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I just read stability of hypothetical lunar atmosphere. From the correct answer, i understand, the low escape velocity from Luna is part of the reason it is unable to retain an atmosphere.

Titan apparently has a comparable escape velocity

  • Titan = 2.65 km/sec
  • Luna = 2.4 km/sec

; yet Titan maintains an atmosphere.

Why? What have I missed? Does Luna's relative proximity to Sol make the difference?

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Both rody_o, and jefromi hit the right points. I've opted to mark jefromi's reply as correct because it is easier for a layman as me to comprehend –  Everyone Jul 13 '12 at 7:24
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3 Answers 3

up vote 6 down vote accepted

There are a few differences between Luna and Titan.

One of the primary mechanisms for atmospheric loss is thermal escape. Titan is much colder. The particles which escape are essentially the tail of the Maxwell-Boltzmann distribution, the portion with velocity higher than the escape velocity. This end of the distribution is dominated by an $e^{-E/kT}$ contribution, so as you'd expect, lower temperature means fewer particles with enough kinetic energy to escape. Note also that since we care about escape velocity, while the distribution is really about energy, more massive particles won't escape as easily. Titan's atmosphere is mostly nitrogen, while the moon is mostly helium and argon. The helium in the moon's atmosphere is easily lost, since it's so much lighter.

Another big cause of atmospheric loss is the solar wind. Titan itself doesn't have a magnetic field to protect it from the solar wind, but it does happen to orbit an enormous planet with a magnetic field. Titan is protected from the solar wind by Saturn's magnetosphere. Titan orbits at about 20 $R_S$, while the magnetopause is somewhere between 16 and 27 $R_S$, so Titan is inside the magnetosphere a substantial amount of the time. There are a lot of complications due to passing through the magnetopause, but from what I understand, the net effect is definitely protective. And of course, Titan is farther from the sun, so the solar wind is weaker.

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My guess would be that since

  • Titan is 80% more massive than Luna, so the escape velocity is somewhat larger as well
  • it is a lot colder there -- N$_2$/CH$_4$ molecules moving a lot slower on average
  • there is considerably less Solar wind to blow particles from the top layers away

Titan can hold its atmosphere indefinitely.

I haven't done any calculations or so, so you might want to check if hydrostatic equilibrium indeed holds for Titan and its atmosphere, or if it's a transient phenomenon.

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The escape velocity difference appears to be minor; hence my question. Titan = 2.65 km/sec Luna = 2.4 km/sec –  Everyone Jul 12 '12 at 23:54
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@Everyone A small difference in escape velocity can make a big difference in the loss rates because the loss happens at the end of a exponentially dropping velocity distribution. –  dmckee Jul 13 '12 at 17:52
    
@dmckee: That didn't occur to me ... good point. –  Everyone Jul 13 '12 at 19:40
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The moon did not have an atmosphere to begin with. It was formed out of debris from when a planetoid crashed into the earth. The resulting lava hardened into the moon. Titan naturally formed with an atmosphere.

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The moon has an atmosphere: see the wiki. The moon is outgassing all the time, but simply unable to hold it there indefinitely. –  Rody Oldenhuis Jul 12 '12 at 19:21
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