Recent Researches on the Determination of the Moon’s Physical Libration Constants

Abstract

Although the problem of determination of the physical Iteration constants has been the object of interest for astronomers since over 150 years, yet various methods applied by various authors yielded up to the present day very divergent values for these constants. Thus, e.g., the values of the two principal unknowns of the libration problem — i.e., of the Moon’s mechanical ellipticity f, characterizing the differences of the Moon’s principal moments of inertia and of the mean inclination I of the Moon’s equatorial plane to the ecliptic — obtained by various investigators for the past few years, are not only discordant among themselves within the limits of their mean errors, but do not even show any tendency of converging to some definitive values. Thus the values of f obtained in recent years ranged from f = 0.50 (Habibulin, 1958) to f =0.89 (Gorynya, 1965). Similarly, the values of I ranged from I =1°30′54″ (Shakirov, 1963) to I =1°33′50″ (Watts, 1955). If we compare these values of the fundamental physical libration constants with those obtained for these constants for the past 120 years, commencing with the first serious discussion of this topic by WICHMANN (1847, 1848), we might come to a discouraging conclusion that the endeavours to solve the problem of the Moon’s physical libration have ended in a deadlock and did not advance for 120 years.