Correction: Analysis of dynamic ephemeris and physical libration of the Moon in order to create a lunar navigational system

Application of the Spectral Analysis for Modeling the Rotations of the Moon The main purposes of this research are the development of the optimal spectral analysis schemes for the investigation of the rotational motion of the Moon and then the comparison between the result of the optimal spectral analysis of the rotational motions of the Earth and the Moon. Dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9 year time interval. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) represented by Cassini relations and the semi-analytical solutions of the lunar physical libration problem (Eckhardt, 1981), (Moons, 1982), (Moons, 1984), (Pešek, 1982). The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the optimal spectral analysis methods for the Newtonian case. All the periodic terms representing the behavior of the residuals are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2010) is constructed, which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2010. The discrepancies between the new numerical solution and MRS2010 do not surpass 20 mas over 418.9 year time interval. The result of the comparison demonstrates that MRS2010 series represent more accurately the Moon rotation than SMR series.

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Differences in the Moon’s moments of inertia

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1967.0018 ◽

1967 ◽

Vol 296 (1446) ◽

pp. 248-253 ◽

Cited By ~ 7

Keyword(s):

Simultaneous Determination ◽

Critical Value ◽

New Method ◽

The Moon ◽

Physical Libration ◽

Moments Of Inertia ◽

Uniqueness Of The Solution

The constants of the Moon’s physical libration constitute the selenodesic basis for lunar cartography. The author worked out a new method for a simultaneous determination of these constants from heliometric observations of the Moon and applied it to four heliometric series comprising 3282 observations covering the period 1877–1915, and performed a joint adjustment of these series by eliminating the Moon’s mean radius corresponding to each series, as it might be affected by the effect of irradiation. At the same time the author gave an exact proof for the uniqueness of the solution for the mechanical ellipticity of the Moon f which turned out to lie below the critical value 0∙662, thus enabling an accurate determination of the differences of the Moon’s moments of inertia.

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Hamiltonian Theory of the Libration of the Moon

International Astronomical Union Colloquium ◽

10.1017/s0252921100062199 ◽

1978 ◽

Vol 41 ◽

pp. 125-135 ◽

Cited By ~ 1

Author(s):

Jacques Henrard ◽

Michèle Moons

Keyword(s):

Perturbation Technique ◽

Mean Value ◽

Canonical Transformations ◽

The Moon ◽

Physical Libration ◽

Transform Method ◽

Lie Transform ◽

Hamiltonian Theory ◽

The Mean ◽

Free Libration

AbstractThe feasibility of applying the Lie transform method to the problem of the physical libration of the Moon is investigated. By a succession of canonical transformations, the Hamiltonian of the problem is brought under a form suitable for perturbation technique. The mean value of the inclination of the angular momentum upon the ecliptic and the frequencies of the free libration are computed.

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