scholarly journals Spacetime coordinates in the geocentric reference frame

1986 ◽  
Vol 114 ◽  
pp. 269-276 ◽  
Author(s):  
M. Fujimoto ◽  
E. Grafarend
Keyword(s):  
Solar System ◽  
Gravity Field ◽  
Reference Frame ◽  
Relative Velocity ◽  
Proper Time ◽  
Frame Of Reference ◽  
Earth Surface ◽  
Riemann Geometry ◽  
The Earth ◽  
Integrating Factors

A geocentric relativistic reference frame is established which is close to the conventional non-relativistic equatorial frame of reference. Within post-Newtonian approximation the worldline of the geocentre is used to connect points by spacelike geodesics on the equal proper time hypersurface and to establish a properly chosen tetrad reference frame. Points on the earth surface and near the earth-space are coordinated making use of the Frobenius matrix of integrating factors which connects the geocentric orthonormal tetrad with the tangent spacetime of relativistic pseudo-Riemann geometry. The gravity field of the earth and its relative velocity with respect to the solar system barycentre cause coordinate effects of the order of 10 cm for topocentric point positioning.

scholarly journals Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser Ranging

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Yi Xie ◽  
Sergei Kopeikin
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Reference Frames ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Local Frame ◽  
The Earth ◽  
Lunar Laser ◽  
Lunar Motion ◽  
New Generation

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.

scholarly journals Gravity Field Theory

2021 ◽  
Author(s):  
Ahmed Shehab Ahmed Al-Banna
Keyword(s):  
Field Theory ◽  
Gravity Field ◽  
Geophysical Methods ◽  
The Other ◽  
Earth Surface ◽  
Gravity Method ◽  
Geophysical Model ◽  
The Earth ◽  
Figure Of The Earth ◽  
Model Understanding

Gravity keep all things on the earth surface on the ground. Gravity method is one of the oldest geophysical methods. It is used to solve many geological problems. This method can be integrated with the other geophysical methods to prepare more accepted geophysical model. Understanding the theory and the principles concepts considered as an important step to improve the method. Chapter one attempt to discuss Newton’s law, potential and attraction gravitational field, Geoid, Spheroid and geodetically figure of the earth, the gravity difference between equator and poles of the earth and some facts about gravity field.

scholarly journals Relativistic effects in geodynamics

1986 ◽  
Vol 114 ◽  
pp. 241-253 ◽  
Author(s):  
C. Boucher
Keyword(s):  
Gravity Field ◽  
Reference Frame ◽  
Relativistic Effects ◽  
Terrestrial Reference Frame ◽  
The Earth ◽  
Lunar Laser ◽  
Time Variations ◽  
Satisfactory Answer ◽  
Definition Of ◽  
Theories Of Gravitation

Geodesy has now reached such an accuracy in both measuring and modelling that time variations of the size, shape and gravity field of the Earth must be basically considered under the name of Geodynamics. The objective is therefore the description of point positions and gravity field functions in a terrestrial reference frame, together with their time variations.For this purpose, relativistic effects must be taken into account in models. Currently viable theories of gravitation such as Einstein's General Relativity can be expressed in the solar system into the parametrized post-newtonian (PPN) formalism. Basic problems such as the motion of a test particle give a satisfactory answer to the relativistic modelling in Geodynamics.The relativistic effects occur in the definition of a terrestrial reference frame and gravity field. They also appear widely into terrestrial (gravimetry, inertial techniques) and space (satellite laser, Lunar laser, VLBI, satellite radioelectric tracking …) measurements.

scholarly journals Reference frames, gauge transformations and gravitomagnetism in the post-Newtonian theory of the lunar motion

2009 ◽  
Vol 5 (S261) ◽  
pp. 40-44 ◽  
Author(s):  
Yi Xie ◽  
Sergei Kopeikin
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Reference Frames ◽  
Laser Ranging ◽  
The Moon ◽  
Field Equations ◽  
Lunar Laser Ranging ◽  
Metric Tensor ◽  
The Earth ◽  
Lunar Motion

