Lunar librational and polar coordinates series

The ME system/frame are related to the PA system/frame through the definition of a rotation transformation. The paper provides a new procedure to determine the transformation procedure between the two systems that is based on a series decomposition of librations and pole motion. The comparison of the position of the lunar laser retro-reflectors obtained with different ephemerides is used to estimate the internal and external uncertainties of the different realisations of the PA and ME systems as well as comparisons between Euler angles and propagation of Euler angle uncertainties.

This paper provides the full expression of the transformation and a new libration and polar motion series of the lunar motion. It also introduces possible realisations of the lunar time-scales depending the usage. The proposed procedure with the opportunities for future improvements can help set new standards for the lunar reference systems and its realisations.