Study of the determination of the topocentric lunar librations by a best fit estimate of the plate constants from digital images with a small telescope

The determination of the lunar optical librations in longitude and latitude from direct observation of the Moon represents an exciting, though possibly challenging, student project with a profound pedagogical potential. In principle, it is possible to compute the optical librations from the small number of observations needed to obtain the plate constants. In practice, however, the plate constants are more effectively obtained by a best fit of the positions of a larger number of lunar features on a digital image by means of the well-known relations to the selenographic coordinates available from a lunar atlas. Firstly, here we report on an analysis of the relationship between the final accuracy in the determination of the librations by this methodology and the several factors that affect the result. For this purpose, the fundamental photogrammetric equations are studied by means of simulations to investigate the effect of the number of features used, their position on the lunar face, and the resolving power of the optical system. Secondly, actual measurements are carried out on digital images acquired by the author by means of a Canon 500D at the prime focus of a Meade ETX-90. These measurements are also further augmented by the estimates of a class of university sophomore students working independently in an Introduction to Remote Sensing class. Additional refinements are considered for future work, such as parallactic effects, the diurnal parallax and the evolution of librations during the lunar orbit.