Zachary Folcik (MIT Lincoln Laboratory), Paul J. Cefola (State University of New York at Buffalo)
Keywords: Astrodynamics
Abstract:
An improved accuracy model for the J2 zonal harmonic second order terms, J2-squared, in a general semi-analytical satellite theory is described. The new model is implemented as an option in the Draper Semi-analytic Satellite Theory (DSST) orbit propagator; the DSST is one of the several orbit propagators included in the Linux version of the R&D Goddard Trajectory Determination System (GTDS) program. The DSST previously modeled the first-order mean equinoctial orbital element rates and short periodic motion for the Earth’s zonal and tesseral gravity harmonics. The current DSST also includes approximate models for the mean equinoctial orbit element rates and the short-periodic motion due to the J2-squared zonal harmonic terms. However, these approximate J2-squared models are truncated on the eccentricity. Building on the work of McClain, Zeis, Slutsky, and Fischer, we develop a method to calculate the J2-squared mean element rates using Gauss-Kronrod numerical quadrature. This quadrature-based method has both analytical and numerical components. The open source symbolic algebra system, Maxima, operating on a Linux platform, is used to construct the analytical portion of the model. The accuracy of both the old and new J2-squared models is demonstrated over a range of eccentricities and inclinations.
Date of Conference: September 11-14, 2012
Track: Astrodynamics