Lunar project ILOM:application of the analytical theory of Lunar physical libration for the simulation of star observations

This study briefly describes the targets and problems of the future Japanese project In situ Lunar Orientation Measurement(ILOM),which is planned for the year 2017.One of the important parts of the project is to place a small optical telescope on the Lunar surface with the purpose to detect the Lunar physical libration with unprecedented accuracy 0.001 arcsec.At the present stage of research the computer simulation of future observations is going on,aiming to determine the moments of transition of a star through the first meridian and the polar distance of the star.Rotation of the Moon is being calculated under the analytical theory developed in the frame of a theme of the grant.A list of stars brighter than 12 m,whose coordinates are close to the Lunar precession pole motion,was constructed on the basis of several star catalogues.On average,for each moment of observation in the field of view of the telescope(1°) there are approximately 20-25 stars.Analyses of simulated stellar tracks observable from the Lunar surface(in a polar zone) reveal the significant difference from daily parallels of stars in comparison with the Earth.During one Lunar "day" equal 237 terrestrial days,a star moves on a spiral.However,depending on a longitude of a star,these spirals can be untwisted or twisted.In the latter case a star can describe a loop in the sky of the Moon during the period of supervision.Such an unusual astrometric phenomenon combined with the slow rotation of the Moon is compared with the Earth and the fast precession motion of the Lunar pole(in comparison with the precession motion of a terrestrial pole).

Determination of the free lunar libration modes from ephemeris DE430

The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013,and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory（GRAIL）. Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies,the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471′′in longitude, 0.025′′in latitude and 8.19′′× 3.31′′for the wobble, with the respective periods of1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.