  A numerical optimization study of minimum-fuel Earth-based orbital transfers
from low-Earth orbit (LEO) to either medium-Earth orbit (MEO), high-Earth orbit
(HEO), or geostationary orbit (GEO), is performed. Various values of maximum
allowable thrust acceleration are considered for each type of transfer
(LEO-to-MEO, LEO-to-HEO, or LEO-to-GEO). A key aspect of the study performed in
this paper is that the optimal thrusting structure is not assumed to be known a
priori, but is determined as part of the solution process. In order to
determine the optimal thrusting structure, a recently developed bang-bang and
singular optimal control (BBSOC) method is employed together with
multiple-domain Legendre-Gauss-Radau quadrature collocation. Key results
obtained in this study include not only the number of switches in the optimized
thrust, but also the total impulse. Furthermore, it is found that, as the
maximum allowable thrust acceleration decreases, the total impulse is less than
the total impulse obtained from a previous study where a burn-coast-burn
thrusting structure was assumed a priori. For each type of transfer a
particular value of maximum allowable thrust acceleration is chosen to
highlight in more detail the key features of the optimal solutions. This study
provides improved results over previous studies and provides improved insight
into the optimal thrusting structure required in order to accomplish each type
of orbital transfer using the least amount of fuel.
