scholarly journals On the Absolute Orientation of the Selenodetic Reference Frame

1981 ◽  
Vol 63 ◽  
pp. 281-286
Author(s):  
V. S. Kislyuk
Keyword(s):  
Coordinate System ◽  
Center Of Mass ◽  
The Moon ◽  
Coordinate Systems ◽  
Inertial Coordinate System ◽  
Reference Coordinate System ◽  
The Earth ◽  
Principal Axes ◽  
The Mean ◽  
Selection Of

The selection of selenodetic reference coordinate system is an important problem in astronomy and selenodesy. For the purposes of reduction of observations, planning and executing space missions to the Moon, it is necessary, in any case, to know the orientation of the adopted selenodetic reference system in respect to the inertial coordinate system.Let us introduce the following coordinate systems: C(ξc, ηc, ζc), the Cassini system which is defined by the Cassini laws of the Moon rotation;D(ξd, ηd, ζd), the dynamical coordinate system, whose axes coincide with the principal axes of inertia of the Moon;Q(ξq, ηq, ζq), the quasi-dynamical coordinate system connected with the mean direction to the Earth, which is shifted by 254" West and 75" North from the longest axis of the dynamical system (Williams et al., 1973);S(ξs, ηs, ζs), the selenodetic coordinate system, which is practically realized by the positions of the points on the Moon surface given in Catalogues;I(X,Y,Z), the space-fixed (inertial) coordinate system. All the systems are selenocentric with the exception of S(ξs, ηs, ζs On the whole, the origin of this system does not coincide with the center of mass of the Moon.

scholarly journals Reference Coordinate Systems for Earth Dynamics: A Preview

1980 ◽  
Vol 56 ◽  
pp. 1-22 ◽  
Author(s):  
Ivan I. Mueller
Keyword(s):  
Coordinate System ◽  
Coordinate Systems ◽  
Inertial Coordinate System ◽  
Terrestrial System ◽  
The Earth ◽  
Earth Dynamics

AbstractA common requirement for all geodynamic investigations is a well-defined coordinate system attached to the earth in some prescribed way, as well as a well-defined inertial coordinate system in which the motions of the terrestrial system can be monitored. This paper deals with the problems encountered when establishing such coordinate systems and the transformations between them. In addition, problems related to the modeling of the deformable earth are discussed.

scholarly journals Origin and Scale of Coordinate Systems in Satellite Geodesy

1980 ◽  
Vol 56 ◽  
pp. 239-250
Author(s):  
J. B. Zieliński
Keyword(s):  
Coordinate System ◽  
Inner Core ◽  
Center Of Mass ◽  
Point Of View ◽  
Satellite Geodesy ◽  
Coordinate Systems ◽  
Scale Problem ◽  
The Earth ◽  
Geocenter Motion

AbstractThe center of mass of the Earth is commonly taken as origin for the coordinate systems used in satellite geodesy. In this paper the notion of the “geocenter” is discussed from the point of view of mechanics and geophysics. It is shown that processes in and above the crust have practically no impact on the position of the geocenter. It is possible however that motions of the inner core may cause variations of the geocenter of the order of 1 m. Nevertheless the geocenter is the best point for the origin of a coordinate system. Mather’s method of monitoring geocenter motion is discussed, and some other possibilities are mentioned. Concerning the scale problem, the role of the constant GM and time measurements in satellite net determinations are briefly discussed.

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.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

scholarly journals Approximate Inertial Coordinate System Selections for Rotation Problems - The Gravitational Field of the Celestial Body Higher than the Object Being Rotated

2015 ◽  
Vol 8 (1) ◽  
pp. 102
Author(s):  
Zifeng Li
Keyword(s):  
Gravitational Field ◽  
Coordinate System ◽  
Celestial Body ◽  
Angular Speed ◽  
Calculation Error ◽  
Cartesian Coordinate System ◽  
Inertial Coordinate System ◽  
The Earth ◽  
The Galaxy ◽  
Cartesian Coordinate

<p class="1Body">Selection of the coordinate system is essential for rotation problems. Otherwise, mistakes may occur due to inaccurate measurement of angular speed. Approximate inertial coordinate system selections for rotation problems should be the gravitational field of the celestial body higher than the object being rotated: (1) the Earth fixed Cartesian coordinate system for normal rotation problem; (2) heliocentric - geocentric Cartesian coordinate system for satellites orbiting the Earth; (3) the Galaxy Heart - heliocentric Cartesian coordinates for Earth's rotation around the Sun. In astrophysics, mass calculation error and angular velocity measurement error lead to a black hole conjecture.</p>

scholarly journals Complex Geodynamical Investigations in the Area of the USSR Academy of Sciences Central Astronomical Observatory at Pulkovo

1990 ◽  
Vol 141 ◽  
pp. 72-72
Author(s):  
V. K. Abalakin ◽  
V. I. Bogdanov ◽  
Yu.D. Boulanger ◽  
V. A. Naumov
Keyword(s):  
Coordinate System ◽  
Ussr Academy ◽  
Astronomical Observatory ◽  
Coordinate Systems ◽  
Inertial Coordinate System ◽  
Gravitation Field ◽  
Practical Applications ◽  
Star Catalogue ◽  
Academy Of Sciences

For astronomical, geodetical and geodynamical investigations as well as for practical applications the inertial coordinate system is widely used which is based on the Fundamental Star Catalogue FK5 together with local coordinate systems in observation stations on the Earth's surface which are intrinsically connected with the geometry of the gravitation field.

scholarly journals The mean distance to the Moon as determined by radar

1965 ◽  
Vol 21 ◽  
pp. 81-93 ◽  
Author(s):  
B. S. Yaplee ◽  
S. H. Knowles ◽  
A. Shapiro ◽  
K. J. Craig ◽  
D. Brouwer
Keyword(s):  
The Moon ◽  
The Earth ◽  
Lunar Topography ◽  
Radar Measurements ◽  
The Mean

The results of 1959-1960 radar measurements of the distance of the Moon are given. The method of reduction of the data is described The possible effects of lunar topography and errors of other origins are discussed, as well as the effects of different constants such as the radii of the Earth and of the Moon.

Justification of kinematic scheme small of the manipulator forestry machines

2015 ◽  
Vol 5 (3) ◽  
pp. 234-239
Author(s):  
Платонова ◽  
Marina Platonova ◽  
Драпалюк ◽  
Mikhail Drapalyuk ◽  
Платонов ◽  
...  
Keyword(s):  
Coordinate System ◽  
Reference System ◽  
Coordinate Systems ◽  
Kinematic Scheme ◽  
Inertial Coordinate System ◽  
Generalized Coordinates ◽  
Right Hand ◽  
The Absolute ◽  
Orthogonal Coordinate Systems ◽  
Base Machine

This article discusses the the selection and justification of the reference system and of the generalized coordinates for the kinematic scheme developed by of the manipulator taking into account these factors. The absolute (inertial) coordinate system associated with the center of the support member (eg turntable), joins the arm to the base machine and the subsequent coordinate system formed in accordance with the rules. On the whole, to describe the position of the investigated little detail of the manipulator in the space of generalized coordinates must be four and five right-hand orthogonal coordinate systems.

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