The forced nutations of an elliptical, rotating, elastic and oceanless earth

Summary. We compute the luni-solar forced nutations of an elliptical, rotating, self-gravitating, elastic, hydrostatically prestressed and oceanless earth. Several recent structural models are considered, each possessing a fluid outer core and solid inner core. Complete results are given for the nutation of the ‘axis of figure for the Tisserand mean surface’ which best represents the observational effects of the Earth's nutational motion. Differences between results for different structural models are observationally insignificant. Differences between our results and Molodensky's are as large as ∼ 0.002 arcsec at six month and at 18.6 yr.

[1]  P. Melchior.  Precession-nutations and tidal potential , 1971 .

[2]  J. Wahr,et al.  A diurnal resonance in the ocean tide and in the Earth's load response due to the resonant free ‘core nutation’ , 1981 .

[3]  Paul Melchior,et al.  The Tides of Planet Earth , 1978 .

[4]  A. Toomre.  On the 'Nearly Diurnal Wobble' of the Earth , 1974 .

[5]  F. Dahlen,et al.  The period and Q of the Chandler wobble , 1981 .

[6]  R. Atkinson.  On the, 'Dynamical Variations" of latitude and time , 1973 .

[7]  M. L. Smith,et al.  The influence of rotation on the free oscillations of the Earth , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  C. Pekeris,et al.  Dynamics of the liquid core of the Earth , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[9]  H. Jeffreys,et al.  The Theory of Nutation and the Variation of Latitude , 1957 .

[10]  Martin L. Smith.  The Scalar Equations of Infinitesimal Elastic-Gravitational Motion for a Rotating, Slightly Elliptical Earth , 1974 .

[11]  E. W. Brown,et al.  Tables of the motion of the moon , 1919 .

[12]  Martin L. Smith.  Translational inner core oscillations of a rotating, slightly elliptical Earth , 1976 .

[13]  Martin L. Smith.  Wobble and nutation of the Earth , 1977 .

[14]  J. Wahr.  A normal mode expansion for the forced response of a rotating earth , 1981 .

[15]  Tsutomu Sasao,et al.  Note on nutation in ephemerides. , 1979 .

[16]  L. Mansinha,et al.  Oscillation, Nutation and Wobble of an Elliptical Rotating Earth with Liquid Outer Core , 1976 .

[17]  F. Gilbert,et al.  An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra , 1975, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[18]  H. Poincaré.  Sur la précession des corps déformables , 1910, Bulletin astronomique.

[19]  S. Sakai,et al.  Dissipative Core-Mantle Coupling and Nutational Motion of the Earth , 1977 .

[20]  H. Jeffreys.  Nutation: comparison of theory and observations , 1959 .

[21]  John M. Wahr,et al.  Body tides on an elliptical, rotating, elastic and oceanless earth , 1981 .

[22]  H. Kinoshita.  Theory of the rotation of the rigid earth , 1977 .

[23]  E. Woolard.  Theory of the rotation of the earth around its center of mass , 1953 .

[24]  H. Jeffreys,et al.  The Theory of Nutation and the Variation of Latitude: The Roche Model Core , 1957 .

[25]  Guy Masters,et al.  Observational constraints on the chemical and thermal structure of the Earth's deep interior , 1979 .

[26]  J. Wahr,et al.  Effect of the fluid core on changes in the length of day due to long period tides. , 1981 .

[27]  Adam M. Dziewonski,et al.  Parametrically simple earth models consistent with geophysical data , 1975 .

[28]  Chi‐yuen Wang,et al.  A Simple Earth Model , 1972 .

[29]  Walter Munk,et al.  The rotation of the earth , 1960 .

[30]  R. Atkinson.  On The Earth's Axes of Rotation and Figure , 1975 .