Precession, Nutation, And Wobble Of The Earth

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Cover Half title Title Copyright Contents Preface Abbreviations 1 Introduction – Fundamental definitions – Motivation 1.1 Rotation and global shape of the Earth 1.2 Orbit of the Earth 1.3 Earth orientation – precession and nutation 1.4 Primary cause of precession and nutation 1.5 Nutation of a non-rigid Earth 1.6 Models of the Earth's interior 1.7 Precession, nutation, and geodynamics 1.8 The Earth's normal modes 1.9 Motivation for the book 1.10 Organization of the book 2 Concepts and elementary theory 2.1 Gravitational potential 2.2 Axes associated with Earth rotation 2.3 Celestial sphere, celestial poles, and equators of axes 2.4 Terminology for nutation 2.5 Normal modes 2.6 Wobble and sway 2.7 Length-of-day (LOD) variation 2.8 Solid Earth and ocean tides 2.9 Inertia tensor; principal axes and moments of inertia 2.10 Low and high frequency nutations 2.11 Interplay of nutation, tides, ocean, and atmosphere 2.12 Remaining concepts such as fundamental reference planes 2.13 Sign conventions 2.14 Reference frames: basic aspects 2.15 Precession and nutation of different axes 2.16 Precession and nutation variables 2.17 Definition of polar motion 2.18 Elliptical motions 2.19 Decomposition into circular motions 2.20 Free rotational modes 2.21 Causes of the forced motions 2.22 Equations of rotational motion 2.23 Gravitational action of a celestial body on the Earth 2.24 Solutions for a simple model 2.25 Polar motion of the pole of the CRS: relation to nutation 2.26 Kinematical relations between wobble and nutation 2.27 Transfer function 2.28 Oppolzer terms 2.29 Notation used in this chapter 3 Reference systems and frames 3.1 Celestial and terrestrial reference systems and frames 3.2 Transformations between reference frames 3.3 Notation used in this chapter 4 Observational techniques – ephemerides 4.1 VLBI 4.2 Construction of the ICRF 4.3 GPS observations 4.4 Orbital motions and fundamental arguments 4.5 Existing ephemerides 4.6 Ephemerides used for the rigid Earth nutation theory 4.7 Other kinds of observations needed for nutation studies 5 Rigid Earth precession and nutation 5.1 Approaches to the determination of rigid Earth nutations 5.2 Hamiltonian approach 5.3 Earth's gravitational potential on a celestial body 5.4 Torque on an axially symmetric Earth 5.5 Tide generating potential (TGP) 5.6 Wobbles and nutations excited by arbitrary potentials 5.7 Torque in the CRF and nutation arguments 5.8 Nutation of the figure axis 5.9 Numerical integration 5.10 Arguments of the nutations: additional remarks 5.11 Orbital motions of the solar system bodies 5.12 Additional small effects 5.13 Precession constant 6 Deformable Earth – Love numbers 6.1 Hydrostatic equilibrium Earth models 6.2 Perturbing potentials 6.3 Deformations of a spherical Earth 6.4 Love numbers 6.5 Load Love numbers 6.6 Equations for displacement and gravitational fields 6.7 Spherical harmonic expansions; radial functions 6.8 The inertia tensor: contribution from deformations 7 Nutations of a non-rigid Earth 7.1 Formulations of the theory for a non-rigid Earth 7.2 Idealized two-layer Earth: Poincare's theory 7.3 Analytical treatment of more general Earth models 7.4 Earth with fluid outer core and solid inner core 7.5 Displacement field approach 8 Anelasticity 8.1 Complex rheological parameters for the anelastic Earth 8.2 Anelasticity contributions to nutation 9 Ocean and atmospheric corrections 9.1 Effects of the fluid layers on Earth rotation 9.2 Links between torque and angular momentum 9.3 Effect of a fluid acting on the solid Earth 9.4 Non-tidal ocean effects on the Earth rotation 10 Refinements of non-rigid nutation 10.1 Effect of a thermal conductive layer at the top of the core 10.2 CMB/ICB coupling effects on nutation 10.3 Electromagnetic coupling 10.4 Viscous and electromagnetic coupling 10.5 Topographic coupling 10.6 Viscosity of the inner core 10.7 Effect of stratification in the core 10.8 Discussion on precession constant 10.9 Triaxiality 10.10 Second-order effects 11 Comparison observation-theory 11.1 Empirical models for nutations (such as IERS96) 11.2 Estimation of basic Earth parameters from VLBI 11.3 Consideration of the ocean tide effects on nutation 11.4 Inclusion of anelasticity effects 11.5 Nutation using estimated parameters (MHB2000) 11.6 Free core nutation model 11.7 Present-day precision 11.8 Future decimal research 12 Conventions 12.1 Definition of equator 12.2 Definition of equinox 12.3 Definition of CIP related to precession and nutations 12.4 Classical representations of the precession–nutation matrix 12.5 Definition of CIO (non-rotating origin) 12.6 Stellar angle 12.7 Link between ICRF and the ITRF involving the NRO 12.8 Alternative derivation of the Earth rotation angle 12.9 Link between ICRF and the ITRF involving CIP and NRO 13 Mars nutations 13.1 Rotation and obliquity of Mars 13.2 Mars normal modes 13.3 Precession and nutation of Mars 13.4 Length-of-day variations and polar motion of Mars 13.5 Rotation measurements of Mars Appendix A: Rotation representation A.1 Rotation and infinitesimal rotations of a vector A.2 Rotation vector and rotation matrix A.3 Rotation from change of pole position A.4 Change in pole position Appendix B: Clairaut theory B.1 Expression of the Earth's gravitational potential B.2 Equipotential surface at the first order – Clairaut's ellipsoid B.3 Gravity on the surface of Clairaut's ellipsoid Appendix C: Definitions of equinoxes C.1 Definition of ecliptic and orbital plane C.2 Definition of "inertial'' and "rotating'' equinox C.3 Expression in inertial frame Bibliography Index