Tidal acceleration of the moon deduced from observations of artificial satellites

Abstract

DOUGLAS et al.1 demonstrated the existence of an apparent latitude dependence of tidal friction by determining disparate values of the second degree Love number (k2) from perturbations of the inclinations of the GEOS-1 and GEOS-2 satellites. Lambeck et al.2 correctly explained this phenomenon as being due to neglect of ocean tide perturbations. Parameter values for some ocean tide components have been obtained from several satellites3, but parameter values for the M2 tide, the dominant (85%) effect of the oceans on the tidal acceleration of the Moon, have not been published. Using an improved method for computing mean elements, we4 obtained an observation equation for the M2 tide from the satellite 1967-92A. Applying this technique to the satellite GEOS-3, we now obtain an additional observation equation for the M2 tide. As shown in ref. 2, solid and fluid tide effects on satellites cannot be separated, requiring assumption of the solid tide amplitude and phase parameters for a fluid tide solution. Assuming k2 = 0.30, δ2 = 0°, and using the values of Lambeck5 for the minor O1 and N2, contributions to ṅt, our fluid tide parameters for the M2 ocean tide yield the value of the tidal acceleration ṅt = −27.4±3 arc s (100 yr)−2, in excellent agreement with the value ṅt = −27.2±1.7 arc s (100 yr)−2 obtained by Muller6 from a combination of ancient and modern observations. These two values are lower than the value ṅt = −35±4 arc s (100 yr)−2 obtained from numerical ocean tide models5. Our assumption of a negligible solid tide phase angle is supported by a recent determination by J. T. Kuo (personal communication) that the phase angle obtained from a transcontinental network of tidal gravimetric stations is < 1°. Changes ⩽ 0.5° in solid tide phase angle change our result for the combined solid/fluid ṅt by no more than 1 arc s per (100 yr) (ref. 2).