Determining parameters of Moon’s orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

Abstract

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo-and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970-2013. Parameters of other models are taken from solutions that were obtained independently from LLR.A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon's extra eccentricity rate, as compared to the original DE430 model with two fit parameters.A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission.Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid

Observational Constraint on the Radius and Oblateness of the Lunar Core‐Mantle Boundary

“…]∕ c is used to describe the oblateness (also called polar flattening) of the core, through its principal components of the MoI tensor  c ,  c , and  c ). While this allowed a close comparison to independent studies (Folkner et al, 2014;Pavlov et al, 2016), the previously reported (Viswanathan et al, 2018) uncertainty on f c does not account for uncertainties from considering a fixed value for c . A different plausible model value of c (e.g., 3 × 10 −4 ) would increase the corresponding value of f c by ≈ 2 × 10 −4 , suggesting an uncertainty Williams et al, 2014).…”

On the Extension of Adams–Bashforth–Moulton Methods for Numerical Integration of Delay Differential Equations and Application to the Moon’s Orbit

“…The first one is the usual forward-backward test. The full dynamical equations of the Moon from [3] were integrated from 1984 to 2014, and the solution at the last point was taken as the initial condition for integrating backwards, from 2014 to 1984. Differences between the two results are shown in fig.…”

“…Let us move on to the equation for which the method descibed in this article was developed. This is the equation for the rotational motion of the Moon [2,3], written in a Moon-fixed frame: where ω is the angular velocity, m is the mass of the Moon, N is the external torque, and I(t) is the inertia tensor of the lunar mantle. The inertia tensor is defined as…”

“…Most importantly, the inertia tensor of the Moon is subject to delayed tidal distortion from Earth and delayed spin distortion. Tidal and spin distortions are evaluated with a delayed argument, so calculation of I(t) involves not r(t) and ω(t), but r(t − τ ) and ω(t − τ ), and τ is a constant time delay (in [3], τ = 0.096 d). Thus, the equation 1 is a delay differential equation of neutral type with constant delays [4], the general form for which would bė…”

“…and is defined for t 0 = JD 2446000.5 (1984-10-27 midnight) [3]. To cover the whole interval of the lunar laser ranging observations, numerical integration has to be performed both forward and backward in time.…”