J/A+A/705/A88 Lunar librational and polar coordinates series (Rambaux+, 2026)
Lunar reference systems and their realisations using INPOP ephemerides.
Rambaux N., Fienga A. , Seyffert Y., Sosnica K., Kaitheri A., Laskar J.,
Gastineau M., Baguet D.
<Astron. Astrophys. 705, A88 (2026)>
=2026A&A...705A..88R 2026A&A...705A..88R (SIMBAD/NED BibCode)
ADC_Keywords: Solar system ; Positional data ; References
Keywords: celestial mechanics - ephemerides - reference systems - Moon
Abstract:
The definition of a reference system plays a crucial role in
quantifying geodetic effects and for surface body cartography. Today,
the development and specification of the lunar reference system is
stimulated by future space missions, some of which will be manned, and
by the needs of lunar space navigation.
The aim of this paper is to describe the lunar reference system in use
and to determine the accuracy of its realisation in space and time. At
present, two lunar reference systems are defined, the PA system
defined according to the Moon principal axes of inertia, and the ME
system defined by the Earth's mean position on the Moon surface. A
first step to relativistic definition of the lunar time scale is also
introduced in agreement with the one proposed by IAU and other recent
realisation.
The realisation of a PA lunar reference system is based on the choice
of an ephemeris, which relies upon the coordinates of the laser
retro-reflectors on the Moon surface. The ME system/frame are related
to the PA system/frame through the definition of a rotation
transformation. The paper provides a new procedure to determine the
transformation procedure between the two systems that is based on a
series decomposition of librations and pole motion.
The comparison of the position of the lunar laser retro-reflectors
obtained with different ephemerides is used to estimate the internal
and external uncertainties of the different realisations of the PA and
ME systems as well as comparisons between Euler angles and propagation
of Euler angle uncertainties. This paper provides the full expression
of the transformation and a new libration and polar motion series of
the lunar motion. It also introduces possible realisations of the
lunar time-scales depending the usage. The proposed procedure with the
opportunities for future improvements can help set new standards for
the lunar reference systems and its realisations.
Description:
The following Tables present the main terms that appear in the
evolution of angles Iσ, ρ, τ, and polar coordinates
p1, p2 as in Rambaux et al., 2011CeMDA.109...85R 2011CeMDA.109...85R.
The argument is a combination of the Delaunay arguments D, l', l, F
that describe the orbital motion of the Moon around the Earth in the
three body problem (Sun, Earth, and Moon). Omega is the ascending node
of the orbit of the Moon, the argument L presents in p1 and p2 is
Omega+F, and the first two letters of the planets represent the mean
longitudes of the planets (Me=Mercury, Ve=Venus, etc.). The angles U,
V, W correspond to the free librations in longitude, latitude, and
wobble. Finally, Un denotes a libration term with frequency
unidentified with a known argument. The Delaunay arguments are
polynomial functions of time at order 4 and the coefficients of the
polynomials are derived from Chapront et al. (2002A&A...387..700C 2002A&A...387..700C).
For the planetary arguments we used Bretagnon et al.
(1982A&A...114..278B 1982A&A...114..278B). The Tables are given in cosine and sine form
where the arguments contain the phases of the Delaunay, planetary or
free terms. The Tables are sorted by the amplitude and then written to
the milliarseconds level.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
isigma.dat 90 180 Series for ISigma
p1.dat 90 182 Series for P1
p2.dat 90 151 Series for P2
rho.dat 90 161 Series for Rho
tau.dat 90 169 Series for Tau
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Byte-by-byte Description of file: isigma.dat rho.dat tau.dat p1.dat p2.dat
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Bytes Format Units Label Explanations
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1- 36 A36 --- Arg Delaunay and planetary arguments
38- 50 F13.3 d Per Period
52- 61 F10.3 arcsec C Cosine Fourier term
63- 72 F10.3 arcsec S Sine Fourier term
74- 81 F8.3 arcsec/cyr PC Cosine Poisson term
83- 90 F8.3 arcsec/cyr PS Sine Poisson term
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Acknowledgements:
Nicolas Rambaux, Nicolas.Rambaux(at)obspm.fr
(End) Nicolas Rambaux [SU-Obspm-LTE, France], Patricia Vannier [CDS] 25-Dec-2025