Reduction of ephemeris error influence in determinations by lunar laser ranging

It has been shown in different previous papers that continuous or quasi continuous ranging at a lunar reflector from a terrestrial observatory will yield the distancew of that observatory to Earth instantaneous axis of rotation, and its longitudeL with respect to Ephemeris meridian. However it has been shown also that these determinations imply a very accurate knowledge of the geocentric range of the same reflector. By developing the difference: true minus computed geocentric ranges as a function of time, we establish relations between the first and second order terms of the above development and the errors entailing the longitude and distance to axis determinations, respectively.On the other hand, the different terms of that same development are related to the first, second, ... variations of true minus computed geocentric ranges of the reflector during lunar passage. Thus, the first two differences are finally related to errors committed onL andw determinations.The above properties have been extended to higher order variations. We show that, as could be expected, those with odd order correlate with longitude errors, and those with even order with distance to axis errors.Inasmuch as the magnitude of successive terms can be expected to decrease as their order increases, it appears thus that the most accurate determinations forL andw should rely on higher order variations, calling for range measurements in large number and evenly distributed during Moon passage.At the same time, comparison betweenw andL values resulting from variations of the same parity but different orders will provide a coherence test for such determinations.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.