Nature 266, 514 - 515 (07 April 1977); doi:10.1038/266514b0

Tidal acceleration of the moon deduced from observations of artificial satellites

C. C. GOAD & B. C. DOUGLAS

National Oceanic and Atmospheric Administration, National Ocean Survey, Geodetic Research and Development Laboratory, Rockville, Maryland 20852

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 (k ₂) 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 M ₂ 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 M ₂ tide from the satellite 1967-92A. Applying this technique to the satellite GEOS-3, we now obtain an additional observation equation for the M ² 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 k ₂ = 0.30, ₂ = 0°, and using the values of Lambeck⁵ for the minor O ₁ and N ₂, contributions to _t, our fluid tide parameters for the M ₂ ocean tide yield the value of the tidal acceleration _t = -27.43 arc s (100 yr)^-2, in excellent agreement with the value _t = -27.21.7 arc s (100 yr)^-2 obtained by Muller⁶ from a combination of ancient and modern observations. These two values are lower than the value _t = -354 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 _t by no more than 1 arc s per (100 yr) (ref. 2).

References

1.	Douglas, B. C., Klosko, S. M., Marsh, J. G. & Williamson, R. G. Celestial Mechanics 10, 165–168 (1974).
2.	Lambeck, K., Cazenave, A. & Balmino, G., Rev. Geophys. Space Phys. 12, 421–434 (1974).
3.	Felsentreger, T. L., Marsh, J. G. & Agreen, R. W. J. geophys. Res. 81, 2557–2563 (1976).
4.	Goad, C. C. & Douglas, B. C. J. geophys. Res. 82, 898–900 (1977).
5.	Lambeck, K. J. geophys. Res. 80, 2917–2925 (1975).
6.	Muller, P. M., Jet Propulsion Laboratory Special Rep. JPL SP 43-36 (1976)