Hacker News Reader

Comment by swamp40 | Hacker News Reader

> "The moon isn’t an obvious reservoir of water. “It’s really weird when you stop to think about it,” said Mark Robinson, a planetary scientist at Arizona State University. Its lack of atmosphere and extreme temperatures should cause any water to almost instantly evaporate."

Wouldn't the water vapor get pulled back to the moon via gravity?

View on HN

Gases escape if their molecular velocity exceeds the escape velocity of the planetary body. That's why smaller and hotter objects lack an atmosphere.

    hydrogen = 1 (atomic weight)
    carbon   = 6
    oxygen   = 8

    H2O = 10
    O2  = 16
    CO2 = 22

Since the moon's gravity is too weak to hold the (heavier) latter two, I conclude that it must also be too weak to hold water molecules, which are lighter still.

Umm, not quite.

H = 1

C = 12 (6 protons, 6 neutrons)

O = 16 (8 protons, 8 neutrons)

H2O = 18

O2 = 32

CO2 = 44

Also, the connection between atmosphere retention and gravity isn't quite so direct. If you positioned a molecule of H2O (or even H2) directly above the surface of the moon with no net velocity, it will fall to the ground. However, once it hit the ground, it would thermalize with the surface and could be ejected in any direction at a range of speeds (or react with the surface and never leave).

The simple/approximate method to compute the stability of the atmosphere is to compute the escape velocity for the body and the Maxwell-Boltzmann distribution of speeds for the gas (which does not depend on gravity). You then integrate the probability distribution P(v) (probability of velocity v) for speeds greater than the escape velocity to infinity. This might result in a case where all gases eventually make their way away from the body, but heavier gases simply take longer.

Not to mention, the gravitational acceleration felt by a body is independent of its mass, so the atomic weight of the gas molecules makes no difference to the acceleration they experience anyway.

The reason "lighter" gases float above "heavier" gases under gravity is not because of different gravitational acceleration but because of buoyancy.

Reply on news.ycombinator.com