Lunar Laser Ranging - Improved Modelling and Parameter Estimation
Creators: name: Singh, Vishwa Vijay
Publisher: name: Hannover : Institutionelles Repositorium der Leibniz Universität Hannover
Year: 2023
Subjects: subject: Lunar Laser Ranging
subject: lunar ephemeris
subject: earth rotation parameters
subject: relativity tests
subject: LLR
subject: Mondephemeriden
subject: Erdrotationsparameter
subject: Relativitätstests
subject: Dewey Decimal Classification::600 | Technik

description: Lunar Laser Ranging (LLR) measures the distance between observatories on Earth and retro-reflectors on Moon since 1969. The LLR analysis is split in various steps: (1) The calculation of lunar and planetary ephemeris, (2) calculating the travel times of the laser pulses and examining its differences to the observed travel times of the pulses based on sophisticated models, and (3) fitting a set of parameters of the Earth-Moon system by a least-squares adjustment based on the Gauss-Markov Model (GMM). In this thesis, all three steps were investigated, and new results are given. Two articles on this work have been published in Advances in Space Research Singh et al. (2021, 2022) and one has been published in Physical Review Letters Singh et al. (2023). The starting point for the numerical integration of the ephemeris calculation in the LLR analysis software (‘LUNAR’) of the Institute of Geodesy (IfE) was changed from June 24, 1969 to January 1, 2000. This change improves the uncertainty of the lunar orbit by about 35 %. The uncertainties of the parameters other than the lunar orbit also change, showing a small systematic improvement. The ephemeris calculation was updated based on the DE440 ephemeris. This change leads to a small improvement in the results, and keeps the dynamical model up to date. The non-tidal loading effect causes deformations of the Earth surface up to the centimetre level. Its addition in LUNAR improves the uncertainties of the station coordinates by about 1 % and also the LLR residuals by up to 9 %. Similarly, the additional modelling of tidal atmospheric loading (TAL) from the IERS 2010 conventions in LUNAR also improves the uncertainty of the station coordinates by up to 7 % and the LLR residuals by up to 24 %. The changed TAL modelling is with respect to an older model in which the atmospheric pressure loading from the IERS 1996 conventions was used. A sensitivity analysis and a validation by resampling was performed by creating various solutions of LUNAR with different conditions to test the need for a scaling factor for the GMM-obtained standard deviation (1σ) values. An up-scaling to provide realistic uncertainties is neither necessary for the standard set of parameters, nor for the polar motion coordinates (x_p and y_p). For ΔUT1 values, however, the uncertainty of recent estimates must be given as 2σ values. The current best uncertainty from their individual estimation are 9.77 ms for ΔUT1, 0.35 mas for x_p, and 0.64 mas for y_p. A possible violation of the equivalence of passive and active gravitational mass, for Aluminium and Iron, using LLR data is also discussed in this thesis. For the test, the method of Bartlett and van Buren (1986) is used. A new limit of the validity of that equivalence of 3.9 x 10^(-14) is given. This is about 100 times better than the previous one.