The escape velocity for earth is $v$. A planet having 8 times the mass of the earth and a radius 2 t

Question

The escape velocity for earth is $v$. A planet having 8 times the mass of the earth and a radius 2 times that of the earth will have an escape velocity of

Professor PC Thomas Classes · Answer

(a) : The escape velocity on the surface of Earth is given by $v = \sqrt{\frac{2 G M_e}{R_e}}$. For the new planet, the mass is $M_p = 8 M_e$ and the radius is $R_p = 2 R_e$. The escape velocity for this planet will be $v_p = \sqrt{\frac{2 G M_p}{R_p}} = \sqrt{\frac{2 G (8 M_e)}{2 R_e}} = \sqrt{4 	imes \frac{2 G M_e}{R_e}} = 2 \sqrt{\frac{2 G M_e}{R_e}}$. Therefore, $v_p = 2v$.