Lunar ranging experiment ephemerides and the reduction of observations (summary only)

1977 ◽  
Vol 284 (1326) ◽  
pp. 467-467
Keyword(s):  
Solid Body ◽  
Equations Of Motion ◽  
The Body ◽  
Lunar Orbit ◽  
Earth Tides ◽  
Lunar Laser Ranging ◽  
Fitting Procedure ◽  
The Earth ◽  
Starting Conditions ◽  
Tesseral Harmonics

The generation of a lunar laser ranging ephemeris uses numerical integrations of the lunar orbit and physical librations and a data fitting procedure. The relativistic equations of motion for the nine planets and the Moon are simultaneously integrated with perturbations on the lunar orbit from zonal harmonics of the Earth through degree four, lunar tesseral harmonics through degree and order three, and a tidal bulge on the Earth. The integration of the lunar rotation follows from the torques of the Earth and Sun on a solid body Moon with gravitational harmonics through degree and order three. The fitting program utilizes the integrations of the orbit and physical librations, nominal values of U.T. 1 and polar motion from the Bureau International de l’Heure, and includes corrections for atmospheric delays, nutations of the Earth’s pole taken to the body axis, solid body Earth tides, monthly and bimonthly tidal corrections in U. T. 1, and relativistic clock transformations. Not only do the fits give new starting conditions for the orbit and libration integrations but improved observatory and retroreflector coordinates, the mass ratio Sun/(Earth + Moon), and harmonics of the lunar gravity field.

Equivalence principle for massive bodies in a generalized theory of gravitation. II

1982 ◽  
Vol 60 (11) ◽  
pp. 1556-1560 ◽  
Author(s):  
J. C. McDow ◽  
J. W. Moffat
Keyword(s):  
Equivalence Principle ◽  
Equations Of Motion ◽  
Upper Bounds ◽  
Laser Ranging ◽  
Coordinate Frame ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Theory Of Gravitation ◽  
Three Body

The three-body equations of motion are examined for periodic perturbations in an earth centered coordinate frame. The lunar-laser-ranging data is then used to place upper bounds on the new l parameters associated with the earth and sun.

Theories of lunar libration

1977 ◽  
Vol 284 (1326) ◽  
pp. 573-585 ◽  
Keyword(s):  
Equations Of Motion ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Computer Laboratory ◽  
The Earth ◽  
Lunar Laser ◽  
Highly Nonlinear ◽  
Librational Motion ◽  
Measured Distance ◽  
Nonlinear Equations Of Motion

The measured distance between a point on the Moon and an observatory on the Earth varies with the librational motion of the Moon about her centre of mass. The motion is caused by the varying attraction of the Earth, Sun and planets upon the Moon and obeys highly nonlinear equations of motion. Because of the high precision of measurements with lunar laser ranging systems, the theory of the motion must be worked out in great detail and the absence of adequate developments limits the interpretation of lunar ranging observations. Numerical integration of the equations of motion is carried out at the Jet Propulsion Laboratory and Eckhardt has developed a semi-literal theory in which coefficients of periodic terms are calculated numerically. There is still need, however, for a literal theory. A brief account will be given of a new literal theory, the algebraic manipulations for which are being carried out by the Camal machine algebraic program developed in the Computer Laboratory at Cambridge. The third harmonic terms in the gravitational potential of the Moon are included and it is intended to include the effect of the Sun.

A Discussion on the measurement and interpretation of changes of strain in the Earth - Earth tides, ocean tides and tidal loading

1973 ◽  
Vol 274 (1239) ◽  
pp. 253-259 ◽  
Keyword(s):  
Potential Field ◽  
The Body ◽  
Earth Tides ◽  
Ocean Tide ◽  
Vertical Acceleration ◽  
Tidal Motion ◽  
The Earth ◽  
Almost Everywhere ◽  
Body Tides ◽  
Self Potential

The distortion of the Earth’s gravitational potential field by the A:f2 ocean tide has been calculated, accounting for both the elastic deformation of the Earth and the self potential of the water. The potential field generated by the ocean tide is almost everywhere greater than a tenth, and over much of the ocean is half as large as the lunar driving potential itself, and may have a significant influence on the tidal motion. Load tides in tilt, strain, and vertical acceleration also arise from the deformation of the Earth by the ocean tide. These load tides are probably of more geophysical and oceanographic interest than the body tides raised by the Sun and Moon.

scholarly journals Analysis of the process of deployment of a lunar tether system taking into account the Earth's gravity

2021 ◽  
Vol 5 (3) ◽  
pp. 153-159
Author(s):  
T. A. Ledkova ◽  
Yu. M. Zabolotnov
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Control Program ◽  
Lunar Orbit ◽  
Transport Systems ◽  
Cylindrical Shape ◽  
Space Tether ◽  
The Earth ◽  
Gravitational Influence ◽  
Theoretical Results

The development of space transport systems for the delivery of payloads and the study of the lunar surface is an important scientific and technical challenge. The article considers a near-lunar space tether system consisting of a station and a microsatellite. The station is considered as a rigid body having a cylindrical shape, and the microsatellite is considered as a spherical rigid body. The tether is considered as a weightless inextensible rod of variable length. The station moves in a near-lunar orbit, which is influenced by the Earth's gravity. The process of deployment of a radially directed near-lunar tether system is considered. The equations of motion of the space tether system are obtained using Newton's second law and the theorem on the change in the angular momentum. To release the tether and bring the orbital tether system to a working state, the article proposes to use the control program of tethers tension force, which ensures the deployment of the tether system to a position close to the vertical. A comparison of the motion of the tether system along the unperturbed lunar orbit and along the perturbed one, taking into account the gravitational influence of the Earth, is made. To substantiate the theoretical results, a numerical simulation was carried out, based on the results of which a conclusion was made about the influence of the Earth's gravity on the amplitude of oscillations of the microsatellite relative to the local vertical.

