EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

On the permanent tide and the Earth dynamical ellipticity

Alberto Escapa1,2, Tomás Baenas3, and José Manuel Ferrándiz2
Alberto Escapa et al.
  • 1Dept. of Aerospace Engineering, University of León, E-24071 León, Spain (
  • 2Dept. of Applied Mathematics, University of Alicante, P.O. 99, E-03080, Alicante, Spain
  • 3University Centre of Defense, MDE-UPCT, E- 30720 Murcia, Spain

As other relevant quantities related to the Earth dynamics, the Earth dynamical ellipticity is influenced by tidal effects. In particular, it is affected by the permanent tide due to the time independent part of the Earth redistribution tidal potential. Hence, it is necessary to distinguish between its tide-free and non tide-free values (e.g., Burša 1995) when determining it from observations (e.g., Marchenko & Lopushanskyi 2018). This question is seldom considered in Earth rotation studies. For example, neither IAU2000/AIU2006 nutation/precession model nor IERS Conventions specify explicitly whether the dynamical ellipticity is a zero-tide parameter or not. However, current accuracy goals might be sensitive to that difference.

Within the framework of a Hamiltonian approach (Baenas, Escapa, & Ferrándiz 2019), we present a consistent treatment of the influence of the permanent tide on the dynamical ellipticity. In particular, we develop an analytical expression of the redistribution tidal potential based on Andoyer canonical variables and a semi-analytical theory of the orbital motions of the Moon and the Sun, following the same procedure as that given in Kinoshita (1977).

This method allows obtaining an expression of the zero frequency term of the redistribution tidal potential that updates that of Zadro & Marussi (1973), usually employed in reporting parameters of common relevance to Astronomy, Geodesy, & Geodynamics (e.g., Burša 1995, Groten 2004). In addition, it clarifies the procedure that must be followed in order that the dynamical ellipticity, fitted to the observations, contains the effects of the permanent tide avoiding in this way potential inconsistencies.

How to cite: Escapa, A., Baenas, T., and Ferrándiz, J. M.: On the permanent tide and the Earth dynamical ellipticity, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21410,, 2020

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Display material version 1 – uploaded on 06 May 2020
  • CC1: Comment on EGU2020-21410, Christian Bizouard, 07 May 2020

    Hi Alberto, according to your presentation, the difference between zero tide H and permanent tide H is about 1e-7. Consequently, the corresponding effect on the 18.6 year nutation is about 1e-7 * 10e3 mas = 1e-3 mas? So, the effect is under the level of observability? For precession, the order of magnitude is 50e3 mas/year * 1e-7 = 5e-3 mas/year? 

    • AC1: Reply to CC1, Alberto Escapa, 08 May 2020

      From an observational point of view the effects of the permanent  tide seem to be not distinguishable, as it is the case of J2 (e.g.,  Kozai 1965). In contrast, the quasi-periodic part of the redistribution tidal potential must be considered in precession/nutation (Baenas, Escapa, &Ferrandiz 2019, sec. 5).

      The importance in establishing the different tidal systems for H relies in that for some purpose, like the derivation of A, B, and C,  it is combined with J2. So, both must be referred to the same tidal system. At any rate, we are examining this question in detail, and the results will appear in a forthcoming paper.