Mathematics – Logic
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..313g&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Mathematics
Logic
Scientific paper
1. Selenocentric systems of coordinates New phase exploration of the Moon requiring detailed measurements of position for purposes of optical and radio observation on Lunar surface, cartography, surface and near-surface navigation, correlation and data reduction of scientific experiments, such as gravimetry, active seismology, geological sampling, etc. Astronomical almanac should contain information about for any time of observation, including the scheme of transition from the lunar time to the universal time and conversely, the program of time signals sending/receiving etc. The Almanac should contain a system of the formulae and constants for reduction of geoequatorial coordinates of a star onto a visible place, which is bound with instantaneous Lunar equator (axis of Lunar rotation). The Lunar equatorial system of coordinates is connected to the system of the principle axes of inertia of the Moon - Dynamical System of Coordinates (DSC) via kinematical Eulerian equations and Eulerian angels τ, ρ, Iσ. The position of axes of inertia in space is described by the theory of the Lunar Physical Libration (LPhL). The first experience of Lunar Selenocentric Navigational Almanac (LSNA) was described in [1]. The more developed approaches to the Lunar Almanac creation were made in [2, 3]. The mean selenocentrical equatorial frame is related to the Cassini's equator (Fig.1), which is moving in retrograde direction due to precession of the Lunar rotation axis. Using the libration angles it is possible to obtain the visible star coordinates (Fig.2). For high accuracy navigation purpose and providing the observations from the Lunar surface in the frame of the ILOM-projects, Japan, 2013 yr [16] the highprecision theory of the Lunar Physical Libration is necessary. At the present time the use of the numerical JPL ephemeris (DE418) with the LP150Q gravity field [17] is recommended. Analytical solution for LPhL has less accuracy than a numerical one, nevertheless, the analytical model is able to predict new harmonics that were previously unknown and not observed in libration's series. Effective combination of numerical and analytical apare dependent on Delaunay arguments and on the new kind of arguments p, q, r, whose frequencies 1 j α can be calculated theoretically, but the phases j0 α and the amplitudes Ai can be determined only from observations.
Gusev Alexander A.
Petrova Natalia
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