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 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.

Orientation of the moon by numerical integration

The Moon ◽  
1973 ◽  
Vol 8 (4) ◽  
pp. 539-545 ◽  
Author(s):  
H. B. Papo
Keyword(s):  
Numerical Integration ◽  
The Moon

scholarly journals Construction of a planetary solution with the help of an n-body program and analytical complements

1986 ◽  
Vol 114 ◽  
pp. 69-69
Author(s):  
P. Bretagnon
Keyword(s):  
Numerical Integration ◽  
Relativistic Effects ◽  
Analytical Form ◽  
Minor Planets ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Planetary Theories

Up to now we have been dealing with the construction of entirely analytical planetary theories such as VS0P82 (Bretagnon, 1982) and T0P82 (Simon, 1983). These theories take into account the whole of the newtonian perturbations of nine point masses: the Sun, the Earth-Moon barycenter, the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus and Neptune. They also take into account perturbations due to some minor planets, to the action of the Moon and the relativistic effects. The perturbations of these last three types are in a very simple way under analytical form but they considerably increase the computations when introduced in the numerical integration programs.

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.

scholarly journals Some Aspects of Constructing Long Ephemerides of the Sun, Major Planets and the Moon: Ephemeris AE95

1997 ◽  
Vol 165 ◽  
pp. 245-250
Author(s):  
G.I. Eroshkin ◽  
N.I. Glebova ◽  
M.A. Fursenko ◽  
A. A. Trubitsina
Keyword(s):  
Mathematical Model ◽  
Solar System ◽  
Numerical Integration ◽  
High Precision ◽  
The Sun ◽  
Specific Character ◽  
The Moon ◽  
Special Edition ◽  
Polynomial Representation

The construction of long-term numerical ephemerides of the Sun, major planets and the Moon is based essentially on the high-precision numerical solution of the problem of the motion of these bodies and polynomial representation of the data. The basis of each ephemeris is a mathematical model describing all the main features of the motions of the Sun, major planets, and Moon. Such mathematical model was first formulated for the ephemerides DE/LE and was widely applied with some variations for several national ephemeris construction. The model of the AE95 ephemeris is based on the DE200/LE200 ephemeris mathematical model. Being an ephemeris of a specific character, the AE95 ephemeris is a basis for a special edition “Supplement to the Astronomical Yearbook for 1996–2000”, issued by the Institute of the Theoretical Astronomy (ITA) (Glebova et al., 1995). This ephemeris covering the years 1960–2010 is not a long ephemeris in itself but the main principles of its construction allow one to elaborate the long-term ephemeris on an IBM PC-compatible computer. A high-precision long-term numerical integration of the motion of major bodies of the Solar System demands a choice of convenient variables and a high-precision method of the numerical integration, taking into consideration the specific features of both the problem to be solved and the computer to be utilized.

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
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