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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Physical libration of the Moon: the results and the
perspectives
N. Petrova 1 , A. Gusev 1 , K. Heki 2 , H. Hanada 2 , N. Kawano 2 and
ILOM Research Group 2
1 Kazan State University, Kazan, Russia
2 National Astronomical Observatory, Mizusawa, Iwate, Japan
Beginning of the new millenium is marked by the reviews of results and
problems in the field of lunar physical libration (LPhL) (Petrova, Gusev, 2001;
Williams et al., 2001). The stage of investigation of the rotation of the Moon as a
rigid body is finished by works of Migus (1981), Eckhardt (1981), Moons (1982,
1984), Petrova (1996). There exist two approaches in LPhL--theory, analytical
and numerical ones. The latter is more accurate and allows to include more easi­
ly any modification of the rotation model. The main advantage of the analytical
approach is the possibility to separate the forced and free librations. An improve­
ment of the model of the lunar gravitational field with the aid of artificial lunar
satellites, very high accuracy and amount of lunar laser ranging observations,
effective mathematical and computer techniques permit to study many refined
phenomena in lunar rotation and thus to take into account a complex interior
composition of the Moon.
Analysis of LLR indicates that strong dissipation affects the rotation. Two
possible sources of dissipation, solid--body tides and turbulent core--mantle
boundary at a fluid core, are considered. The best fit to observations is achieved
by means of numerical integration by taking into account the effects of tidal spe­
cific dissipation Q slowly increasing with period and small fluid iron core with
the radius of 352 km or a core of Fe­FeS eutectic composition with radius 374 km
(Williams et al.,2001).
Analytical theory of LPhL constructed by Moons (1982, 1984) is now com­
pleted by J. Chapront et al. (1999), by including the perturbations due to tidal
effect (for elastic and anelastic models), indirect perturbations induced by the
planets and by Earth figure and direct and indirect perturbations due to the
ecliptic motion. For the first time Chapront et al. have added terms to the ana­
lytical solution for a forced part of the LPhL which depend on parameters of the
free libration in the form of trigonometrical series. Coefficients and phases of the
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free libration were obtained by comparing with the laser observations and with
the results of numerical integration. Due to the frequency analysis Chapront and
Chapront­Touz'e completed the analytical solution by a small number of trigono­
metric terms whose coefficients, frequencies, and phases are purely numerical.
As result, the semi--analytical series of physical libration have been obtained.
Residuals of this solution when compared with the ephemerides DE245 are below
0:03 00 .
According to the theory of rotation of a two--layer body containing a solid
mantle and a liquid core the new mode, called free core nutation (FCN), should
appear in the polar rotation of the celestial body. The FCN phenomenon is a
consequence of the fact that the core's rotation pole does not align with the
mantle's pole. The FCN detection and its period in the rotation of the Moon
will allow: a) to clarify the physical nature of the lunar core (FCN is possible
only for the liquid core); b) to determine the core radius and its flattening; c) to
determine the density jump at the core--mantle boundary and CMB flattening.
The preliminary estimation of the FCN--period (Petrova, Gusev, 2001) gives the
value of 144 years hardly accessible for ground--based observations owing to the
small size, small ellipticity and slow rotation of the lunar core.
In this respect the planned Japanese space experiments In--situ Lunar Orienta­
tion Measurement (ILOM) can help to discover even such long--period variations
with small amplitudes, which may have the FCN frequencies. ILOM Research
Group (Heki et al, 2000) are proposing the in­situ measurement of the physical
libration with the optical telescope at the lunar pole as one of the missions in the
second SELenological and ENgineering Explorer (SELENE 2). A telescope with
lens of 20 cm in diameter, 2 m in focal length is equipped with a 4000 \Theta 4000
CCD array to determine the stellar positions accurate to one milliarcsecond and
a mercury pool that compensates the tilt of the telescope. The scientific targets
of ILOM project are the investigation of physical properties of the Moon Q, k 2
,
R core
, core density, density jump at the CMB and CMB flattening, excitation and
maintenance mechanism of the free libration and free core nutation, core--mantle
different rotation. For successful determination of the FCN--parameters a further
detailed elaboration of the analytical theory of physical libration of the two--layer
Moon is required.
References
1. Chapront J., Chapront--Touz'e M., Francou G. Complements to Moon's lunar
libration theory. Cel.Mech. & Dyn. Astr., 1999, 73, 317--328.
2. Heki K., Hanada H., Iwata T. et al. In--situ Measurement of the Physical
Libration and Tidal Deformation of the Moon, presented at ETS2000, Mizu­
sawa, 2000.
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3. Petrova N., Gusev A. New trends in the development of the lunar physical
libration theory. Cel. Mech. & Dyn. Astr., 2001, 80, 215.
4. Williams J. G., Boggs D. H., Yoder C. F., Ratcliff T, Dickey J. O. Lunar
rotation dissipation in solid body and molten core. J. Geoph. Res., 2001,
106, No. E11, 27.
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