Question

Solve the problem.

If the 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

Escape velocity for Earth is

\[v_{esc} = \sqrt{\frac{2G M_e}{R_e}} = 11 . 2 km/s\]

Given:
Mass of the planet, M_p = 8 `× ` Mass of the Earth (M_e) 
Radius of the planet, R_p = 2 `× `Radius of the Earth (R_e)
Thus, the escape velocity of the planet is

\[v_{esc}' = \sqrt{\frac{2G M_p}{R_p}} = \sqrt{\frac{8}{2}}\sqrt{\frac{2G M_e}{R_e}} = \sqrt{4} \times 11 . 2 = 22 . 4 km/s\]

Answer 2

Given:

Mass of the planet, M_P = 8 M_E
Radius of the planet, R_P = 2 R_E
Escape velocity for the Earth, V_escE = 11.2 km/s
Escape velocity for the planet, V_escP =? 

`V_("escP") = sqrt((2"GM"_"p")/("R"_"p")) `

=`sqrt((2"G"(8"M"_"E"))/(2"R"_"E"))`

`=sqrt(8/2 xx (2"GM"_"E")/("R"_"E")`

`= sqrt(8/2) xx sqrt((2"GM"_"E")/"R"_"E")`

`= sqrt(4) xx "V"_("escE")`    

∵ `"V"_("escE") = sqrt((2"GM"_"E") /("R"_"E") `

`= 2 xx 11.2`

`"V"_("escP")` = 22.4 Km/s

Escape velocity for the planet = 22.4 km/s