# What is the critical mass of a planet to have an atmosphere like Earth's?

Small planets/orbits like Moon cannot have atmosphere because of their masses. They don't have enough gravity to hold an atmosphere. Then what is the critical mass that makes enough gravity to keep an atmosphere?

Please explain by Mathematical equations with the data given below:
Density of the planet is uniform everywhere; 5 g/cm3.
The atmosphere consists of pure O2 gas.
Temperature of the the atmosphere is uniform everywhere and fixed to 300K.
What is the critical size of radius or mass of this planet that makes it possible to have an atmosphere?

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Is this homework? –  Jaime Nov 30 '12 at 17:33
@Jaime: No, it is not. –  hkBattousai Nov 30 '12 at 21:32
You can calculate the mass of the planet, therefore the gravitational attraction. You can also calculate thermal escape from the planet. An atmosphere can be held if escape is not too large. In reality you also need to take into account the stellar wind but from the questioning it looks like it's negligible. It does look like an exercise from a textbook. –  gerrit Dec 1 '12 at 16:01