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.

Influence of the layered Moon and Earth’s orientation on lunar rotation

One of the most efficient ways to probe the lunar inner structure at present is through the study of its rotation.Range and range rate(Doppler) data between the Chang’E-3 lander and station on the Earth were collected from the beginning of the Chang’E-3 lunar mission in 2013.These observation data,taken together with the existing lunar laser ranging data,provide a new approach to extend research on the Earth-Moon system.The high precision of current observation data imposes exacting demands,making it necessary to include previously neglected factors.In this paper,motivated by progress of the Chinese lunar exploration project and to use its data in the near future,two lunar models:a one-layer model and a two-layer model with a fluid core,were applied to the rotational equations based on our implemented algorithm of the Moon’s motion.There was a difference of about 0.5′′in φ and ψ,but 0.2′′in θ between the two models.This result confirms that stratification of the inner structure of the Moon can be inferred from rotation data.We also added precise Earth rotation parameters in our model;the results show that this factor is negligible at present,due to the limited precision of the existing data.These results will help us understand the rotational process clearly and build a more realistic Earth-Moon model when we combine Lunar Laser Ranging data with high precision radio data to fit lunar motion in the near future.

Computation of the atmosphere-less light intensity curve during a total solar eclipse by using Lunar Reconnaissance Orbiter topography data and the DE430 astronomical ephemeris

Observations of the sky irradiation intensity in the visible wavelengths during a solar eclipse permit to model the Sun diameter,a key number to constrain the internal structure of our star.In this paper,we present an algorithm that takes advantage of the precise Moon topography from Lunar Reconnaissance Orbiter to compute,with a high resolution in time,the geometrical part(i.e.top-of-atmosphere,and for a given wavelength)of the sky irradiation at any given location on the Earth during these events.The algorithm is also able to model the Baily’s beads.We give as an application the theoretical computation of the light curve corresponding to the solar eclipse observed at Lakeland(Queensland,North Australia)on 2012 November 13.The application to real data,with the introduction of atmospheric and instrumental passbands,will be considered in a forthcoming paper.