- 2018 Univelt Inc. All rights reserved. Coordinate choices have significant consequences in the analytical and computational approaches to solve celestial mechanics problems. The present study focuses on the impact of various coordinate representations of the dynamics on the solution of the ensuing state/co-state two-point boundary-value problems that arise when solving the indirect optimal control necessary conditions. Minimum fuel trajectory designs are considered for a geocentric spiral from GTO to GEO. Eight different coordinate/element sets are investigated. Specifically, two different sets of orbit elements are considered: Equinoctial elements and a six element set consisting of the angular momentum vector and the eccentricity vector. Furthermore, four hybrid coordinate sets associated with an osculating triad defined by the instantaneous position and velocity vectors that consist of a mixture of slow and fast variables are introduced and studied. Reliability and efficiency of convergence to the known optimal solution are studied statistically against the Cartesian and spherical coordinates, which constitute eight element/coordinate sets; the results are interesting and of significant practical utility.