|MadSci Network: Astronomy|
A particle will escape a planetary body if it is moving away from the planet at or greater than escape velocity, and if it does not collide with another particle prior to escaping. Sir James Jean first made this calculation for Earth and it is called Jean's escape. Basically, you need to know the altitude of the exobase (altitude above which the mean free path is on the order of the scale height), the escape velocity at that altitude, and environmental parameters such as the temperature, composition, and number density. On Earth, the exobase is around 500 km where the temperature is 600 K, the escape velocity is 10.8 km/s and hydrogen atoms move at an average speed of 3 km/s. For your atmosphere infused moon, you will need to make some estimates. Now, assuming that it's even possible to pump air into the lunar atmosphere at a rate capable of bringing the surface level pressure up to 1 bar (not necessarily a reasonable assumption), you will also need the following: 1. Altitude dependent scale height of the lunar exobase H(z) = kT/mg where k=Boltzmann's constant, t = temp (function of surface heating, black body temperature, and dry adiabatic laps rate), m = mass of moon, g = gravitational acceleration (function of altitude). 2. Number density at the exobase (can be calculated using H(z) and integrating the weight of spherical shells from the surface to the exobase) 3. Collisional cross section (sigma) of Oxygen and Nitrogen atoms (most likely dissociated in vi photolysis and ionization in the exosphere which you can look up in phsyics books). If you can calculate these parameters, then you can derive for the altitude of the exobase by solving for the condition where 1/(n*sigma) = kT/mg. Once you have the number density, altitude and temperature of the exobase, you can use the escape flux equation computed by James Jeam (you can look it up) and calculate a general lifetime of the lunar atmosphere. (His calculation includes the Maxwell-Boltzmann distribution of speeds). The above calculations are not easy! They require knowledge of calculus and some general physics and chemistry. But if you get discouraged, remember that our friend James Jean did the same calculation back in 1928 when there were no observational data for the Earth's exobase/exosphere. Good luck!
Try the links in the MadSci Library for more information on Astronomy.