Influence of the Dynamical Figure of the Moon on Its Rotational-Translational Motion

Symposium - International Astronomical Union ◽

10.1017/s0074180900070571 ◽

1974 ◽

Vol 62 ◽

pp. 201-207

Author(s):

G. I. Eroshkin

Keyword(s):

Translational Motion ◽

Lunar Orbit ◽

Force Function ◽

The Moon ◽

Physical Libration ◽

Third Order ◽

Major Semi Axis ◽

Constant Coefficients ◽

Expansion Form

The influence of the dynamical figure of the Moon on its rotation with respect to its mass centre (the physical libration) is determined by means of the theorem on the angular moment of a rigid body. In the expansion of the Moon's force function in spherical harmonics all the second and the third order harmonics are taken into consideration. For the determination of the Moon's physical libration components a linear system of differential equations of the second order with constant coefficients is constructed.The integration displays the essential influence of the new terms in the force function expansion. For evaluation of the disturbed elements of the lunar orbit due to the nonsphericity of the Moon's dynamical figure the Lagrange's equations are solved. The disturbing function is taken in an expansion form in powers of the eccentricity of the lunar orbit and of the inclinations of the Moon's equator and its orbit with respect to the ecliptic. The commensurability of the Moon's mean motion and its angular velocity of rotation produces in the major semi-axis of the lunar orbit secular perturbations of the first order.

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The Lunar orbit paradox

Theoretical and Applied Mechanics ◽

10.2298/tam1301135t ◽

2013 ◽

Vol 40 (1) ◽

pp. 135-146

Author(s):

Aleksandar Tomic

Keyword(s):

Inertial Mass ◽

Lunar Orbit ◽

The Sun ◽

The Moon ◽

The Earth ◽

Three Body ◽

Origin Of The Moon ◽

Force Intensity ◽

Critical Consideration

Newton's formula for gravity force gives greather force intensity for atraction of the Moon by the Sun than atraction by the Earth. However, central body in lunar (primary) orbit is the Earth. So appeared paradox which were ignored from competent specialist, because the most important problem, determination of lunar orbit, was inmediately solved sufficiently by mathematical ingeniosity - introducing the Sun as dominant body in the three body system by Delaunay, 1860. On this way the lunar orbit paradox were not canceled. Vujicic made a owerview of principles of mechanics in year 1998, in critical consideration. As an example for application of corrected procedure he was obtained gravity law in some different form, which gave possibility to cancel paradox of lunar orbit. The formula of Vujicic, with our small adaptation, content two type of acceleration - related to inertial mass and related to gravity mass. So appears carried information on the origin of the Moon, and paradox cancels.

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Differences in the Moon’s moments of inertia

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1967.0018 ◽

1967 ◽

Vol 296 (1446) ◽

pp. 248-253 ◽

Cited By ~ 7

Keyword(s):

Simultaneous Determination ◽

Critical Value ◽

New Method ◽

The Moon ◽

Physical Libration ◽

Moments Of Inertia ◽

Uniqueness Of The Solution

The constants of the Moon’s physical libration constitute the selenodesic basis for lunar cartography. The author worked out a new method for a simultaneous determination of these constants from heliometric observations of the Moon and applied it to four heliometric series comprising 3282 observations covering the period 1877–1915, and performed a joint adjustment of these series by eliminating the Moon’s mean radius corresponding to each series, as it might be affected by the effect of irradiation. At the same time the author gave an exact proof for the uniqueness of the solution for the mechanical ellipticity of the Moon f which turned out to lie below the critical value 0∙662, thus enabling an accurate determination of the differences of the Moon’s moments of inertia.

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Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Universe ◽

10.3390/universe7020034 ◽

2021 ◽

Vol 7 (2) ◽

pp. 34

Author(s):

Liliane Biskupek ◽

Jürgen Müller ◽

Jean-Marie Torre

Keyword(s):

Equivalence Principle ◽

Gravitational Constant ◽

Lunar Orbit ◽

Laser Ranging ◽

The Moon ◽

Lunar Laser Ranging ◽

Lunar Laser ◽

Infra Red ◽

Ppn Parameters

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here, we show current results for relativistic parameters like a possible temporal variation of the gravitational constant G˙/G0=(−5.0±9.6)×10−15yr−1, the equivalence principle with Δmg/miEM=(−2.1±2.4)×10−14, and the PPN parameters β−1=(6.2±7.2)×10−5 and γ−1=(1.7±1.6)×10−4. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein’s theory is found and the results set improved limits for the different effects.

