A Satellite Determination of Tidal Parameters and Earth Deceleration

Abstract

This paper uses perturbations in the inclination and in the longitude of the node for four nearly polar satellites to find values of the tidal number k and of the phases for the lunar and solar semi-diurnal tides. In order to obtain the desired accuracy, it was necessary to include the following perturbations in the analysis: (1) differences between UT2c and UT1, (2) the motions of the true coordinate systems of date, including the rotation of the ecliptic, (3) atmospheric drag, (4) radiation pressure, including radiation scattered or emitted by the satellite and including radiation scattered by the Earth as well as direct sunlight, (5) the atmospheric tide, (6) the gravitational perturbations produced by the Sun and Moon, and (7) the perturbations due to the zonal gravity harmonics. For many of these, existing perturbation procedures are not accurate enough, and new methods were devised. The new methods are described. By-products of the perturbation analysis include a small change in the method of inferring wind velocities from orbital data at altitudes around 600 km, and a substantial change in the value of the estimated torque due to the atmospheric tide. The value found for the ratio of lunar to solar tidal friction torques is considerably greater than that given by any existing model, but is closer to the value generally given for linear friction than to that for non-linear friction. This does not imply that the friction is linear. It is shown that the relation between the torque ratio and the type of friction depends upon an unknown parameter of the oceans. Over a large range of this parameter, which includes plausible values, the ratio of the friction torques is independent of the law of friction. The value found for k is 0·336 × 0·028. The deceleration of the Earth's rotation due to the combination of the gravitational and atmospheric tides is estimated to lie between 16·8 and 21·4 parts in 1011 per year. This is lower than other recent estimates and is in better agreement with the value deduced from ancient eclipses.