Abstract
The effect of the geodetic rotation (which includes two relativistic effects: geodetic precession and geodetic nutation) is the most significant relativistic effect in the rotation of the celestial bodies. For the first time in this research, this relativistic effect is determined in the rotation of dwarf planets (Ceres, Pluto, and Charon) and asteroids (Pallas, Vesta, Lutetia, Europa, Ida, Eros, Davida, Gaspra, Steins, and Itokawa) in the Solar System with known values of their rotation parameters. Calculations of the values of their geodetic rotation are made by a method for studying any bodies in the Solar System with a long-term ephemeris. Values of geodetic precession and geodetic nutation for all these celestial bodies were calculated in ecliptic Euler angles relative to their proper coordinate systems and in their rotational elements relative to the fixed equator of the Earth and the vernal equinox (at the epoch J2000.0). The obtained analytical values of the geodetic rotation for the celestial bodies can be used to numerically investigate their rotation in the relativistic approximation, and also used to estimate the influence of relativistic effects on the orbital–rotational dynamics for the bodies of exoplanetary systems.