Earth Rotation Motion Research Articles

ConstrainingCPT-even and Lorentz-violating nonminimal couplings with the electron magnetic and electric dipole moments

We analyze some dimension-five $CPT$-even and Lorentz-violating nonminimal couplings between fermionic and gauge fields in the context of the Dirac equation. After evaluating the nonrelativistic Hamiltonian, we discuss the behavior of the terms under discrete symmetries and analyze the implied effects. We then use the anomalous magnetic dipole moment and electron electric dipole moment measurements to reach upper bounds of 1 part in ${10}^{20}$ and ${10}^{24}\text{ }\text{ }(\mathrm{eV}{)}^{\ensuremath{-}1}$, improving the level of restriction on such couplings by at least 8 orders of magnitude. These upper bounds are also transferred to the Sun-centered frame by considering the Earth's rotational motion.

An enigma in estimates of the Earth's dynamic ellipticity

The precession and obliquity frequencies of the Earth's rotational motion are functions of the dynamic ellipticity of the Earth's gravitational figure, and this connection has provided a novel bridge between studies of palaeoclimate and geodynamics. In particular, analyses of tuned climate proxy records have yielded bounds on the mean relative perturbation in dynamic ellipticity over both the last 3 Myr and 25 Myr that are less than ∼3 per cent of the non-hydrostatic component of the ellipticity. We demonstrate that this apparent consistency actually defines an important geophysical enigma. Over the last 3 Myr, changes in the Earth's figure are likely dominated by ice age forcings—in this case, a small perturbation to dynamic ellipticity implies significant isostatic compensation of the ice-ocean surface mass loads and, hence, a relatively low mantle viscosity. In contrast, over the last 25 Myr, changes in the Earth's long-wavelength gravitational form are likely dominated by mantle convective flow, and in this case, the small perturbation to dynamic ellipticity implies sluggish convection and a relatively high mantle viscosity. There are at least four possible routes to resolving this enigma: The viscosity in the Earth's mantle is transient (i.e. dependent on the timescale of the applied forcing), tidal dissipation changed in a manner between the last 3 Myr and 25 Myr that was sufficient to resolve the issue, the observationally inferred bounds are unrealistically restrictive, or earth models exist in which the ice age and convection effects approximately cancel leading to no net perturbation. In this paper, we compute a suite of numerical predictions of ice age and convection-induced perturbations to the dynamic ellipticity to illustrate the enigma described above.

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journees 2004: Systemes de reference spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrandiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.

15:1 Resonance effects on the orbital motion of artificial satellites

The motion of an artificial satellite is studied considering geopotential perturbations and resonances between the frequencies of the mean orbital motion and the Earth rotational motion. The behavior of the satellite motion is analyzed in the neighborhood of the resonances 15:1. A suitable sequence of canonical transformations reduces the system of differential equations describing the orbital motion to an integrable kernel. The phase space of the resulting system is studied taking into account that one resonant angle is fixed. Simulations are presented showing the variations of the semi-major axis of artificial satellites due to the resonance effects.

Repeated Shadow Track Orbits for Space-SunSetter Missions

This paper introduces a new set of orbits, the “Repeated Shadow Track Orbits.” In these orbits, the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days. The perturbation is utilized to synchronize the spacecraft shadow motion with both the Earth rotational motion and the Earth-Sun vector rotation. Motivation for the design of new shadow track orbits comes from the need to save energy. The general mathematical model to design a Repeated Shadow Track Orbit (RSTO) is presented within this paper. RSTOs' conditions are formulated and numerically solved. Results show the feasibility of RSTOs. An optimization process is also developed to maximize the shadow duration over a given site. A Genetic Algorithm (GA) technique is utilized for optimization.

