High-precision analytical representation of lunar ephemeris

A study was conducted to find put the high-precision analytical representation of the lunar coordinates. The method included the use of geoequatorial rectilinear lunar coordinates, presented by the modern long-term LE-406 ephemeris to calculate the tables for the lunar coordinates within the time period from 3000 B.C. to 3000 A.D. The spectral analysis method helped in decomposing the spherical coordinates of the moon into the segments of the Poisson series. Two variants were obtained for the expression of the lunar spherical coordinates in the Poisson series. The LEA-406 analytical expansion of the lunar coordinates and the ELP/MPP02 analytical theory of the lunar motion were adapted to the modern numerical LF-405/406 lunar ephemeris. Results show that the accuracy of the new LEA-406 expansion exceeds that of the ELP/MPP02 theory for both short and long time intervals.