An Elementary Proof Of the Optimality of Hohmann Transfers

The Hohmann (1925) transfer is analytically proved by means of a gradient method to be the optimal two-impulse transfer between coplanar circular orbits in a central force field with a Newtonian attraction. By an extension of the method, it is further shown that a Hohmann-type transfer is the optimal two-impulse transfer between coplanar orbits, one of which is circular and the other elliptical. The gradient method clearly shows that the characteristic velocity attains a minimum on the boundary of the region where the transfer orbits lie.