The kinematic equation of Earth rotation and nutation effect of pole motion

The establishment and maintenance of the high-precision International Celestial Reference Frame (ICRF) and International Terrestrial Reference Frame (ITRF), as well as the accurate transformation between them, rely on a precisely defined celestial reference pole (reference axis). The celestial intermediate pole (CIP) is currently adopted by the IERS 2010 conventions as the celestial reference pole. In the Geocentric Celestial Reference System (GCRS), the third axis—denoted as C3—is derived through frame bias, precession, and nutation models. In the International Terrestrial Reference System (ITRS), the third axis—denoted as T3—is determined via polar motion calculations. Theoretically, C3 and T3 represent the same vector, collectively referred to as the celestial reference axis. However, due to modeling errors in precession, nutation and polar motion, C3 and T3 do not exactly coincide. Based on the transformation model between GCRS and ITRS provided by IERS 2010, this study proposes a new kinematic equation of Earth′s rotation. This equation incorporates the polar motion of Earth′s rotation axis, as well as the polar motion and nutation of the celestial reference axis. Therefore, the new formulation enables the definition of a more accurate celestial reference pole in the future. For instance, a reasonable definition of the free pole motion of the celestial reference axis makes its free nutation zero. Additionally, the Earth rotation kinematic equation is used to derive the polar motion corresponding to the IAU2000AR06 nutation model. The nutation-induced effect on polar motion is approximately 3 mas—around 100 times larger than the libration effect—which has not yet been considered in existing polar motion models.