Question

if a mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth, what will be the escape velocity for that planet?

Answer 1

calculation of the escape velocity

Explanation:

Escape Velocity:

The escape velocity is the velocity required for an object to overcome the gravitational pull of the planet that object is on and the escape velocity of Earth is given by:

$v_{e} = \sqrt{\frac{2GM}{r}}$                                                       (1)

where,   G=6.67*$10^{-11}$$m^{3}kg^{-1}s^{-2}$

              r=6.38*$10^{6}$m

              M=5.98*$10^{24}$kg

Hence the value of escape velocity of earth by substituting these values is given by:

$v_{e}$ =11.2km$s^{-1}$                                                     (2)

Now according the question the mass of planet is 8 times the mass of earth and radius is twice the earth:

So using these conditions in equation (1)

we will have

$v_{p} = \sqrt{\frac{2G(8M)}{2r}}$  

which implies

$v_{p} = \sqrt{\frac{G(8M)}{r}}$

$v_{p} = \sqrt{\frac{4*2GM}{r}}$    

$v_{p} =2* \sqrt{\frac{2GM}{r}}$

 $v_{p} =2* v_{e}$

Substitute the value from equation (2)

$v_{p} =2* 11.2kms^{-1}$

$v_{p} =22.4kms^{-1}$