A space station is at a height equal to the radius of the Earth. If ' ( V_ E ) ' is the escape velocity on the surface of the Earth, the same on the space station is __ times ( V_ E ).

Step-by-step solution

Given, a space station is at a height equal to radius of Earth, ( 1 2 M v_ s ²= G M m (R+h) ) Here, ( h=R ) and ( v_ s ) is velocity of space station [ array l 1 2 M v_ s ²= G M m 2 R v_ s = G M R array ] Now, we know that escape velocity is [ array l v_ e = 2 G M R = 2 G M 2 v_ e = 2 v_ s or v_ s = 1 2 v_ e array ]