Influence of ITRS/GCRS implementation for astrodynamics: Coordinate transformations

Converting between the Geocentric Celestial Reference System (GCRS) and International Terrestrial Reference System (ITRS) is necessary for many applications in astrodynamics, such as orbit determination and analyzing geoscience data from satellite missions. The implementation of this frame transformation and the manner in which the Earth orientation parameters (EOPs) are used have a notable impact on station coordinates and satellite positions. After briefly reviewing the various theories and their mathematical description, we investigate the impact of EOP interpolation methods, ocean tide corrections, precession-nutation simplifications, and Julian date handling on the ITRS/GCRS coordinate transformation. Estimates of the impact on position concern a range of altitudes, from the Earth's surface to geosynchronous orbit (GEO), and apply to a wide array of astrodynamics applications. We demonstrate that EOP interpolation methods and ocean tide corrections impact the ITRS/GCRS transformation between 5 cm and 20 cm on the surface of the Earth and at the Global Positioning System (GPS) altitude, respectively. We conclude with a summary of recommendations on EOP usage and bias-precession-nutation model implementations for achieving a wide range of transformation accuracies at several altitudes. This comprehensive set of recommendations allows astrodynamicists, flight software engineers, and Earth scientists to make informed decisions when choosing the best implementation for their application, balancing accuracy and computational complexity.