Determining an Earth Observation Repeat-Ground-Track Orbit for an Optimization Methodology

This paper presents a new methodology for a quick and efficient numerical determination of the condition for repeat ground tracks to be employed in an orbital optimization design methodology. This methodology employs the simplicity and reliability of the epicyclical motion condition for a repeat ground track to find a semimajor axis for a given repetition cycle and inclination. Then the semimajor axis is refined for application to any elliptical motion. This methodology was discovered by comparing two recent methods in addition to a new proposed method offered in this paper investigating both nonlinear algebraic and polynomial formulations of the governing repeat-ground-track condition relationship. A lesser known simplified method is used for preliminary solution refinement. The advantages and disadvantages of each approach are weighed with each method's reliability, performance, and computational ease based on a case study. From these criteria, one method is recommended for use in repeat-ground-track orbit design optimization methodology.