Lunar Navigation Almanac

1. Cm Ac Cc CMB Fe 7 g/cm3 Am Lunar Navigation Almanac Alexander Gusev & Natalia PetrovaKazan University, Russia

2. Thousand-year Kazan city (Russia) • Tatarstan is the most northern frontier between Muslim and Orthodox Christian worlds, a secular republic with stability based on a high percentage of mixed marriages, official support for two languages and cultural tolerance. Kazan, the capital of Tatarstan, is a city of over one million people and the largest port on Volga river, referred to as "the port of five seas". About the size of Ireland or Portugal, Tatarstan has four million inhabitants. As a transportation hub, Kazan serves a region encompassing over 80 million people. • The beautiful city Kazan, situated 800 km East from Moscow, is one of the most remarkable and ancient towns at the left bank of the greatest river Volga, Russia. The ancient monuments of Kazan, together with its beauty and cultural and scientific atmosphere, made it historic centre as a Russian Treasure. Kazan, one of the biggest and most important cultural and industrial centres on the Volga River, referred to as "the port of five seas, with a population nearing 1.2 million made up of 77 different ethnic groups, is the capital of the Republic of Tatarstan.

3. Kazan State University I.M.Simonov N.I.Lobachevsky The Kazan State University is one of the oldest and largest institutes of higher learning in the Russia. It was founded on November 5, 1804. The history of Kazan University abounds in the names of outstanding scientists, staunch revolutionaries, eminent public figures, educators, painters actors. The history of the University is the history of Russian science, social thought and culture: N.I. Lobachevsky - the founder of non-Euclidean geometry (1826); N.N.Zinin obtained aniline (1842), K.K. Klauss - discoverer of ruthenium (1844), A.M. Butlerov propounded the theory of composition of organic compounds; I.M. Simonov discovered the Antarctic during the round-the-world expedition of 1819-1821 led by F.F. Belinsghausen and M.P.Lazarev. Prof. M. Kovalsky predicted the rotation of our Galaxy. Kazan University takes pride in its graduates the great Russian writer Leo Tolstoy, composer M.A. Balakirev, writers S.T. Aksakov, P.I. Mel'nikov-Pechersky and Velimir Khlebnikov. Researchers who brought fame to Kazan university in the post-Second World War years were E. Zavoisky (physics), A.Arbuzov and G. Kamai (chemistry), N. Chetaev (engineering) and N.Chebotarev (mathematics). Kazan University is orientated towards international cooperation and strives for the level of the latest international achievements in different areas. The University participates in international programmes and projects and strengthens its connections with different universities, institutions, researchers and experts from all the continents.

4. Astronomy in Kazan University I. Littrov • Engel'gardt Astronomical Observatory is one of well known • observatories of Russia. The scientific instrumental basis of this • observatory was presented by V.P. Engel'gardt. He was respected and well educated person in Russia. Being very interested in astronomy, V.P. Engel'gardt in the second half of 19 century decided to build his private observatory. But it was not allowed according to the Zhar' law. So this observatory with a good astronomical equipment was build in Drezden (Germany). Later V.P.Engel'gardt decided to present all astronomical instruments to some Russian university. His choice was Kazan University. • At the first time EAO developed traditional for Kazan astronomical investigations, mainly in astrometry. Later prof. D.Ya. Martynov and B.A.Krat published excellent papers on eclipsing binaries, and EAO became as well known center of investigations in this field of astronomy. Other investigations of the Moon, in celestial mechanics, in meteor study, in atmospheric refraction, in model stellar atmospheres in Galactic structure are also well known. A couple years ago the new 1.5 meter • telescope AZT-22 has been installed (in the south). I. Simonov D. Dubyago M. Kovalskiy Sh. Khabibullin

5. Lunar navigational almanacon the basis of SELENE-data for the ILOM-project The Lunar navigational almanac is necessary for realization of any observations from the surface of the Moon. The almanac should contain precise and detailed information about position of stars, Sun, planets, transition from the lunar time to the universal time and inversely, program for sending of signals of time. The lunar navigation at the observations from a lunar surface requires the high-accurate theory of the lunar rotation

