The Hohmann Transfer Orbit maneuver is used by spaceships to transfer from one circular orbit around a planet to another, by temporarily entering an intermediate elliptical orbit. The spaceship starts on a small circular orbit of radius r around a planet of mass M. At point A in the diagram below, it fires its propellers to put itself onto an intermediate elliptical orbit. At point B, it fires its propellers again, and ends on the larger circular orbit of radius 2r. You may assume that the propellers are so powerful that the changes in velocity occur instantaneously at each point. Between point A and B space ship experience only gravitational force from planet.
Find ΔVA (the amount by which the velocity needs to be changed at point A) needed to achieve this travel path.