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Automated Determination of the Position of Ships by Satellites

Journal of Navigation ◽

10.1017/s0373463300024528 ◽

1967 ◽

Vol 20 (03) ◽

pp. 281-285

Author(s):

H. C. Freiesleben

Keyword(s):

Celestial Body ◽

World Wide ◽

Artificial Satellites ◽

Radio Waves ◽

The Moon ◽

Position Determination ◽

The Earth ◽

Navigational Aids ◽

Automated Determination

It has recently been suggested that 24-hour satellites might be used as navigational aids. To what category of position determination aids should these be assigned ? Is a satellite of this kind as it were a landmark, because, at least in theory, it remains fixed over the same point on the Earth's surface, in which case it should be classified under land-based navigation aids ? Is it a celestial body, although only one tenth as far from the Earth as the Moon ? If so, it is an astronomical navigation aid. Or is it a radio aid ? After all, its use for position determination depends on radio waves. In this paper I shall favour this last view. For automation is most feasible when an object of observation can be manipulated. This is easiest with radio aids, but it is, of course, impossible with natural stars.At present artificial satellites have the advantage over all other radio aids of world-wide coverage.

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Astronomy at the service of the Islamic society

Proceedings of the International Astronomical Union ◽

10.1017/s1743921311002778 ◽

2009 ◽

Vol 5 (S260) ◽

pp. 514-521

Author(s):

Ilias M. Fernini

Keyword(s):

Proper Time ◽

Astronomical Observatory ◽

The Sun ◽

The Moon ◽

Scientific Institutions ◽

Mathematical Astronomy ◽

Islamic Empire ◽

New Moon ◽

Islamic Society

AbstractThe Islamic society has great ties to astronomy. Its main religious customs (start of the Islamic month, direction of prayer, and the five daily prayers) are all related to two main celestial objects: the Sun and the Moon. First, the start of any Islamic month is related to the actual seeing of the young crescent after the new Moon. Second, the direction of prayer, i.e., praying towards Mecca, is related to the determination of the zenith point in Mecca. Third, the proper time for the five daily prayers is related to the motion of the Sun. Everyone in the society is directly concerned by these customs. This is to say that the major impetus for the growth of Islamic astronomy came from these three main religious observances which presented an assortment of problems in mathematical astronomy. To observe these three customs, a new set of astronomical observations were needed and this helped the development of the Islamic observatory. There is a claim that it was first in Islam that the astronomical observatory came into real existence. The Islamic observatory was a product of needs and values interwoven into the Islamic society and culture. It is also considered as a true representative and an integral par of the Islamic civilisation. Since astronomy interested not only men of science, but also the rulers of the Islamic empire, several observatories have flourished. The observatories of Baghdad, Cairo, Córdoba, Toledo, Maragha, Samarqand and Istanbul acquired a worldwide reputation throughout the centuries. This paper will discuss the two most important observatories (Maragha and Samarqand) in terms of their instruments and discoveries that contributed to the establishment of these scientific institutions.

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Direct observation of interlayer molecular translational motion in a smectic phase and determination of the layer order parameter

Physical Review Research ◽

10.1103/physrevresearch.1.012008 ◽

2019 ◽

Vol 1 (1) ◽

Cited By ~ 2

Author(s):

Makina Saito ◽

Jun Yamamoto ◽

Ryo Masuda ◽

Masayuki Kurokuzu ◽

Yohei Onodera ◽

...

Keyword(s):

Direct Observation ◽

Order Parameter ◽

Translational Motion ◽

Smectic Phase

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NASA's Planned Return to the Moon: Global Access and Anytime Return Requirement Implications on the Lunar Orbit Insertion Burns

AIAA/AAS Astrodynamics Specialist Conference and Exhibit ◽

10.2514/6.2008-7508 ◽

2008 ◽

Cited By ~ 9

Author(s):

Michelle Garn ◽

Min Qu ◽

Jonathan Chrone ◽

Philip Su ◽

Chris Karlgaard

Keyword(s):

Lunar Orbit ◽

The Moon ◽

Global Access ◽

Orbit Insertion

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A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

Journal of Porphyrins and Phthalocyanines ◽

10.1142/s1088424604000684 ◽

2004 ◽

Vol 08 (11) ◽

pp. 1311-1324 ◽

Cited By ~ 18

Author(s):

Maddalena Pizzotti ◽

Elisabetta Annoni ◽

Renato Ugo ◽

Silvia Bruni ◽

Silvio Quici ◽

...

Keyword(s):

Ab Initio ◽

Planar Structure ◽

Third Order ◽

Incident Wavelength ◽

Pull System ◽

Nlo Response ◽

Self Consistent ◽

Order Of Magnitude ◽

Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

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