6. List of the sections for LNA Time: • Transition from the lunar time to the universal time and inverse • The program of sending of signals of time • The mean longitude of the ascending node • The physical libration in the longitude, presented in time • Correction for irregularity of the true tropical time Stars: • The visible selenoequatorial coordinates of the brightest star • The maps of polar regions of the sky; visible places of the polar stars • The altitudes and azimuths of the polar stars • Selection of navigational stars Earth: • The selenographical coordinates • The sunrise-, sunset-moments • The passage of the Earth’s surface points through the observable terminator

7. MOON ROTATION STUDIES

8. Geophysical cross-section of the Moon

9. Cm Ac Cc CMB Am Fe 7 g/cm3 Evidences of existence of a lunar core and preliminary estimations of its parameters • The structure of the gravity field: the present determination of the is consistent with an iron core with a radius of 220 to 450 km or a Fe-FeS core with a radius 330-590 km (Konopliv, 1998, Williams, 2001). • Analyses of lunar rotational dissipation, obtained by LLR has shown, that the core radius could be as much as 352 km if iron and 374 km for the Fe-FeS eutectic composition. • The magnetometric measurements give an independent conformation of the metal core with a radius from 250 up to 430 km. • An interpretation of the polar momentum when combined with compositional, thermal, and density models of the lunar crust and mantle (Dickey et al., 1994; Kuskov, Kronrod, 2001), can allow some useful inferences to be drown about the mass and size of the core. • The remnant magnetization of lunar rocks is itself an argument in favor of the field being generated by a dynamo process in a liquid iron core at this early period of the lunar evolution (Runcorn, 1996, Stegman et al., 2003).

10. Multi-layer lunar core

11. The Chandler Wobble (CW) is a motion of the rotation axis of the Moon around its dynamical figure axis due to the bulges of the lunar body. For the completely solid Moon the CW has long period 74.6 year in a frame tied to the Moon and is prograde. This mode was detected from LLR observation as 3”8” (6928 м) elliptical component in the oscillation (Newhall and Williams, 1997). The Free Core Nutation (FCN) represents a differential rotation of the liquid core relatively the rotation of the mantle. This mode does exist only if a core is liquid. It has a quasi-diurnal period in a frame connect to the Moon and is retrograde.. SIC FOC Cm Visco-Elastic mantle Ac Cc CMB Fe 7 g/cm3 Am Two - layer model of the Moon

12. FCN strongly correlates to CMB-dissipation • The CW-period does not feel the dissipation: this is an internal process for the whole Moon and it should not have an effect for these oscillations. • For the FCN the strong correlation with the dissipation is observed for core's radiuses Rc less than 400 km. • This fact is very interesting indicator of internal processes, which may be derived from observations – ILOM-project (Japan-2013).

13. Three - layer model of the Moon

14. Fe-Fes 5.3 g/cm3 CMB Fe 7 g/cm3 SIC FOC Elastic mantle Сalculation of the CW- and FCN-periods

15. Cm Ac Cc CMB Fe 7 g/cm3 Am Conclusions • Conception of the Lunar navigational almanac on the basis of SELENE-data for the ILOM-project was discussed • In view of the Lunar mission SELENE (Japan)with geodetic experiments on board and with an optical telescope on the lunar pole, a contribution of the theory of lunar rotation was considered. • Our present knowledge of the interior structure is reviewed, and it is shown that new data from SELENE can improve this knowledge. • The emphasis was put on the evidences of lunar core existence and on the necessity to take this fact into account in the lunar libration theory. • The periods of free librations were evaluated. The model of the two-layer Moon gives several normal rotational modes - Chandler Wobble and Free Core Nutation. They can play an important role in the determination of the core's parameters: radius, density and geochemical composition.

16. Thank you for your attention !