1st Q: It's been said that an astronomical body can keep it's atmosphere if the escape velocity is more than six times the average speed of the molecules.
Gravity isn't the only factor that permits an object to retain an atmosphere. The Moon has gravity yet is virtually a vacuum, Mars has a surface pressure less than 1% of Earth and continues to lose its remaining atmosphere.
Titan has the protection of Saturn's magnetic field, and none of its own. If Titan were moved closer to the Sun the solar wind would quickly strip it's atmosphere.
Wikipedia: Moon
- Surface gravity 1.62 m/s2 (0.1654 g)
- Escape velocity 2.38 km/s
- Surface pressure 10−7 Pa (1 picobar) (day), 10−10 Pa (1 femtobar) (night)
- Temperature - lowest: Lunar Reconnaissance Orbiter measured the lowest summer temperatures in craters at the southern pole at 35 K (−238 °C; −397 °F) and just 26 K (−247 °C; −413 °F) close to the winter solstice in north polar Hermite Crater. This is the coldest temperature in the Solar System ever measured by a spacecraft, colder even than the surface of Pluto.
- Magnetic field - The Moon has an external magnetic field of about 1–100 nanoteslas, less than one-hundredth that of Earth.
Wikipedia: Atmosphere of the Moon
"The atmosphere of the Moon is a very scant presence of gases surrounding the Moon. For most practical purposes, the Moon is considered to be surrounded by vacuum. The elevated presence of atomic and molecular particles in its vicinity compared to interplanetary medium, referred to as "lunar atmosphere" for scientific objectives, is negligible in comparison with the gaseous envelopes surrounding Earth and most planets of the Solar System. The pressure of this small mass is around 3×10−15 atm (0.3 nPa), varying throughout the day, and in total mass less than 10 metric tonnes.2 Otherwise, the Moon is considered not to have an atmosphere because it cannot absorb measurable quantities of radiation, does not appear layered or self-circulating, and requires constant replenishment due to the high rate at which its gases get lost into space.".
Wikipedia Mars
- Surface gravity 3.72076 m/s210 (12.2072 ft/s2; 0.3794 g)
- Escape velocity 5.027 km/s (18100 km/h; 11250 mph)
Surface pressure 0.636 (0.4–0.87) kPa 0.00628 atm
$\begin{array}{lc}\text{Surface temp.} & \text{min} & \text{mean} & \text{max} \\
\text{Kelvin} & 130 \text{ K} & 210 \text{ K} & 308 \text{ K} \\
\text{Celsius} & −143 \text{ °C} & −63 \text{ °C} & 35 \text{ °C} \\
\text{Fahrenheit} & −226 \text{ °F} & −82 \text{ °F} & 95 \text{ °F}\end{array}$
Magnetic field - Incomplete. Mars does not have a global magnetic field which guides charged particles entering the atmosphere.
Wikipedia: Atmosphere of Mars
"The atmosphere of Mars is the layer of gas surrounding Mars. It is primarily composed of carbon dioxide (94.9%), molecular nitrogen (2.6%) and argon (1.9%). It also contains trace levels of water vapor, oxygen, carbon monoxide, hydrogen and other noble gases. The atmosphere of Mars is much thinner than Earth's. The surface pressure is only about 610 Pascal (0.088 psi; 6.1 mbar), which is less than 1% of the Earth's value. The currently thin Martian atmosphere prohibits the existence of liquid water at the surface of Mars, but many studies suggest that the Martian atmosphere had been much thicker in the past. The atmosphere of Mars has been losing mass to space throughout history, and the leakage of gases still continues today.".
Wikipedia: Titan
- Surface gravity 1.352 m/s2 (0.138 g) (0.835 Moons)
- Escape velocity 2.639 km/s (0.236 Earths) (1.11 Moons)
- Surface pressure 146.7 kPa (1.45 atm)
- Temperature 93.7 K (−179.5 °C)
- Magnetic field - Temporary, courtesy of Saturn.
Atmosphere: "Saturn's moon Titan and Jupiter's moon Io have atmospheres and are subject to atmospheric loss processes. They have no magnetic fields of their own, but orbit planets with powerful magnetic fields, which protects these moons from the solar wind when its orbit is within the bow shock. However Titan spends roughly half of its transit time outside of the bow-shock, subjected to unimpeded solar winds. The kinetic energy gained from pick-up and sputtering associated with the solar winds increases thermal escape throughout the transit of Titan, causing neutral hydrogen to escape.15 The escaped hydrogen maintains an orbit following in the wake of Titan, creating a neutral hydrogen torus around Saturn.".
2nd Q: Does this mean if a moon like Titan was moved to the habitable zone and heated up to livable temperatures, then it's atmosphere would escape?
Yes.
On June 13 2007 (and other dates) Titan ventured outside of the protection of Saturn's magnetic field, it remained temporary magnetized for 3 hours. It happened that Cassini was in a good position to get a few photos (scroll to the bottom).
Earth's magnetic field protects it from solar wind, and preserves our atmosphere.
Some interesting (but lesser related to the question) videos of Titan's atmosphere:
A video of Titan's surface is available from NASA: "A World Unveiled: Cassini at Titan" (Aug 11 2017). The video: "Titan Touchdown" shows the landing on the surface (Jan 11 2017). Data from Cassini's radar converted into a colorized movie is shown in the video: "Flying over an Extraterrestrial Land of Lakes" (Dec 12 2013). A narrated video of the landing: "View of Titan From Huygens" is also available.
