AAS 98-155

AN ANALYSIS OF THE BEHAVIOR OF THE J2000 REDUCTION MATRICES

D. A. Vallado - Phillips Laboratory

Abstract

Accurate orbit determination relies on dense observational data and numerical processing. As existing analytical methods are replaced with highly accurate numerical techniques, a need exists to permit numerical integration methods to efficiently implement reduction calculations. The theory for FK5(J2000) is well known, as well as numerical integration methods. The desirability to integrate and produce state vectors in varying frames requires efficient methods to convert between frames. In addition, the numerical integration is often performed in the "inertial" mean-of-date frame, while the measurements and force model accelerations are found in the true-of-date frames. In particular, this paper investigates the behavior of the reduction matrices for precession, nutation, sidereal time, and polar motion as applied to numerical propagation. It finds that the time required to determine the complete reduction matrices isn't always beneficial, depending on the accuracy requirements. It also shows graphical and timing analyses that show the approximations can save significant amount of time while maintaining modest accuracy. The new ICRS system should nullify many of the concerns of the different frames, but this analysis should prove useful until the ICRS is fully implemented. The overall conclusion is that the complete matrices should be used for all highly accurate calculations, and the reduction matrices need only be updated every week or more, depending on the desired accuracy.

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