Question

show that the escape velocity of a body from the surface of a planet of radius R and mean density p is R√8/3Gπp.​

Answer 1

Answer:

Kinetic Energy = 1/2 m v^2

Potential Energy = - G M m / R

1/2 m v^2 - G M m / R = 0     total energy at infinity = zero

v^2 = 2 G M / R

M = 4/3 pi p R^3

v^2 = 8/3 G p pi R^2

v = R  (8/3 G p pi)^1/2