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# Escape Velocity of Gas Molecules

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What would the temperature of the Earth's atmosphere have to be such that the average speed of a hydrogen molecule(H2) is Equal to the Earth's escape velocity? What about an oxygen molecule (O2)?

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The escape velocity for a planet or satellite is equal to the square root of 2 times the mass and gravitational constant, divided by the radius. For Earth, in SI units, this equals:

Vesc = SQRT (2*Mass*G/r)
Vesc = SQRT (2 * 5.976e24 * 6.672e-11/6378000)
Vesc = 11182 ms-1

Where G = 6.672e-11 Nm^2Kg^-2 is the ...

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