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Aims. The aim of this study is to develop new analytical series representing lunar coordinates to accuracy compatible with the accuracy of the modern numerical ephemeris of the Moon.Methods. An improved method of spectral analysis of tabulated function is used to make harmonic development of the latest long-term numerical ephemeris of the Moon LE-406 which covers a six thousand-year interval. A feature of the method is that the development is made directly to Poisson series where both amplitudes and arguments of the series' terms are high-degree polynomials of time.Results. The new analytical development includes 42 270 Poisson series' terms of minimal amplitude equivalent to 1 cm and is valid over 1500-2500. A simplified version of the development includes 7952 series' terms of minimal amplitude equivalent to 1 m and is valid over 3000BC-3000AD. Over 1500-2500 the maximum difference between lunar coordinates calculated by means of the new analytical series and numerical ephemeris LE-406 is 3.2 m in geocentric distance, 0. 0056 in ecliptic longitude, and 0. 0018 in ecliptic latitude. This is 9-70 times better than the accuracy of the latest analytical theory of lunar motion ELP/MPP02, and the number of terms in the new development is less than that in ELP/MPP02.

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Planetary cycles have been argued to be detected in key geophysical time series 11 and attributed to planetary influence on solar activity 12 • These quasi-periods can be identified in the oscillations of the Earth's orbital 13 movement, which directly modulate incoming solar fluxes 14 • A hypothesis that some of these quasi-periods could be fully or partially origi-15 nated in changes of the Sun-Earth geometry is put forth

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