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.

‘Man Is Ill Because He Is Badly Constructed’: Artaud, Klossowski and Deleuze in Search for the Earth Inside

2011 ◽  
Vol 5 (1) ◽  
pp. 18-34 ◽  
Author(s):  
Rick Dolphijn
Keyword(s):  
Performance Art ◽  
Holy Spirit ◽  
The Body ◽  
Deleuze And Guattari ◽  
The Earth ◽  
The Holy Spirit ◽  
Life Itself ◽  
Body Without Organs ◽  
Ways Of Thinking ◽  
And Performance

Starting with Antonin Artaud's radio play To Have Done With The Judgement Of God, this article analyses the ways in which Artaud's idea of the body without organs links up with various of his writings on the body and bodily theatre and with Deleuze and Guattari's later development of his ideas. Using Klossowski (or Klossowski's Nietzsche) to explain how the dominance of dialogue equals the dominance of God, I go on to examine how the Son (the facialised body), the Father (Language) and the Holy Spirit (Subjectification), need to be warded off in order to revitalize the body, reuniting it with ‘the earth’ it has been separated from. Artaud's writings on Balinese dancing and the Tarahumaran people pave the way for the new body to appear. Reconstructing the body through bodily practices, through religion and above all through art, as Deleuze and Guattari suggest, we are introduced not only to new ways of thinking theatre and performance art, but to life itself.

‘A pinch of unseen, unguarded dust’: The World and Self in Thomas Hardy's Poems

2018 ◽  
Vol 8 (1) ◽  
pp. 49-66
Author(s):  
Monika Szuba
Keyword(s):  
The Body ◽  
The Self ◽  
Phenomenological Philosophy ◽  
The Earth ◽  
The World ◽  
The Universe ◽  
Recurrent Theme ◽  
Body Subject

The essay discusses selected poems from Thomas Hardy's vast body of poetry, focusing on representations of the self and the world. Employing Maurice Merleau-Ponty's concepts such as the body-subject, wild being, flesh, and reversibility, the essay offers an analysis of Hardy's poems in the light of phenomenological philosophy. It argues that far from demonstrating ‘cosmic indifference’, Hardy's poetry offers a sympathetic vision of interrelations governing the universe. The attunement with voices of the Earth foregrounded in the poems enables the self's entanglement in the flesh of the world, a chiasmatic intertwining of beings inserted between the leaves of the world. The relation of the self with the world is established through the act of perception, mainly visual and aural, when the body becomes intertwined with the world, thus resulting in a powerful welding. Such moments of vision are brief and elusive, which enhances a sense of transitoriness, and, yet, they are also timeless as the self becomes immersed in the experience. As time is a recurrent theme in Hardy's poetry, this essay discusses it in the context of dwelling, the provisionality of which is demonstrated in the prevalent sense of temporality, marked by seasons and birdsong, which underline the rhythms of the world.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Effect of non-tidal station loading on Lunar Laser Ranging observatories and on the estimation of Earth orientation parameters

2021 ◽  
Author(s):  
Vishwa Vijay Singh ◽  
Liliane Biskupek ◽  
Jürgen Müller ◽  
Mingyue Zhang
Keyword(s):  
Research Centre ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Earth Orientation Parameters ◽  
Tidal Station ◽  
Earth Orientation ◽  
The Earth ◽  
Lunar Laser ◽  
Orientation Parameters

<p>The distance between the observatories on Earth and the retro-reflectors on the Moon has been regularly observed by the Lunar Laser Ranging (LLR) experiment since 1970. 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, and a higher number of LLR observations in total. Providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics, LLR can also support the estimation of Earth orientation parameters (EOP), like UT1. The increased number of highly accurate LLR observations enables a more accurate estimation of the EOP. In this study, we add the effect of non-tidal station loading (NTSL) in the analysis of the LLR data, and determine post-fit residuals and EOP. The non-tidal loading datasets provided by the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS), and the EOST loading service of University of Strasbourg in France are included as corrections to the coordinates of the LLR observatories, in addition to the standard corrections suggested by the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions. The Earth surface deforms up to the centimetre level due to the effect of NTSL. By considering this effect in the Institute of Geodesy (IfE) LLR model (called ‘LUNAR’), we obtain a change in the uncertainties of the estimated station coordinates resulting in an up to 1% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%. In a second part of the study, we investigate whether the modelling of NTSL leads to an improvement in the determination of EOP from LLR data. Recent results will be presented.</p>

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

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