Dynamical Paradox in Theory of Lunar Motion

Author(s):  
V.A. Vujičić
Keyword(s):  
1969 ◽  
Vol 1 (1) ◽  
pp. 127-129
Author(s):  
J. Derral Mulholland
Keyword(s):  

1997 ◽  
Vol 165 ◽  
pp. 205-214
Author(s):  
Kenneth Nordtvedt ◽  
David Vokrouhlický

AbstractLunar motion serves for a number of important tests of the relativity theory. Although the final quantitative results come out from the direct numerical treatment of the lunar laser ranging data, the analytical solutions yield important keys for understanding sensitivity of the lunar motion on diverse effects. In the last few years, important relativistic phenomena, notably the equivalence principle violation and the preferred direction effects, have been reexamined using detailed Hill-Brown type theories. Surprising amplification of the former effect, indicated also from the numerical tests, has been explained by intricate coupling with the tidal deformation of the lunar orbit. Similar treatment proved that the lunar motion hides potentially a high-quality test of the preferred frame effects. In both cases, fundamental resonances of the problem cause singular amplification of the effects for particular lunar-like orbits.


1986 ◽  
Vol 114 ◽  
pp. 407-410
Author(s):  
Bahram Mashhoon

A summary of the main relativistic effects in the motion of the Moon is presented. The results are based on the application of a novel approach to the restricted three-body problem in general relativity to the lunar motion. It is shown that the rotation of the Sun causes a secular acceleration in the relative Earth-Moon motion. This might appear to be due to a temporal “variation” of the gravitational constant.


1984 ◽  
Vol 5 (4) ◽  
pp. 428-434
Author(s):  
R. P. Norris

AbstractOver the last two decades there has been an accumulation of exciting evidence that appears to show that, as early as 5000 years ago, people in Britain were making precise observations of the Sun, Moon, and stars, and studying small perturbations in the lunar motion. Structures such as Stonehenge, and the s thousands of other megalithic sites in Britain, are then seen as prehistoric observations. Within these, data would be (accumulated to enable the prediction of celestial phenomena such as eclipses, and allow the construction of a calendar. Recently however a small number of rigorous statistical studies of the sites have cast doubt on the astronomical hypotheses, and have posed the question of whether some of the support for these hypotheses has been generated by well-intentioned but over-enthusiastic selections of chance alignments. In this review, the arguments and counter arguments are presented and examined, and we see what can be salvaged from the astronomical hypotheses after the statistical smoke has cleared.


Author(s):  
Yi Xie ◽  
Sergei Kopeikin

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser RangingWe overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, β and γ, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames - geocentric (GRF) and selenocentric (SRF) - have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable quantities such as the proper time and the round-trip laser-light distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the post-Newtonian multipole moments of the gravitational field of Earth and Moon. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom.


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