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Improving the dynamical model of the Moon using lunar laser ranging (LLR) and spacecraft data

Abstract : The main goal of the Ph.D. thesis of Vishnu Viswanathan was to improve the dynamical model of the Moon within the numerically integrated ephemeris (INPOP) and to derive results of scientific value from this improvement through the characterization of the lunar internal structure and tests of general relativity.At first, raw binaries of LLR echoes obtained from the Grasse ILRS station was used to analyze the algorithm used by the facility, for the computation of a normal point from the full-rate data. Further analysis shows the dependence of the algorithm on the reported uncertainty contained within the distributed LLR normal points from Grasse. The importance of the normal point uncertainty is reflected in the weighted least square procedure used for parameter estimation, especially in the absence of a standardized algorithm between different LLR ground stations. The thesis also benefitted in terms of a more dense dataset due to technical improvements and the switch of operational wavelength to infrared at the Grasse LLR facility (Courde et al. 2017).The reduction of the LLR observations was carried out on GINS orbit determination software from CNES. The modeling follows the IERS 2010 recommendations for the correction of all known effects on the light-time computation. The subroutines were verified through a step by step comparison study using simulated data, with LLR analysis groups in Paris and Hannover, maintaining any discrepancies in the Earth-Moon distance below 1mm. Additionally, correction of effects due to hydrological loading observed at the Grasse station has been implemented. An improved version of the LLR reduction model was submitted to the space geodesy team of CNES (GRGS).The lunar dynamical model of INPOP was first developed by Manche (2011). However, due to the absence of the fluid core within the previous version of INPOP (13c), the residuals obtained after a least-square fit were in the level of 5cm for the modern day period (2006 onwards). A detailed comparison of the dynamical equations with DE430 JPL ephemeris helped to identify required changes within INPOP for the activation of the lunar fluid core. Other modifications allowed the use of a spacecraft determined lunar gravity field within the dynamical model. The use of a bounded value least square algorithm during the regression procedure accounted for variability to well-known parameters from their reported uncertainties. The resulting iteratively fit solution of INPOP ephemeris then produces a residual of 1.4-1.8 cm, on par with that reported by Folkner et al. 2014 and Pavlov et al. 2016. The new INPOP ephemeris (INPOP17a) is distributed through the IMCCE website ( with a published documentation (Viswanathan et al. 2017) in the scientific notes of IMCCE.Furthermore, on providing tighter constraints on the lunar gravity field from GRAIL-data analysis within the dynamical model, a characteristic lunar libration signature with a period of 6 years was revealed with an amplitude of +/- 5mm. Several tracks were investigated for the identification of the unmodelled effect, involving higher degree tidal terms and torque components. This remains as a work in progress, which will be continued through a postdoctoral contract in Paris. A publication is under revision on this subject.Residuals at the level of a centimeter allow precision tests of the principle of equivalence in the solar system. The fitted value of the parameter characterizing the differential acceleration of the Earth and the Moon towards the Sun was obtained with numerically integrated partial derivatives. The results are consistent with the previous work by Williams et al (2009, 2012), and Hofmann et al. (2010, 2016). An article on this work is in preparation.
Keywords : Llr Grail Inpop
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Submitted on : Tuesday, May 15, 2018 - 4:19:07 PM
Last modification on : Sunday, October 18, 2020 - 4:04:06 AM
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Vishnu Viswanathan. Improving the dynamical model of the Moon using lunar laser ranging (LLR) and spacecraft data. Astrophysics [astro-ph]. Université Paris sciences et lettres, 2017. English. ⟨NNT : 2017PSLEO005⟩. ⟨tel-01792665⟩