scholarly journals Encounter in the Keplerian Field: Analytical Treatment

1993 ◽  
Vol 132 ◽  
pp. 289-289
Author(s):  
V.A. Brumberg ◽  
T.V. Ivanova
Keyword(s):  
Point Of View ◽  
Lunar Theory ◽  
Theoretical Point ◽  
The Sun ◽  
The Moon ◽  
Type Solution ◽  
Analytical Treatment ◽  
Hill’S Problem ◽  
Hill's Problem ◽  
Resonance Character

AbstractIn extending the results of Henon and Petit (Celes.Mech., 38,67, 1986) an algorithm is suggested to construct the series representing the general encounter-type solution of the spatial eccentric Hill’s problem. The series are arranged in powers of the eccentricity E of Hill’s problem and two integration constants e and k characterizing eccentricity and inclination of the relative motion. A particular non-periodic solution of Henon and Petit corresponding to E = e = k = 0 is taken as an intermediary. The perturbations to this solution are constructed similar to the Lunar theory of Hill and Brown with; the Universal Poissonian Processor. From theoretical point of view Hill’s problem for the encounter case is of particular interest. In distinction from the Lunar problem we do not have here angular arguments with different frequencies. Moreover, the perturbations related with the external eccentricity E (analogous to the perturbations in the motion of the motion of the Moon caused by the eccentricity of the orbit of the Sun) are of resonance character.

scholarly journals Connection of large earthquakes occurring moment with the movement of the Sun and the Moon and with the Earth crust tectonic stress character

2010 ◽  
Vol 10 (7) ◽  
pp. 1629-1633 ◽  
Author(s):  
M. K. Kachakhidze ◽  
R. Kiladze ◽  
N. Kachakhidze ◽  
V. Kukhianidze ◽  
G. Ramishvili
Keyword(s):  
Tectonic Stress ◽  
Point Of View ◽  
The Sun ◽  
Compression Stress ◽  
The Moon ◽  
Caucasus Region ◽  
The Earth ◽  
Triggering Factor ◽  
Exogenous Factors ◽  
Large Earthquakes

Abstract. It is acceptable that earthquakes certain exogenous (cosmic) triggering factors may exist in every seismoactive (s/a) region and in Caucasus among them. They have to correct earthquake occurring moment or play the triggering role in case when the region is at the limit of the critical value of the geological medium of course. Our aim is to reveal some exogenous factors possible to initiate earthquakes, on example of Caucasus s/a region, taking into account that the region is very complex by the point of view of the tectonic stress distribution. The compression stress directed from North to South (and vice versa) and the spread stress directed from East to West (and vice versa) are the main stresses acted in Caucasus region. No doubt that action of the smallest external stress may "work" as earthquakes triggering factor. In the presented work the Moon and the Sun perturbations are revealed as initiative agents of earthquakes when the directions of corresponding exogenous forces coincide with the directions of the compression stress or the spreading tectonic stress in the region.

Overturning Thresholds of a Rocking Block Subjected to Harmonic Excitation: Computer Simulations and Analytical Treatment

2003 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Point Of View ◽  
Theoretical Point ◽  
Rigid Block ◽  
Periodic Excitation ◽  
Analytical Treatment ◽  
Rocking Block ◽  
Combined Use ◽  
Analytical Tools

When a rigid block resting on a horizontal rigid foundation is shaken by a periodic excitation it can topples if the excitation amplitude is sufficiently high. This question is addressed in this work by the combined use of numerical and analytical tools. Numerical computations are first performed aimed at understanding the overall overturning behavior, and how it is modified by varying relevant parameters, such as the excitation phase and the coefficient of restitution at impacts. Then the problem is addressed from a theoretical point of view, with the objective of analytically detecting the most relevant features highlighted by previous numerical simulations. We succeed in obtaining closed form and manageable criteria for overturning.

scholarly journals Theory of the Libration of the Moon

1983 ◽  
Vol 74 ◽  
pp. 37-37
Author(s):  
M. Dubois-Moons
Keyword(s):  
Gravity Field ◽  
Orbital Motion ◽  
Lunar Theory ◽  
The Sun ◽  
Lunar Gravity ◽  
The Moon ◽  
Fourth Degree ◽  
Lunar Gravity Field ◽  
The Earth ◽  
Second Degree

AbstractThe paper presents a new theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field. This field is represented through its fourth degree harmonics for the torque due to the Earth (the second degree for the torque due to the Sun). The Moon is assumed to be rigid and its orbital motion is described by the ELP 2000 solution (Chapront and Chapront-Touzé 1981) for the main problem of lunar theory with planetary perturbations and influence of the non-sphericity of the Earth. Comparisons with other theories (Migus 1980 and Eckhardt 1981) are also presented.

scholarly journals Analysis of the Secular Variations of Longitudes of the Sun, Mercury and Venus from Optical Observations

