Lunar dynamics and selenodesy: Results from analysis of VLBI and laser data

Very-long-baseline interferometry (VLBI) observations of lunar radio transmitters have been combined with data from laser ranging to lunar retroreflectors to estimate simultaneously (i) parameters in models of the lunar orbit and libration; and (ii) the selenodetic coordinates of the radio transmitters and retroreflectors. For the ratio of the mass of the sun to that of the earth plus moon, we obtain 328,900.50 ± 0.03. For the lunar moment-of-inertia ratios we find β[Ξ(C-A)/B] = (631.27 ± 0.03) x 10-6 and ϒ[Ξ(B-A)/C] = (227.7 ± 0.7) x 10-6. The value implied for C/MR2 is 0.392 ± 0.003, with the uncertainty being dominated by that of the coefficient, J2, of the second zonal gravity harmonic, obtained by Gapcynski et al. from analysis of Explorer spacecraft orbital data. The values and most of the uncertainties that we obtain for the third-degree harmonics of the moon’s gravity field are comparable to those which have been obtained by others from observations of lunar-orbiting spacecraft. However, our determination of β appears to be the best available, and our results for two third-degree gravity coefficients, C31 = (26 ± 4) x 10-6 and C33 = (2 ± 2) x 10-6, have much less uncertainty than determinations based on laser data alone. For the relative-position vectors of both the lunar radio transmitters and the retroreflectors our estimates have uncertainties of about 30 m along the earth-moon direction and about 10 m in each of the two transverse coordinates.

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