Question

Determine the escape speed of Moon. Given, the radius of Moon is `1.74 xx 10^(6) m`, its mass is `7.36 xx 10^(22) kg`. Does your answer throw light on why the moon has no atmosphere?
`G = 6.67 xx 10^(-11) n m^(2) kg^(-2)`.

Answer 1

Here, `R = 1.74 xx 10^(6) m`,
`m = 7.36 xx 10^(22) kg`, ,
`G = 6.67 xx 10^(-11) Nm^(2) kg^(-2), upsilon_(e) = ?`
`upsilon_(e) = sqrt((2GM)/(R )) = sqrt((2 xx 6.67 xx 10^(-11) xx 7.36 xx 10^(22))/(1.74 xx 10^(6)))`
`= 2375 ms^(-1) = 2.38 km s^(-1)`
Since, the average thermal speed of the gas molecules like oxygen, hydrogen etc. on the surface of Moon is greater than the escape speed of moon `(= 2.38 km s^(-1))`, hence these gases have escaped from the surface of Moon and Moon has no atmosphere.