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Titan which is smaller than mars has an atmosphere but mars is not able to maintain atmosphere. Even Luna doesn't have an atmosphere.

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    $\begingroup$ Old question, but I don't see it mentioned below. Titan's atmosphere may be replenished by out-gassing from it's icy surface, crust and perhaps, methane lakes. That may partially explain Venus' atmosphere as well, though with Venus, the process is very different. nature.com/nature/journal/v440/n7080/abs/nature04497.html $\endgroup$ – userLTK Nov 18 '15 at 1:17
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You are right that it's surprising that Titan, being just a moon, has a thick atmosphere. Usually, the answer includes magnetism: Earth has an atmosphere because the liquid magma inside the planet produces a magnetic field. This magnetic field changes the paths of the particles in the solar wind, thus perserving the volatile gases intact. Mars did use to have an atmosphere, just like Earth, but it being farther away from the Sun, the magma froze and lost its magnetic properties.

Titan itself doesn't have a magnetic field, but Saturn does. Saturn's magnetosphere is produced by the motion of the super-compressed hydrogen gas inside the planet (metallic fluid). The field is so strong it encompasses the satellites, including Titan.

Saturn doesn't have the same magma as Earth. Earth is a rocky planet. This means that it was formed so close to the sun that light gases (such as hydrogen) could not coalesce due to the high temperature and the solar wind. Therefore, the inner planets (Mercury to Mars) are composed mostly of rock and metal. It's the liquid iron in the outer core that makes Earth magnetic.

Gaseus planets instead have a small solid metal/rocky core (therefore, no magnetic field from there), and a huge layer of light gases (hydrogen and helium). The gases are not usually magnetic, but under such an enormous pressure they take a 'metallic' structure, which means they can conduct electricity like a metal. This same property allows them to generate a magnetic field.

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  • $\begingroup$ Why did saturn's magma didn't freeze? It is even more farther than the mars from Sun $\endgroup$ – Strikers Dec 24 '14 at 5:53
  • $\begingroup$ The answer was a bit long, so I just inserted it into the answer above. The last two paragraphs. $\endgroup$ – L.R. Dec 24 '14 at 8:46
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Solar wind (a flux of charged particles emitted by the star) is the main cause for celestial body losing its atmosphere. So, to keep an atmosphere celestial body would need a magnetosphere, that it, a magnetic field which deflects protons and electrons of solar wind and prevents them from giving molecules an energy to escape from upper layers of atmosphere.

According to current studies, the source of planetary magnetic field are eddy currents in liquid metal of rotating outer core, caused by convection and Coriolis force, so called "geomagnetic dynamo".

Now, Luna is pretty much geologically dead now. For the case of Mars, it has been hypothesized what its "dynamo" stopped by some reason, in any case it is a fact what Mars has weak and irregular magnetic field. But in case of Titan (which doesn't even have much metal in core), a gas giant with powerful magnetic field comes to rescue and protects its atmospheres from adverse effect of solar wind.

https://upload.wikimedia.org/wikipedia/commons/5/54/Plasma_magnet_saturn.jpg

As an interesting trivia note, it has been hypothesized what this neighboring with radiation belt is the cause of higher hydrocarbons abundance on Titan.

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    $\begingroup$ What about Venus? It has no magnetic field and is much more exposed to solar wind than other atmospheric worlds. (I'm sorry to ask about Venus, since the answers about it generally seem to be: "We don't know") $\endgroup$ – LocalFluff Dec 24 '14 at 5:49
  • $\begingroup$ @LocalFluff, you got me on that! Seriously, it's a really good question and I'd really like to know the answer for (and I wish there would be more Venus studies instead of daydreaming about Mars). Care to post that as question? $\endgroup$ – Free Consulting Dec 24 '14 at 7:24
  • $\begingroup$ It isn't useful to ask questions about it, since there are no answers. Venus is kind of a planet non grata, maybe because it is most like Earth. It is an outlier in most theories. IAU should've defined Venus, not Pluto, to be not a planet. If you like to learn about what is not known about Venus, I recommend Dave Stevenson, here's non-informative lecture of his: youtube.com/watch?v=ORUkiyoYy0E $\endgroup$ – LocalFluff Dec 24 '14 at 7:39
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It's cold out by Saturn, which reduces the tendency of gases to evaporate off into space.

Black body temperature of solar system objects:

  • Earth: distance D = 1 AU (288 K) 16°C
  • Mars: D =1.5 (232 K) -40°C
  • Jupiter: D = 5.2 ( 134 K) -138°C
  • Saturn: D = 9.5 (103 K) -169°C
  • ...........Titan (94 K) -178°C -measured vs calc for others
  • Uranus: D = 19.2 ( 73 K) -199°C
  • Neptune: D = 30.1 ( 63 K) -209°C

    Ganymede, massing 1.5X10^23 kg, vs Titan at 1.3X10^23 kg, has no substantial atmosphere, but it's also a lot warmer due to its proximity to the sun. Nitrogen boils at −196 °C, so it's not impossible that cold days on Titan involve nitrogen rainstorms. Methane and ethane have even higher boiling points

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Simply said, the ability of planet or other body to maintain atmosphere depends on three factors:

  1. Its gravity
  2. Atmosphere temperature
  3. Chemical composition of atmosphere

You can estimate that using the simple formula

$$kT \ll \frac{GMm}{r}$$

Where $k$ is Boltzmann's constant, $T$ is absolute temperature of the gas, $G$ is the gravitational constant, $M$ is planet mass, and $m$ is the mass of particular molecule. If gas molecules satisfy the formula above, their kinetic energy is much less than the depth of potential well of planet's gravity, therefore they cannot escape. So the planet will keep its atmosphere.

In case of Earth, for example, its gravity is not enough to keep Hydrogen and Helium, which have smallest molecular masses ($m$=2 proton mass).

In case of cold atmosphere, the mass of celestial body able to keep it may be quite small. This is the reason, that Titan or Pluto have an atmosphere but Mercury or Moon have not.

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