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LUNAR FIGURE AND LUNAR LIBRATION


AS A CLUE TO LUNAR INTERIOR

Alexander Gusev, Natasha Petrova, Naufal Rizvanov,
Kazan state university & Engelgrdt's astronomical observatory,
Dpt. of Astron. & Gravit., Kremljevskaja str. 18. Kazan 420008, Russia
e-mail:Alexander.Gusev@ksu.ru

The study of geometrical and dynamical figure of the Moon is one of
the important elements of the complex approach to investigation of our
satellite. Correlation of visible limb and real relief, mass distribution
in lunar body, relative position of center figure and center of mass,
geometrical sizes and dynamical parameters - all these questions are
connected with the study of lunar figure. Data concerning lunar relief
give evidence of the processes happening and on the surface both in lunar
interior at the different stages of lunar evolution: early volcanism epoch,
the period of bombarding by large planetozimals, late volcanism stage,
formation of lunar maria and craters. Series of works directed on the
study of gravitational field of the Moon with the help of artificial lunar
satellites significantly advances our knowledge about dynamical figure.
This allowed to construct the more accurate theories of lunar rotation, to
model the processes in deep interior of the Moon. The nearness of Moon to
Earth allows to use all complex of scientific methods to its investigation.
Traditional astronomical observations: astrophysical (albedo, spectral
analysis), astrometrical data are combined with results obtained by
geophysical and geochemical methods (seismic ranging by landing modules of
spacecrafts), with laser ranging data and etc. Because of this the Moon
always was, is being and will be the interesting object for the study and
as the nearest natural cosmic laboratory. In this connection the programs
of international space lunar experiments are very intensive and extensive.
[23]

KAZAN LUNAR INVESTIGATIONS
Ground-based astronomical observations fill their own place in the
complex approach to investigation of the Moon. Although they have a less
precision, the long series of ground-based observation are used for the
study of long-period, secular variations of orbital and rotational
parameters of the Moon. Interpretation of large-scale star-calibrated
lunar photographs gives the possibility to obtain the data of the Moon's
relief from the near side directly in the celestial system of coordinates.
Heliometric and photographic observations of the Moon were carried
out in the Engelgardt's Astronomical Observatory (AOE) for the purpose: a)
to study the lunar rotation ; b) to determine the selenodetic coordinates
of lunar craters and c)to establish the uniform scale of ephemeris time.
First in selenodesy the catalogue of 264 crater selenocentric coordinates
was constructed by ``absolute method'', that is, relatively to star
coordinate system. Dynamical range of topography of about 10km was
discovered in the region of the Mare Oriental [21]. N.Rizvanov investigated
the geometrical figure of lunar near side using the large-scale star-
calibrated photographs [22]. He discovered that according his catalogue,
the north of the parallel +10o the relief of lunar surface is about 2.5 km
lower comparatively to generally accepted level determined by other ground-
based observation of the Moon. This effect was conformed by analyses of
lunar photographs obtained by ``Zond-6, -8''.
The work of Sh.Khabibullin ``Nonlinear theory of the physical
libration of the Moon'' [4] has initiated theoretical investigation of
lunar rotation in Kazan University. Prof. Khabibullin and his disciples
have constructed the tables of LPhL for proceeding of libration
observations with the aim to improve parameters of lunar dynamical figure,
to reveal the free librations [5-10]. The attempt was made to consider the
influence of internal structure on lunar rotation. On the basis of modern
lunar motion tables the analytical tables of LPhL was constructed by
Petrova [15,16]. Development of the theory is being continued by
consideration of the complex stratigraphy of lunar interior. [2, 17 - 19].

TOPOGRAPHY, ALTIMETRY AND GRAVITY MODEL
FROM CLEMENTINE and LUNAR PROSPECTOR
Towards the end of the 20th century our knowledge about the
geometrical and dynamical figure of the Moon is significantly improved. The
advance is achieved due to the development as the ground-based observations
so the cosmic experiments, due to the application of Lunar Laser Ranging,
of Lunar satellite Doppler data and, especially, of last cosmic
experiments such as the Clementine-mission [28] and the Lunar Prospector
[11].
Detailed maps of the lunar surface, an improved gravity model are
obtained. The data have revealed some surprising features in the Lunar
figure that distinguishes significantly from the Earth's one:
. the most pronounced topographic feature on the Moon is the South Pole-
Aitken Basin as a largest and deepest impact basin in the solar system;
. distribution of elevations on the Moon determined by the Clementine
deviates strongly from a normal distribution,
. suggesting that several geological processes have influenced the
topography;
. the Clementine and the Lunar pospector missions provide data which
strengthen the contrast between near and far sides: the geochemical
dichotomy between the near and far- side; the farside crust is, an
average, thicker (68 km) than on the near side (60 km), accounting for
much of the offset in center-of-figure from the center-of-mass;
. the terrestrial hypsogarm is bimodal and reflects a marked difference
between the oceanic and continental lithospheres, the lunar hypsogram,
although not distinctly bimodal, clearly shows more structure than the
simple normal distribution of altitudes that might be expected from a
saturated cratered surface;
. new large mass concentrations (mascons) in the lunar crust, and
especially, four mascons in the large farside basins are opened, this
discovery rises the question of the formation and support mechanism of
the mascons as uncompensated buried loads (excess mass) in basin.
We propose that mascons in the thick (up to 100km) lunar continental
crust might be produced by convective processes in the upper mantle of the
Moon at the early stage of its thermal evolution}. Processes of mascon
formation are apparently analogous to those in the Earth [4,17]: the top of
the plume rising from core-mantle boundary (CMB) was conserved in the thick
lunar crust. The analogous model of convective evolution of the lunar
mantle is proposed by [12]: the partial melting occurs in the upper mantle
as a consequence of hot upwelling plumes generated by instabilities of the
hot core-mantle thermal boundary layer.


