A spacecraft of mass m describes a circular orbit of radius r1 around the earth. (a) Show that…

A spacecraft of mass m describes a circular orbit of radius r1 around the earth. (a) Show that the additional energy DE which must be imparted to the spacecraft to transfer it to a circular orbit of larger radius r2 is

where M is the mass of the earth. (b) Further show that if the transfer from one circular orbit to the other is executed by placing the spacecraft on a transitional semielliptic path AB, the amounts of energy DEA and DEB which must be imparted at A and B are, respectively, proportional to r2 and r