Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_241

3/241 A space vehicle moving in a circular orbit of radius \(r_1\) transfers to a larger circular orbit of radius \(r_2\) by means of an elliptical path between \(A\) and \(B\). (This transfer path is known as the Hohmann transfer ellipse.) The transfer is accomplished by a burst of speed \(\Delta v_A\) at \(A\) and a second burst of speed \(\Delta v_B\) at \(B\). Write expressions for \(\Delta v_A\) and \(\Delta v_B\) in terms of the radii shown and the value of \(g\) of the acceleration due to gravity at the earth’s surface. If each \(\Delta v\) is positive, how can the velocity for path 2 be less than the velocity for path 1? Compute each \(\Delta v\) if \(r_1 = (6371 + 500) \text{ km}\) and \(r_2 = (6371 + 35\ 800) \text{ km}\). Note that \(r_2\) has been chosen as the radius of a geosynchronous orbit.