Numerical model of the Moon's rotation

• DOI: 10.1007/bf00897102
• Publication Date: 2004-12-28T22:32:30Z
• Authors: R. J. Cappallo; R. W. King; C. C. Counselman; I. I. Shapiro
• Keywords: Root mean square; Libration (molecule); Moment of inertia; Rotation period

We have integrated numercially the differential equtions for the Moon's rotation with respect to an inertial coordinate system, and the variational equations for (i) the six initial conditions of the rotation; (ii) the moment-of-inertia ratios β and γ; and (iii) the coefficients of the third-degree gravitational harmonics. When these integrations are used in conjunction with our current lunar-orbit and Earth-rotation models, and all of the relevant initial conditions and parameters are adjusted to fit five years of McDonald Observatory lunar laser ranging observations, the root-mean-square (rms) of the postfit range residuals is 28 cm. When we adjust the lunar-rotation initial conditions separately to fit the physical libration angles given by the numerical model of Williams (1975), we find an rms orientation difference over a six-year interval of ∼0.03 arcsecond, after removal of a constant bias. A similar comparison of our model with the semi-analytical model of Eckhardt (1981) yields an rms orientation difference of ∼0.2 arcsecond.