  The problem of minimum-time, low-thrust, Earth-to-Mars interplanetary orbital
trajectory optimization is considered. The minimum-time orbital transfer
problem is modeled as a four-phase optimal control problem where the four
phases correspond to planetary alignment, Earth escape, heliocentric transfer,
and Mars capture. The four-phase optimal control problem is then solved using a
direct collocation adaptive Gaussian quadrature collocation method. The
following three models are used in the study: (1) circular planetary motion;
(2) elliptic planetary motion; and (3) elliptic planetary motion with gravity
perturbations, where the transfer begins in a geostationary orbit and
terminates in a Mars-stationary orbit. Results for all three cases are
provided, and one particular case is studied in detail to show the key features
of the optimal solutions. Using the particular value thrust specific force of
$0.00098\times 10^{-4}~\textrm{m}\cdot\textrm{s}^{-2}$, it was found that the
minimum times for cases (1), (2), and (3) are, respectively, 215 d, 196 d, and
198 d with departure dates, respectively, of 1 July 2020, 30 June 2020, and 28
June 2020. Finally, the problem formulation developed in this study is compared
against prior work on an Earth-to-Mars interplanetary orbit transfer where it
is found that the results of this research show significant improvement in
transfer time relative to the prior work.