LUNAR LASER RANGING

Contributions from LLR includes the three-orders-of -magnitude
improvement in accuracy in the lunar ephemeris, a several- orders-of-
magnitude improvement in the measurement of the variations in the Moon's
rotation, and the verification of the principle of equivalence for massive
bodies with unprecedented accuracy.
The data set considered by [13,14] consists of more than 9900 normal
points ranges spanning the period between 1969 and 1995. The analysis of
LLR data provides a wealth of information concerning the dynamical figure
and internal structure of the Moon. Presently the most accurate estimate of
the lunar moment of inertia is obtained from combining the determinations
of moment of inertia differences ( and ( from the LLR solution and the
lunar gravity field coefficients J2=[C- (B+A)/2]/MR2] and C22=[(B-A)/4MR2]
obtained from analysis of lunar satellite data and LLR. The resulting polar
moment from this combination is C=(0.3935(0.0011)MR2 [1]. The same value,
obtained later by [24], is 0.3929(0.0009MR2.
An interpretation of polar moment gives [1] in terms of a 60-km-thick
lunar crust with density of 2.75 g/cm3 a constant density ( of the lunar
upper mantle, a lower mantle with contrast in (( relative to the upper
mantle, and a variable-radius iron core with density of 7g/cm3.The maximum
core size is in the range of 220 to 350~km.
An improved gravity model from the Lunar Prospector gives the improved
normalized polar moment of inertia C/MR2=0.3932(0.0002 that is consistent
with an iron core with a radius of 220 to 450km. If the maximum radius of
the core is 450 km as derived from seismic and magnetic data, then the core
is probably Fe or Fe-rich, although an FeS core is not excluded by the data
and models [11].
The inferred from LLR data core radius [26] has a limit of 352 km for
iron and up to 374 km if sulfur presented.

LUNAR PHYSICAL LIBRATION

The study of geometrical and dynamical figure of the Moon is
impossible without the observations of rotational motion of the Moon and,
consequently, without the development of the lunar rotation theory.
The observations of the fine effects in the lunar rotation by the LLR
analyses allow also to inference into the lunar interior, because the
rotation is influenced by solid-body tides and interaction at a liquid-
core/solid-mantle boundary. For example, the dissipation in the Moon causes
a small 0."26 advance in the lunar rotation axis. According to [27] this
offset, a unique signature of dissipation, is observed as a small, meter-
sized, monthly variation. From additional LLR data and an improved gravity
field from Lunar Prospector Williams et al [26] have found four such
dissipation terms, that can be explained with the combined effects of tide
plus core (2/3 of the 0.26" term comes from a monthly tidal Q of 37 and 1/3
comes from the core.
Theoretical solution of libration equations [18] for two-layer Moon
(rigid mantle-liquid core) gives two modes of free lunar libration in the
case of polar motion: a Chandler-like wobble with a period PCW=74.06 yr
(when expressed in the rotating lunar frame), and a Free Core Nutation with
a period PFCN=144.73 yr (when expressed in the inertial frame).
The FCN detection of the Moon and its period will allow [24]:
a) to decide on the physical nature of the lunar core - it is
possible only for the liquid core;
b) to determine core radius and its flattening;
c) to determine density jump at the CMB and CMB flattening.

CONCLUSION

All these discoveries require to take a new view of the evolution of
the Moon, its origin and thermal history, to develop the experimental and
theoretical investigations of our satellite.
In the light of the presented observed and theoretical data concerning
the lunar figure, we attempted to propose a different line of attack on
some local problems.
- The detailed analyses of hypsometric maps obtained by Clementine
will allow to answer the question: is there 2.5 km lowering of the relief
on the near side to the North from the +10 degrees parallel of latitude as
against the generally accepted one?
- Results of the seismic observations by Japanese mission, LUNAR-A
are expected to provide key data on the size of the lunar core and its
physical properties. The heat flow measurements will also provide
important data on thermal structure and concentrations of heat-generating
elements in the Moon. These data will help to test our hypothesis about the
origin of mascons discovered by Clementine in the thick continental crust
of lunar far side.
- We propose to develop the theory of physical libration through
consideration of visco-elastic proprieties of lunar body and core mantle
differential rotation to adequately describe the observational data.

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