  This work focuses on minimum-time low-thrust orbit transfers from a
prescribed low Earth orbit to a specified low lunar orbit. The well-established
indirect formulation of minimum-time orbit transfers is extended to a multibody
dynamical framework, with initial and final orbits around two distinct
primaries. To do this, different representations, useful for describing orbit
dynamics, are introduced, i.e., modified equinoctial elements (MEE) and
Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or
Moon, allows simple writing of the boundary conditions about the two celestial
bodies, but requires the formulation of a multiple-arc trajectory optimization
problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In
the numerical solution process, the transition between the two MEE
representations uses CC, which play the role of convenient intermediate,
matching variables. The multiple-arc formulation at hand leads to identifying a
set of intermediate necessary conditions for optimality, at the transition
between the two legs. This research proves that a closed-form solution to these
intermediate conditions exists, leveraging implicit costate transformation. As
a result, the parameter set for an indirect algorithm retains the reduced size
of the typical set associated with a single-arc optimization problem. The
indirect heuristic technique, based on the joint use of the necessary
conditions and a heuristic algorithm (i.e., differential evolution in this
study) is proposed as the numerical solution method, together with the
definition of a layered fitness function, aimed at facilitating convergence.
The minimum-time trajectory of interest is sought in a high-fidelity dynamical
framework, with the use of planetary ephemeris and the inclusion of the
simultaneous gravitational action of Sun, Earth, and Moon, along the entire
transfer path.
