A Hohmann transfer analog for power-limited, continuous thrust transfers between coplanar circular orbits

The problem of transferring a spacecraft between two coplanar circular orbits, by ejecting a minimum amount of propellant, is analytically solved for the case in which the transfer duration tends to infinity. This lies diametrically opposite to the case of the so-called Hohmann transfer between the same orbits. The Hohmann transfer corresponds to applying infinite thrust over an infinitesimal time interval. The present solution corresponds to applying infinitesimal thrust over an infinite time interval. Just as a Hohmann transfer can be performed in practice only nearly optimally by applying large thrust over a finite time interval, the present solution can be performed in practice only nearly optimally by applying low thrust over a large, but finite, transfer duration. In fact, comparisons with exact numerical optimization results indicate, that, for transfers between two coplanar circular orbits that take more than a few revolutions about the Earth the solution and the thrust acceleration program presented here are as good as their optimal counterparts for all practical purposes.