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

Abstract

DOI: 10.2514/1.A32038 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 givenrepetitioncycleandinclination.Thenthesemimajoraxisisrefinedforapplicationtoanyellipticalmotion.This methodology wasdiscovered bycomparing tworecent methodsin addition to anew proposedmethod offeredin 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 computationaleasebasedonacasestudy.Fromthesecriteria,onemethodisrecommendedforuseinrepeat-groundtrack orbit design optimization methodology. Nomenclature a = semimajor axis, km d = number of rotations the Earth completes during the period of repetition e = eccentricity hp = perigee height above Earth’s surface, km i = inclination, rad J2 = second-order zonal effects J4 = fourth-order zonal effects k = number of revolutions along the orbit in one period of repetition M = mean anomaly, rad _ M = rate of change in the mean anomaly due to nominal motion and perturbations, rad=s Mo = initial mean anomaly, rad Nd = number of sidereal days the Earth completes during the period of repetition Np = number of revolutions along the orbit in one period of repetition n = satellite’s mean motion, rad=s ne = epicycle frequency, rad=s p = semiparameter, km RE = Earth radius, 6378.1363 km T = anomalistic period, s Tr = period of repetition, s T� = nodal period of the satellite, s