Geodetic Precession of the Sun, Solar System Planets, and their Satellites

The effect of the geodetic precession is the most significant relativistic effect in the rotation of celestial bodies. In this article, the new geodetic precession values for the Sun, the Moon, and the Solar System planets have been improved over the previous version by using more accurate rotational element values. For the first time, the relativistic effect of the geodetic precession for some planetary satellites (J1–J4, S1–S6, S8–S18, U1–U15, N1, and N3–N8) with known quantities of the rotational elements was studied in this research. The calculations of the values of this relativistic effect were carried out by the method for studying any bodies of the Solar System with long-time ephemeris. As a result, the values of the geodetic precession were first determined for the Sun, planets in their rotational elements, and for the planetary satellites in the Euler angles relative to their proper coordinate systems and in their rotational elements. In this study, with respect to the previous version, additional and corrected values of the relativistic influence of Martian satellites (M1 and M2) on Mars were calculated. The largest values of the geodetic rotation of bodies in the Solar System were found in Jovian satellite system. Further, in decreasing order, these values were found in the satellite systems of Saturn, Neptune, Uranus, and Mars, for Mercury, for Venus, for the Moon, for the Earth, for Mars, for Jupiter, for Saturn, for Uranus, for Neptune, and for the Sun. First of all, these are the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14) and the satellites of Saturn: Pan (S18), Atlas (S15), Prometheus (S16), Pandora (S17), Epimetheus (S11), Janus (S10), and Mimas (S1), whose values of geodetic precession are comparable to the values of their precession. The obtained numerical values for the geodetic precession for the Sun, all the Solar System planets, and their satellites (E1, M1, M2, J1–J5, J14–J16, S1–S6, S8–S18, U1–U15, N1, and N3–N8) can be used to numerically study their rotation in the relativistic approximation and can also be used to estimate the influence of relativistic effects on the orbital–rotational dynamics of bodies of exoplanetary systems.