Juan Getino

PRECESSION OF THE NONRIGID EARTH: EFFECT OF THE FLUID OUTER CORE

We show that, unlike commonly believed, the presence of a fluid core does affect the precessional motion of Earth by a nonnegligible amount, equivalent to a variation of several parts per million in the value of the precession constant or, correspondingly, the dynamical ellipticity of Earth. This contribution arises from the second-order terms of the averaged Hamiltonian after the application of perturbation methods to remove the periodic terms, some of the former being amplified as a consequence of resonance induced by the fluid core. Our evaluation corresponds to a simplified Earth model of the Poincare kind (rigid mantle and liquid core). Under these assumptions, the effect of the fluid core is larger than -002 per century, which represents a significant contribution to the total amount of precession, since it is about two-thirds of the total planetary effect.

Indirect effect of the triaxiality in the Hamiltonian theory for the rigid Earth nutations

In this investigation we determine a new contribution to the nutation series due to an indirect eect of the triaxiality of the rigid Earth. We undertake this work in the context of the Hamiltonian theory for the rigid Earth, developed by Kinoshita (1977) and recently updated by Souchay et al. (1999). To do this, we express the potential energy in terms of the action{angle variables for the triaxial Earth. Then, we work out analytical formulae for the new contributions, showing that their numerical values are within the truncation level adopted by REN{2000 (Souchay et al. 1999), which was xed to 0:1 as.

GENERAL THEORY OF THE ROTATION OF THE NON-RIGID EARTH AT THE SECOND ORDER. I. THE RIGID MODEL IN ANDOYER VARIABLES

This paper is the first part of an investigation where we will present an analytical general theory of the rotation of the non-rigid Earth at the second order, which considers the effects of the interaction of the rotation of the Earth with itself, also named as the spin-spin coupling. Here, and as a necessary step in the development of that theory, we derive complete, explicit, analytical formulae of the rigid Earth rotation that account for the second-order rotation-rotation interaction. These expressions are not provided in this form by any current rigid Earth model. Working within the Hamiltonian framework established by Kinoshita, we study the second-order effects arising from the interaction of the main term in the Earth geopotential expansion with itself, and with the complementary term arising when referring the rotational motion to the moving ecliptic. To this aim, we apply a canonical perturbation method to solve analytically the canonical equations at the second order, determining the expressions that provide the nutation-precession, the polar motion, and the length of day. In the case of the motion of the equatorial plane, nutation-precession, we compare our general approach with the particular study for this motion developed by Souchay et al., showing the existence of new terms whose numerical values are within the truncation level of 0.1 μas adopted by those authors. These terms emerge as a consequence of not assuming in this work the same restrictive simplifications taken by Souchay et al. The importance of these additional contributions is that, as the analytical formulae show, they depend on the Earth model considered, in such a way that the fluid core resonance could amplify them significatively when extending this theory to the non-rigid Earth models.

The Rotation of a Non-Rigid, Non-Symmetrical Earth II: Free Nutations and Dissipative Effects

The study of the rotation of a non-rigid, non-symmetrical Earth with a heterogeneous and stratified liquid core was recently accomplished by González and Getino (1997) through the Hamiltonian formalism. In this work that model is extended by including the effect of the dissipation arising from the mantle–core interaction due to the viscous and electromagnetic coupling. A canonical transformation to a new set of non-singular variables is performed, in order to avoid small divisors in the system of equations. Numerical estimations of the effect of the dissipation are given in form of tables and graphics, and the significance of this effect is discussed.

Improved nutation series for the non–rigid earth with a precise adjustment of parameters with nonlinear dependence

In this paper, the previous nutation series corresponding to the rotation of a non‐rigid earth composed of a rigid mantle and a liquid core obtained by Getino and Ferrándiz in 1997 are notably improved by using a high performance data fitting method. This method can be applied to many other problems presenting a non‐linear dependence on the free parameters.

Consistency Problems in the Improvement of the IAU Precession–Nutation Theories: Effects of the Dynamical Ellipticity Differences

The complexity of the modeling of the rotational motion of the Earth in space has produced that no single theory has been adopted to describe it in full. Hence, it is customary using at least a theory for precession and another one for nutation. The classic approach proceeds by deriving some of the fundamental parameters from the precession theory, like, e.g., the dynamical ellipticity

Dynamical adjustments in IAU 2000A nutation series arising from IAU 2006 precession

H_{mathrm{d}}

ORBITAL EVOLUTION OF HIGH-ALTITUDE BALLOON SATELLITES

Hd, and then using those values in the nutation theory. The former IAU 1976 precession and IAU 1980 nutation theories followed that scheme. Along with the improvement of the accuracy of the determination of Earth orientation parameters, IAU 1980 was superseded by IAU2000, based on the application of the MHB2000 transfer function to the previous rigid Earth analytical theory REN2000. The latter was derived while the precession model IAU 1976 was still in force, therefore it used the corresponding values for some of the fundamental parameters, as the precession rate, associated to the dynamical ellipticity. The new precession model P03 was adopted as IAU 2006. That change introduced some inconsistency since P03 used different values for some of the fundamental parameters that MHB2000 inherited from REN2000. Besides, the derivation of the basic Earth parameters of MHB2000 itself comprised a fitted variation of the dynamical ellipticity adopted in the background rigid theory. Due to the strict requirements of accuracy of the present and coming times, the magnitude of the inconsistencies originated by this twofold approach is no longer negligible as earlier, hence the need of discussing the effects of considering slightly different values for