A fully analytical approach to the harmonic development of the tide-generating potential accounting for precession, nutation, and perturbations due to figure and planetary terms.
The development of the tide generating potential (TGP) was first carried out in harmonic form by Doodson in 1921. In the recent decades Doodson's 388 tidal constituents of theTGP have been extended to reach the level of several thousand partial waves. While a few authors follow Doodson's analytical approach, the longest expansions all utilize a numerical filtering approach and a numerical lunisolar ephemeris. The need for such extended schedule of tidal constituents is required by the accuracy attained in modern applications, such as the detection of the motion of the Earth's core, the reduction of gravimetric measurements and the computations of tidal perturbations on satellites. The availability of modern algebraic manipulation systems and of an accurate theory of the lunar motion can make the daunting task of the elaborate analytical computations leading to the TGP an almost trivial matter. It is shown in this paper that the application of the Wigner's rotation theorem for spherical harmonics can be invoked to transform the Sun's and the Moon's motions from the ecliptical to the equatorial system in a manner perfectly adaptable to algebraic manipulation up to any desired spherical harmonics degree. It is also shown that the formulation proposed can easily handle the accurate modelling of the precessional and nutational motions of the Earth and the perturbations due to the figure of the Earth as well as the perturbations due to the planets, both direct and indirect.
AAS/Division of Dynamical Astronomy Meeting #35
- Pub Date:
- May 2004