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Relativistic effects in the rotation of dwarf planets and asteroids

Pashkevich Vladimir V., Vershkov Andrey N.

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, No. 3

158--184

EN

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.

2

Geodetic precession of the Sun, Solar System planets, and their satellites

Pashkevich Vladimir V., Vershkov Andrey N.

Artificial Satellites : Journal of Planetary Geodesy

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2022

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Vol. 57, No. 1

77--109

EN

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.

3

Effect of the Gravitational Aberration on the Earth Gravity Field

Zieliński Janusz B., Pashkevich Vladimir V.

Artificial Satellites : Journal of Planetary Geodesy

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2021

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Vol. 56, No. 1

1--9

EN

Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard-Wiechert solution of the retarded potentials. The term gravitational counter-aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites.

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Relativistic effects in the rotation of Jupiter's inner satellites

Pashkevich Vladimir V., Vershkov Andrey N.

Artificial Satellites : Journal of Planetary Geodesy

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2020

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Vol. 55, No. 3

118--129

EN

The most significant relativistic effects (the geodetic precession and the geodetic nutation, which consist of the effect of the geodetic rotation) in the rotation of Jupiter's inner satellites were investigated in this research. The calculations of the most essential secular and periodic terms of the geodetic rotation were carried out by the method for studying any bodies of the solar system with long-time ephemeris. As a result, for these Jupiter’s satellites, these terms of their geodetic rotation were first determined in the rotational elements with respect to the International Celestial Reference Frame (ICRF) equator and the equinox of the J2000.0 and in the Euler angles relative to their proper coordinate systems. The study shows that in the solar system there are objects with significant geodetic rotation, due primarily to their proximity to the central body, and not to its mass.