Innovative Earth Gravity Reformulation and Numerical Integration for Responsive SSA

Currently, computation of the geopotential acceleration and its partial derivatives consumes a large portion of numerical integration time in special perturbations (SP) applications. The standard geopotential formulation is expressed as a spherical harmonic expansion in geocentric latitude, geocentric longitude, and radial distance. Recent research by Dr. Beylkin of the University of Colorado has demonstrated efficient techniques in evaluation of such functions, taking advantage of readily available memory and upfront computations on a spherical grid. These techniques have the potential to greatly speed up SP processing of the high accuracy catalog in the Joint Space Operations Center (JSpOC), thus improving timeliness of operational SP products and relieving analyst work load. Phase 1 will show the applicability of Dr. Beylkin''s research in an operational context, measuring the speed-up attained by his approach relative to the current model for both geopotential-only and full-up numerical integration. The associated memory cost and numerical integration accuracy will be assessed for operational viability and model optimization. Phase I will lead to a prototype that can be incorporated into the SP automatic catalog update application for full, operationally-oriented testing in Phase II. It will also shed light on the effectiveness of techniques applicable to other force model perturbations. BENEFIT: Many Air Force agencies use SP software similar to the current JSpOC SP applications. Therefore, the potential for greatly improved computational efficiency in SP processing has far reaching applicability to a wide range of DoD users.