The escape velocity for a planet of mass M and radius R is given by
[tex]v= \sqrt{ \frac{2GM}{R} } [/tex]
where
[tex]G=6.67 \cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the gravitational constant.
Using the data of the Earth:
[tex]M=5.97 \cdot 10^{24} kg[/tex]
[tex]R=6.4 \cdot 10^6 m[/tex]
we find the escape velocity for Earth:
[tex]v= \sqrt{ \frac{2 (6.67 \cdot 10^{-11} m^3 kg^{-1}s^{-2})(5.97 \cdot 10^{24} kg)}{(6.4 \cdot 10^6 m)} }=1.12 \cdot 10^4 m/s = 11.2 km/s[/tex]