Earth rotation based on the celestial coordinates of the celestial intermediate pole

We present a study of the Earth's rotational motion in terms of the Earth Orientation Parameters (EOP) of the new paradigm that is recommended by the IAU 2000 resolutions to transform between the celestial and terrestrial reference systems. This paper presents the first part of the study whose purpose is to establish the dynamical equations of the rotation of a rigid Earth as a function of these new parameters. Starting from Euler dynamical equations for a rigid Earth, and using expressions for the components of the instantaneous rotation vector as functions of the celestial coordinates X, Y of the Celestial intermediate pole (CIP) and of the Earth rotation angle (ERA), the equations of Earth rotation were obtained explicitly in terms of those parameters. Taking into account the order of magnitude of the terms of these equations, we obtain the most appropriate form of the equations for a practical integration. We then investigated the possible methods of integration for providing semi-analytical solutions for the X and Y variables in the axially symmetric case. We also perform a number of tests regarding the efficiency of these methods, based on the IAU 2000 precession-nutation. We extended this approach to a deformable Earth, based on integration constants compliant with the new P03 precession model.

Possible planetary excitation of earthquakes

Several recent studies show the possibility of an important connection between the Earth's rotational motion and the number of earthquakes (Stavinschi and Souchay 2001, Shanker et al. 2001). We discuss the long-term periodic variations (30 years and 60 years) in these two geophysical processes, as well in solar activity and the Sun's celestial orbit. The similarities in such periodicities suggest that solar system dynamics may contribute to both solar and geophysical phenomena.

Deformations of the Earth and the Thermal Core-Mantle Couplings

Zonal modes of mantle deformation may couple with the Earth's rotational motion. Increases of the LOD (slowing down of the Earth's rotational speed) suggest a coupling with increases of the vertical in the low latitude zone. This relation may be due to the angular momentum redistribution in the mantle associated with motions in the fluid core. Thermal core-mantle interaction is proposed to explain the coupling between the fluid motion near the CMS and the elastic mantle in a simple model valid at the equator near the CMB. Transport of mass in the fluid core near the CMB along the north direction can be large enough to explain the observed values of the variation of the vertical.

The post - Newtonian rotation of Earth: a first approach

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

Electromagnetic-gravitational energy systems

Two methods axe considered to “tap” the earths' rotational energy. This ancient “collapsed gravitational energy” exceeds the earth-lunar binding energy. One involves an orbiting “electromagnetic-gravitational” coupling system whereby the earth's rotation, with its nonuniform mass distribution, first uses gravity to add orbital energy to a satellite, similar to a planetary “flyby.rd The second stage involves enhanced satellite “drag” as current-carrying coils withdraw the added orbital energy as they pass through the earth's nonuniform magnetic field. A second more direct method couples the earth's rotational motion using conducting wires moving through the noncorotating part (ionospheric current systems) of the geomagnetic field. These methods, although not immediately feasible, are considerably more efficient than using pure gravitational coupling to earth-moon tides.

Radial penetration of a hot plasma associated with a large-scale electric field in the magnetosphere, and some related problems

The inward penetration of a hot plasma as an energy accumulation process for magnetospheric substorms, and some related topics are discussed in the present paper. First, we consider the possibility that the large-scale electric field within the magnetosphere is induced as a result of the macroscopic interaction of the magnetic field disturbances in the solar wind with the magnetosphere. It is emphasized that the associated problem is essentially time dependent, and the change of the north-south component of the interplanetary magnetic field is interpreted as the incompressible Alfvén mode. Second, the problem of the inward penetration of the symmetric distributed energetic particles by the enhancement of the asymmetric electric field is quantitatively studied, using the drift kinetic approximation method. Taking account of the non-linear feedback effect of the asymmetric part of the particle distribution, we obtain the secular equation for the time development of the symmetric distribution function. Some numerical solutions of this equation are given as an application to the ring current proton penetration problem. For steady state penetration, the Earth's rotational motion and the tailward stretching of the field lines are important to the resonant protons with energy of 1–10 keV. Third, interrelation between the coherent adiabatic large-scale dynamical motion of the plasma as an energy accumulation process, and incoherent stochastic resonant wave-particle interactions, are discussed in relation to the energy accumulation and relaxation processes. The adiabatic drift instability condition, which would be satisfied in the front side of the penetrated proton ring current, is also considered. Finally, the possibility of runaway electrons in the topside ionosphere as a source of the magnetospheric electrons during the substorm is also considered, and the associated limiting flux intensity is estimated.