A space vehicle approaching a planet has a speed v, very long way out and is on a trajectory which would miss the centre of the planet by a distance R if it continued to move in a straight line path. If the planet has Mass M and radius r, then find the smallest value of R if the vehicle just grazes past the earth's surface.
(1) 2GMR/rv
(2) [(1/r)-(v^2/2GM)]^-1
(3) r/v(v^2 + 2GM/r)^1/2
(4) [(v^2/2GM)-(1/r)]^-1
(Answer:3)
