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 ṅ_t, our fluid tide parameters for the M₂ ocean tide yield the value of the tidal acceleration ṅ_t = −27.4±3 arc s (100 yr)⁻², in excellent agreement with the value ṅ_t = −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 ṅ_t = −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 ṅ_t by no more than 1 arc s per (100 yr) (ref. 2).