Earth tide information from two counter-orbiting polar satellites

Earth satellites are subject to appreciable twice-yearly and twice-monthly orbit plane fluctuations due to solar and lunar gravity. The elastic-tidal response of the Earth to the Sun and Moon also affects a satellite orbit, thus increasing the direct effect of the Sun and Moon by as much as 17% for a low satellite. A relativistic experiment, recently proposed by Van Patten and Everitt, involves two counter-orbiting polar drag-free satellites which are to pass each other regularly over the Earth's poles, at which times the closest approach distance is measured by a Doppler signal with an accuracy of perhaps 1 cm. This will provide orbit plane perturbation information at least two orders of magnitude better than heretofore, and it is of interest to know whether geographical variations in the Earth's elastic response could be detected. Analysis reveals (1) that a 1% North-South asymmetry in the Earth's average elastic response could give rise to a twice-yearly fluctuation of a few cm in the relative altitude of the two satellites at the poles; and (2) that the geographical separation of the oceans should give rise to twice-yearly and twice-monthly fluctuations of a few cm in the amplitude of the twice-daily fluctuation in the orbit plane separation at the poles, associated mainly with the J 22 term in the Earth's potential.