Generation of a secular system in the analytical theory for the motion of the moon

2013 ◽  
Vol 47 (5) ◽  
pp. 359-362
Author(s):  
T. V. Ivanova
Keyword(s):  
Analytical Theory ◽  
The Moon

scholarly journals Analytical Theories of the Motion of the Moon

1981 ◽  
Vol 63 ◽  
pp. 227-232
Author(s):  
Jacques Henrard
Keyword(s):  
Numerical Integration ◽  
Analytical Theory ◽  
The Moon

AbstractAlmost every aspect of the analytical theory of the motion of the Moon has been reinvestigated lately. This paper is a review of these investigations.The improvement upon the I.L.E. (the best known earlier theory based upon the work of Brown) is spectacular, but it is still too early to assess the exact value of these theories with respect to numerical integration.

scholarly journals Application of the Spectral Analysis for Modeling the Rotations of the Moon

2010 ◽  
Vol 45 (4) ◽  
pp. 153-162 ◽  
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Spectral Analysis ◽  
Numerical Solution ◽  
Rotational Motion ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Physical Libration ◽  
Newtonian Case ◽  
Rotational Motions

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.

Analytical Theory of an Artificial Satellite of the Moon

2004 ◽  
Vol 1017 (1) ◽  
pp. 434-449 ◽  
Author(s):  
BERNARD DE SAEDELEER ◽  
JACQUES HENRARD
Keyword(s):  
Artificial Satellite ◽  
Analytical Theory ◽  
The Moon

Analytical theory of the libration of the Moon

1982 ◽  
Vol 27 (3) ◽  
pp. 257-284 ◽  
Author(s):  
M. Moons
Keyword(s):  
Analytical Theory ◽  
The Moon

scholarly journals Comparison of ELP-2000 to a JPL Numerical Integration

1981 ◽  
Vol 63 ◽  
pp. 257-264
Author(s):  
Jean Chapront ◽  
Michelle Chapront-Touzé
Keyword(s):  
Analytical Solution ◽  
Numerical Integration ◽  
Orbital Motion ◽  
Complete Solution ◽  
Analytical Theory ◽  
The Moon ◽  
Full Paper ◽  
Lunar Laser ◽  
Lunar Ephemeris

This contribution is an outline of the main results obtained by the authors in comparing their solution ELP-2000, to a JPL numerical integration, LE-51. A full paper containing discussions and comments on the results will be proposed to Astronomy ’ Astrophysics.A solution for the orbital motion of the Moon has been built by the authors. It is named ELP-2000, the epoch of reference being J2000. It is a semi-analytical solution, its structure being quite similar to Brown-Eckert’s one, as it appears in the Improved Lunar Ephemeris, ILE, j=2, (Eckert et al., 1954). The main purpose of this work is to present the results of a comparison of a provisional but complete solution, to an external numerical integration, LE-51, built at JPL (Williams, 1980), and fitted to lunar laser rangings. The JPL numerical integration is regarded as an “observational model”. It is a first attempt to compare as a whole, a new lunar ephemeris, derived from a semi-analytical theory, to observations, via a numerical integration.

Lunar orbital theory

1977 ◽  
Vol 284 (1326) ◽  
pp. 565-571 ◽  
Keyword(s):  
Numerical Integration ◽  
Gravitational Theory ◽  
The State ◽  
Analytical Theory ◽  
Laser Ranging ◽  
The Moon ◽  
Orbital Theory ◽  
Lunar Laser Ranging ◽  
Lunar Laser ◽  
Better Than

The present and expected accuracies of lunar laser ranging imply that the gravitational theory of the motion of the Moon should be consistent with at least the same precision. It is therefore necessary to aim at internal relative consistencies better than 10 -11 or 10 -12 . Several theories based on numerical integration have been built and are currently being used in reducing the lunar laser ranging data. However, literal or semi-literal analytical theories have several im portant advantages over purely numerical ephemerides. This is why important programmes of building such theories are now in progress, particularly in the U. S. A. and in France. Characteristics and the state of advancement of these theories will be reviewed and the possibility of constructing an analytical theory with the above mentioned accuracy discussed.

Use of an Analytical Theory for the Physical Libration of the Moon to Detect Free Nutation of the Lunar Core

2018 ◽  
Vol 62 (12) ◽  
pp. 1021-1025 ◽  
Author(s):  
N. K. Petrova ◽  
Yu. A. Nefedyev ◽  
A. A. Zagidullin ◽  
A. O. Andreev
Keyword(s):  
Analytical Theory ◽  
The Moon ◽  
Physical Libration ◽  
Free Nutation ◽  
Lunar Core

scholarly journals Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals

2011 ◽  
Vol 46 (2) ◽  
pp. 63-73
Author(s):  
V. Pashkevich ◽  
G. Eroshkin
Keyword(s):  
Numerical Solution ◽  
High Precision ◽  
Initial Conditions ◽  
Analytical Theory ◽  
Time Interval ◽  
The Moon ◽  
Time Intervals ◽  
Good Consistency ◽  
Newtonian Case ◽  
Long Time

Construction of the New High-Precision Moon Rotation Series at a Long Time Intervals The main purposes of this research are the construction of the new high-precision Moon Rotation Series (MRS2011), dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris, over long time intervals. The comparison of the new highprecision Moon Rotation solutions of MRS2011 with the solution of MRS2010 (Pashkevich and Eroshkin, 2010), which is dynamically adequate to the DE200/LE200 ephemeris over 418.9 year time interval, is performed. The dynamics of the rotational motion of the Moon is studied numerically by using Rodrigues-Hamilton parameters over 418.9, 2000 and 6000 years. The numerical solution of the Moon rotation is implemented with the quadruple precision of the calculations. The results of the numerical solution of the problem are compared with the composite semi-analytical theory of the Moon rotation (SMR) (Pashkevich and Eroshkin, 2010) with respect to the fixed ecliptic of epoch J2000. The initial conditions of the numerical integration are taken from SMR. The investigation of the discrepancies is carried out by the least squares and spectral analysis methods for the Newtonian case. All the secular, periodic and Poisson terms, representing the behavior of the residuals, are interpreted as corrections to SMR semi-analytical theory. As a result, the Moon Rotation Series (MRS2011) is constructed, which is dynamically adequate to the DE404/LE404 and the DE406/LE406 ephemeris over 418.9, 2000 and 6000 years. A numerical solution for the Moon rotation is obtained anew with the new initial conditions calculated by means of MRS2011. The discrepancies between the new numerical solution and the semi-analytical solution of MRS2011 do not surpass 20 mas over 418.9 year time interval, 64 mas over 2000 year time interval and 8 arc seconds over 6000 year time interval. Thus, the result of the comparison demonstrates a good consistency of MRS2011 series with the DE/LE ephemeris.

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