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

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

scholarly journals Simulation Study of Moon-Based InSAR Observation for Solid Earth Tides

2020 ◽  
Vol 12 (1) ◽  
pp. 123
Author(s):  
Kai Wu ◽  
Ce Ji ◽  
Lei Luo ◽  
Xinyuan Wang
Keyword(s):  
Solid Earth ◽  
Large Scale ◽  
Artificial Satellite ◽  
Satellite System ◽  
Global Scale ◽  
Deformation Monitoring ◽  
Earth Tides ◽  
The Moon ◽  
Single Station ◽  
Solid Earth Tides

The observation of solid earth tides (SET) provides an important basis for understanding the structure of the earth’s interior, and has long been the focus of research in geoscience. However, actually, there still exist some limitations in capturing its global-scale information only with ground stations. Remote sensing technology can realize large-scale deformation monitoring of high point density constantly. However, it is still difficult for the artificial satellite system to meet the requirements of SET monitoring in terms of field of view and temporal resolution now. In this work, the moon is hypothesized as a new platform for SET observation combined with interferometric synthetic aperture radar (InSAR) technology. Based on the tidal model and lunar ephemeris, the spatial and temporal characteristics of the SET from the lunar view were analyzed. Furthermore, the calculations demonstrate that more abundant SET information can be observed in this view. After comparing various observation modes, the single-station with repeat-pass differential InSAR was selected for this simulation. We mainly considered the restriction of observation geometry on moon-based InSAR under three signal bandwidths, thereby providing a reference for the sensor design. The results demonstrate that the moon-based platform offers the potential to become an optimal SET observation method.

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.

scholarly journals Nonsphericity of the Moon and Near Sun-Synchronous Polar Lunar Orbits

2009 ◽  
Vol 2009 ◽  
pp. 1-24 ◽  
Author(s):  
Jean Paulo dos Santos Carvalho ◽  
Rodolpho Vilhena de Moraes ◽  
Antônio Fernando Bertachini de Almeida Prado
Keyword(s):  
Numerical Simulations ◽  
Artificial Satellite ◽  
Nonuniform Distribution ◽  
Second Order ◽  
The Moon ◽  
Disturbing Potential ◽  
Short Period ◽  
Coupling Terms ◽  
Lunar Artificial Satellite ◽  
Hori Method

Herein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness (J2) and the equatorial ellipticity (sectorial termC22). Using Lie-Hori method up to the second order short-period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun-synchronous polar lunar orbit is presented.

Sign in / Sign up

Export Citation Format

Share Document