The last decade or so has seen the practical development of a number of high-precision, space-related geodetic techniques, specifically, lunar laser ranging (LLR), satellite ranging, and very long baseline interferometry (VLBI). One consequence has been an enlarged and improved data base available for studies of lunar motion and earth rotation.
The impact on lunar studies has been particularly striking. The vast improvement in lunar positioning data provided by the LLR experiment has revived interest in the previously lethargic business of modeling the lunar orbit and librations (librations are rotational displacements of the moon about its center of mass). Several numerical and analytical models of the orbit and librations have been developed over the past few years. Numerical models, constructed by numerically solving appropriate differential equations, are generally more accurate than existing analytical models and are, in principal, better suited to removing the effects of lunar motion from the LLR residuals. On the other hand, results from numerical models are less amenable to physical interpretation, and so analytical models continue to receive attention. Analytical models are particularly useful in trying to understand the lunar librations, both because of the possibility of excited free librations and because the dynamical behavior of the moon during the forced librations is not completely understood.