2002 ◽  
Vol 12 ◽  
pp. 330-333
Author(s):  
Y.B. Kolesnik
Keyword(s):  
Secular Variation ◽  
Optical Observations ◽  
Lunar Theory ◽  
The Sun ◽  
The Moon ◽  
Significant Discrepancy ◽  
Secular Variations ◽  
Tidal Acceleration

AbstractAbout 240 000 optical observations of the Sun, Mercury and Venus, accumulated during the era of classical astrometry from Bradley up to our days, are incorporated to analyse the secular variation of the longitudes of innermost planets. A significant discrepancy between modern ephemerides and optical observations is discovered. The possible sources of discrepancy are discussed. The tidal acceleration of the Moon has been revised to conform the lunar theory with the ephemerides of the planets. The offset and residual rotation of Hipparcos-based system with respect to the dynamical equinox is determined. Interpretation of this rotation is given.

scholarly journals Figures and Mirrors in Demetrios Triklinios's 'Selenography'

2021 ◽  
pp. 54-73
Author(s):  
Divna Manolova
Keyword(s):  
Fourteenth Century ◽  
Visual Cognition ◽  
The Other ◽  
Lunar Theory ◽  
The Sun ◽  
The Moon ◽  
The Earth ◽  
Mediterranean World ◽  
The One

This article is about the interplay between diagrammatic representation, the mediation of mirrors, and visual cognition. It centres on Demetrios Triklinios (fl. ca. 1308–25/30) and his treatise on lunar theory. The latter includes, first, a discussion of the lunar phases and of the Moon's position in relation to the Sun, and second, a narrative and a pictorial description of the lunar surface. Demetrios Triklinios's Selenography is little-known (though edited in 1967 by Wasserstein) and not available in translation into a modern scholarly language. Therefore, one of the main goals of the present article is to introduce its context and contents and to lay down the foundations for their detailed study at a later stage. When discussing the Selenography, I refer to a bricolage consisting of the two earliest versions of the work preserved in Bayerische Staatsbibliothek, graecus 482, ff. 92r–95v (third quarter of the fourteenth century) and Paris, Bibliothèque nationale de France, graecus 2381, ff. 78r–79v (last quarter of the fourteenth century). I survey the available evidence concerning the role of Demetrios Triklinios (the author), John Astrapas (?) (the grapheus or scribe-painter), and Neophytos Prodromenos and Anonymus (the scribes-editors) in the production of the two manuscript copies. Next, I discuss the diagrams included in the Selenography and their functioning in relation to Triklinios's theory concerning the Moon as a mirror reflecting the geography of the Earth, on the one hand, and to the mirror experiment described by Triklinios, on the other. Finally, I demonstrate how, even though the Selenography is a work on lunar astronomy, it can also be read as a discussion focusing on the Mediterranean world and aiming at elevating its centrality and importance on a cosmic scale.

Hill's Problem in lunar theory

1978 ◽  
Vol 17 (2) ◽  
pp. 195-204 ◽  
Author(s):  
Jacques Henrard
Keyword(s):  
Lunar Theory ◽  
Hill’S Problem ◽  
Hill's Problem

Methodological Issues concerning the Astronomy of Qumran

2015 ◽  
Vol 22 (2) ◽  
pp. 202-209 ◽  
Author(s):  
Eshbal Ratzon
Keyword(s):  
Dead Sea Scrolls ◽  
Dead Sea ◽  
Angular Distance ◽  
Lunar Theory ◽  
The Sun ◽  
The Moon ◽  
Methodological Issues ◽  
Astronomical Data ◽  
The Times

In the 21st issue of Dead Sea Discoveries, Dennis Duke and Matthew Goff offered their collaboration as physicist and Dead Sea Scrolls scholar in order to study the lunar theory of the Aramaic Astronomical Book (aab). They use the astronomical model of lunar elongation—the angular distance between the moon and the sun on the observed heavenly sphere—to compute the times of the moon’s visibility and invisibility. They conclude that the times written on the Aramaic fragments are closer to reality than the times written in the Babylonian sources of the aab. This paper concludes that lunar elongation is not the best explanation of the astronomical data of the aab, and Duke and Goff’s computations should be refined according to some astronomical, cosmological, textual, and historical considerations.

Timber Auctions in the Context of the Modern Auction Theory

2007 ◽  
pp. 86-94
Author(s):  
A. Manakov
Keyword(s):  
Theoretical Analysis ◽  
Auction Theory ◽  
Point Of View ◽  
Theoretical Point ◽  
English Auction ◽  
Analysis And Evaluation

The article provides theoretical analysis and evaluation of the timber auctions reforms in Russia. The author shows that the mechanism of the "combined auctions", which functioned until recently, is more appropriate from the theoretical point of view (and from the point of view of the Russian practice) as compared to the officially approved format of the English auction.

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