Tass wrote:The result is that for a truly tiny planet to hold on to an atmosphere, it needs to be so dense that its gravity is actually stronger than earths. -The air has such a short distance to travel to freedom so the pull needs to be greater.
Obviously, the solution is to make gravity 10x that of earth's gravity, so we can increase our power levels.
On a more on-topic note, I've been making a Matlab calculator for this, where you enter the Radius and Surface Gravity of a sphere, and it gives you the mass, density, and escape velocity (yet to add Atmosphere size). I tested it with Earth's Radius and with g = 9.81m/s^2, and so far it agrees with the wikipedia.
With a 0.4 Earth Radius body, the escape velocity is ~7km/s, compared to Earth's 11km/s. It's density would have to be 14,000kg/m3, compared to Earth's 5,500kg/m3.
edit: Actually, upon thinking and research, technically the atmosphere would slowely decrease over time unless there was an input, due to the statistical nature of the speed of particles in a gas in relation to temperature. Therefore, The Little Prince's atmosphere would be dependant on his volcanoes outputting enough gas to keep the atmosphere thick enough to breath, although a 15m/s escape velocity won't help him too much...
edit again to prevent doubleposting. I found This source
which, on page 4, has a diagram that suggests that the smallest escape velocity that allows for an earth-like atmosphere would be 1.2 km/s with an upper atmosphere at a temperature of 50K (and I will assume that it is that low due to a lack of solar winds and UV rays heating the upper atmosphere). My model, uppon trying a number of radii, had an escape velocity of 1200m/s at a surface gravity of 10m/s^2 and a radius of 75km
. This is pretty small, about 7% the radius of Pluto, but it would have a mass of 8.43 * 10 ^ 20kg (or 843 zettagrams, which is just 1000 times lighter than earth) and a density of 4.77*10^5 Kg/m^3 (47g/cm^3), or roughly 100 times as dense as earth.
For reference, Minmus in KSP is 60km in radius, although because it's density is 1/20th that of our theoretical planet, it would not support an atmosphere as we know it.
Laythe, with a radius of 500km and a gravity of 0.8G, fits within that atmosphere band as well, and would only be 10 times as dense (5.7 kg/m^3) and 1% the mass of earth, despite being half the radius of Pluto.
So in summary, the smallest possible livable atmosphere would be for a planet of 75km radius, but something the size of Laythe is probably more possible, given densities required. In either case, this theoretical planet is going to be made of something dense. Something like Laythe, if it had earth gravity, would be 500km @ 10m/s^2, with density of 7100 kg/m^3 (or 7g/cm^3). The element 'mercury', or the earth's iron core, has a density of 13g/m^3, so if our planet had a core made of mercury, with a silicon crust on top and a nice gas giant nearby to shield it from radiation, it could feasibly exist.TLDR
: Laythe is theoretically possible, as well as Endor or Yavin IV from Starwars, or any other small moon-sized earth-like planet.