I could find them I used melting & boiling points for 0.1 atmosphere pressures. When I couldn't find those I used those for 1.0 atmosphere.
4. Tweaking the fudge factor is tricky. Tweak it too high and Mars gets too much atmosphere. Tweak it too low and Titan doesn't get enough. I think I found a happy compromise since Ganymede doesn't get any, Titan has one as long as there's some replenishment, and Mars lost most of its atmosphere.

Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Vesta and Ceres are just inside and outside the snow/frost line based upon my calculations. This may or may not be true.

Yes

With several caveats.

Volatiles

As @Saidoro mentioned, you need to introduce all the volatiles required for life. This includes atmosphere, hydrosphere, and Nitrogen.

It's easy to find enough water and oxygen in the various ice moons and comets throughout the Solar System. However, compared to the amount needed, nitrogen is pretty rare. You'll need to expend some thought about how to get enough.

Longevity

As you can tell by looking at the Moon, the volatiles won't stay around the Moon over geological ages.

So if you do provide the Moon with volatiles, how long can you expect them to stick around?

There are many Atmospheric Loss Mechanisms. Unfortunately, only one of these (Jean's Escape) is easily calculated.

Wikipedia has an excellent and scientific chart showing different body's ability to retain an atmosphere over geologic ages.

However, I've created my own chart based upon Jean's escape. I apply a "fudge factor" to cover the other escape mechanisms and it gives the half-life of different gases around a given body. Be aware that my chart assumes that the body has a thick atmosphere to begin with so certain loss mechanisms such as sublimation and sputtering aren't an issue.

According to my chart, you could expect water added to a thick atmosphere around the Moon to have a half-life of around 200,000 years. A very long time compared to human civilization. A very short time compared to geologic time.

Half-life of gases around major Solar System bodies:

Measured in years

Notes:

1. Any half-life with a value of $\cdot 10^{98}$ is a liquid or solid at the conditions on the surface of that body. Meaning as long as it is surrounded by an atmosphere, there will be no loss of this compound (the reality is that airless bodies will still see some losses).
2. The body Ceres is just outside the snow/frost line based upon my calculations.
3. When I could find them I used melting & boiling points for 0.1 atmosphere pressures. When I couldn't find those I used those for 1.0 atmosphere.
4. Tweaking the fudge factor is tricky. Tweak it too low and Mars too much atmosphere. Tweak it too high and Titan gets too much. I think I found a happy compromise since Ganymede doesn't get any, Titan has one as long as there's some replenishment, and Mars lost most of its.