Solid Earth and ocean tides estimated from satellite orbit analyses

The earth's tidal deformations cause perturbations in the motions of close earth satellites, observations of which give estimates of the Love number k2 and phase lag δ. The contribution of the ocean tides has generally been considered unimportant, but this is not so. These ocean tides cause the same spectrum of orbital perturbations as the solid tide, and a complete separation, by analyzing satellite orbits of different elements, is not possible. Neglect of the ocean tide will introduce errors in k2 of as much as 15% and in phase angle of as much as 10° depending on the orbit. This explains the low values for k2 near 0.25 that have been obtained recently from orbital analyses. Comparison of several models for the principal lunar tide (M2) of the ocean indicates that these models are insufficient for making precise orbital corrections. For the other tidal frequencies that often have important effects on satellite orbits, no satisfactory tide models exist. The equilibrium theory does not suffice for these corrections, and improved values for k2 and particularly for the phase lag δ can only come from a concomitant improvement in our knowledge of the ocean tides. It is possible to extract some information on the ocean tides from the orbital analyses, and this could be used as a constraint in numerical ocean tide computations. We have analyzed the orbit of the satellite Geos 2 for the lunar M2 tide. After correcting for the ocean tides the value found for k2 varies between 0.27 and 0.30, depending on which ocean tide model is used. The solutions for the phase angles are quite unsatisfactory, and this condition stems from insufficiently precise tracking data and inadequate coverage as well as from inadequate tide models. We have applied approximate ocean tide corrections to the tide parameters determined by several authors to give a mean value of k2=0.31 and δ2=0.5°. This phase lag corresponds to a mantle Q of about 60.