The constants of the moon's physical libration derived on the basis of four series of heliometric observations from the years 1877 to 1915

Abstract

A new method for the adjustment of heliometric libration observations of the Moon is given; it is simple from the mathematical point of view, satisfies the principles of the least-squares method, and can easily be applied to programming of calculations of electronic computers. On the basis of 3282 observations of the Moon carried out in four heliometric series from the years 1877 to 1915, the author has determined the forced libration constants, simultaneously with those of free libration in longitude, by using his new method of adjustment of heliometric observations. A joint adjustment has been performed by eliminating the Moon's mean radius corresponding to each series, as it might be affected by irradiation. At the same time an exact proof is given for the uniqueness of the solution for the mechanical ellipticity of the Moon f, which lies below the critical value 0.662. From the libration constants obtained new values for the differences of the Moon's principal moments of inertia are derived. Moreover, the coordinates of crater Mösting A, which constitutes a first order point of triangulation on the Moon, are obtained with high accuracy. A conclusion is drawn that, in the problem discussed, a simultaneous analysis—based on a correct adjustment method—of several heliometric series with a sufficient number of observations covering a sufficiently long period, is necessary to obtain reliable results, fully satisfying the requirements of scientific exactitude.