Investigations for the improvement of Brownian Moon ranges based on the variations of the integration constants and other parameters

Possibilities to improve Moon theories to determine translational Moon motion were investigated, using Brown's Moon theory and later improvements (e.g., Eckert). After a comparison between Brownian ephemerides and more recent precise Moon ephemerides, parameter estimates were performed for interpolation and extrapolation of Moon ranges. The integration procedure allows deeper insight into the time dependent changes of the variable constants and in the mechanical model. The extrapolation procedure is not suited for precise predictions. The results of the test calculation, based on the supposition of supplements which are constant in time, are not suited for predictions with a better precision than 100 to 200 m. The variations resulting from the parameter suppositions have generally a periodic effect on the Moon ranges.