Question

Using the escape velocity calculator what is the escape velocity for earth? note the mass of earth is 5.97 x 1024 kg and a radius of 6.4 x 106 m

Answer 1

The escape velocity for a planet of mass M and radius R is given by

`v= \sqrt{ (2GM)/(R) }`
where

`G=6.67 \cdot 10^(-11) m^3 kg^(-1) s^(-2)` is the gravitational constant.

Using the data of the Earth:

`M=5.97 \cdot 10^(24) kg`

`R=6.4 \cdot 10^6 m`

we find the escape velocity for Earth:

`v= \sqrt{ (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`