AbstractWe construct a set of reference frames for description of the orbital and rotational motion of the Moon. We use a scalar-tensor theory of gravity depending on two parameters of the parametrized post-Newtonian (PPN) formalism and utilize the concepts of the relativistic resolutions on reference frames adopted by the International Astronomical Union in 2000. We assume that the solar system is isolated and space-time is asymptotically flat. The primary reference frame has the origin at the solar-system barycenter (SSB) and spatial axes are going to infinity. The SSB frame is not rotating with respect to distant quasars. The secondary reference frame has the origin at the Earth-Moon barycenter (EMB). The EMB frame is local with its spatial axes spreading out to the orbits of Venus and Mars and not rotating dynamically in the sense that both the Coriolis and centripetal forces acting on a free-falling test particle, moving with respect to the EMB frame, are excluded. Two other local frames, the geocentric (GRF) and the selenocentric (SRF) frames, have the origin at the center of mass of the Earth and Moon respectively. They are both introduced in order to connect the coordinate description of the lunar motion, observer on the Earth, and a retro-reflector on the Moon to the observable quantities which are the proper time and the laser-ranging distance. We solve the gravity field equations and find the metric tensor and the scalar field in all frames. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom of the solutions of the field equations. We discuss the gravitomagnetic effects in the barycentric equations of the motion of the Moon and argue that they are beyond the current accuracy of lunar laser ranging (LLR) observations.

scholarly journals Coordinate system in general relativity

1988 ◽  
Vol 128 ◽  
pp. 105-106
Author(s):  
Toshio Fukushima
Keyword(s):  
Solar System ◽  
Coordinate System ◽  
Reference Frame ◽  
Coordinate Transformation ◽  
Time Coordinate ◽  
Coordinate Axis ◽  
The Earth ◽  
Natural Coordinate System ◽  
Natural Coordinate ◽  
Barycentric Coordinate

The proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordinate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame named the Natural Coordinate System (NCS) is proposed as the basic coordinate system in the astrometry. By means of the concept of the natural coordinate system, the relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly. To illustrate the concept of NCS, we quote in the following the definition of the non-rotating NCS comoving with the Earth, i.e. the Terrestrial Coordinate System (TCS) (Fukushima et al., 1986a, 1986b):1) Consider a fictitious spacetime with the metric obtained by subtracting the direct terms due to the Earth from the true metric in the solar system Barycentric Coordinate System (BCS).2) The time coordinate axis of the TCS is defined as the worldline of the geocenter, i.e. the timelike geodesic of the geocenter in the above ficititious spacetime.3) The unit of time in the TCS, terrestrial second sT, is defined as the unit of time in the BCS, barycentric second, multiplied by a certain factor so that there exist periodic differences only between the time coordinate of any event in the TCS, i.e. TDT, and the corresponding time coordinate in the BCS, i.e. TDB.4) The space coordinate axes of the TCS are defined as three geometrically straight lines satisfying that they and the time coordinate axis of the TCS are orthogonal to each other at the geocenter in the above fictitious spacetime, and that the coordinate triad constructed by them is symmetric.5) The unit of length in the TCS, terrestrial meter mT, is defined as the length so that c = 299792458 mT/sT.

scholarly journals On the Kerr metric in a synchronous reference frame

2021 ◽  
pp. 2150071
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Reference Frame ◽  
Initial Conditions ◽  
Proper Time ◽  
Frame Of Reference ◽  
Kerr Metric ◽  
Initial Values ◽  
Synchronous Reference Frame

The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).

scholarly journals On the Relativity of the Speed of Light

2020 ◽  
Author(s):  
XD Dongfang
Keyword(s):  
Reference Frame ◽  
Relative Velocity ◽  
Propagation Speed ◽  
Frame Of Reference ◽  
Constant Speed ◽  
Inertial Reference Frame ◽  
Speed Of Light ◽  
Velocity Of Light ◽  
Relative Variable ◽  
Variable Light

Einstein's assumption that the speed of light is constant is a fundamental principle of modern physics with great influence. However, the nature of the principle of constant speed of light is rarely described in detail in the relevant literatures, which leads to a deep misunderstanding among some readers of special relativity. Here we introduce the unitary principle, which has a wide application prospect in the logic self consistency test of mathematics, natural science and social science. Based on this, we propose the complete space-time transformation including the Lorentz transformation, clarify the definition of relative velocity of light and the conclusion that the relative velocity of light is variable, and further prove that the relative variable light speed is compatible with Einstein's constant speed of light. The specific conclusion is that the propagation speed of light in vacuum relative to the observer's inertial reference frame is always constant $c$, but the propagation speed of light relative to any other inertial reference frame which has relative motion with the observer is not equal to the constant $c$; observing in all inertial frame of reference, the relative velocity of light propagating in the same direction in vacuum is $0$, while that of light propagating in the opposite direction is $2c$. The essence of Einstein's constant speed of light is that the speed of light in an isolated reference frame is constant, but the relative speed of light in vacuum is variable. The assumption of constant speed of light in an isolated frame of reference and the inference of relative variable light speed can be derived from each other.

scholarly journals Large Fundamental and Global Transit Circle Catalogs

1995 ◽  
Vol 166 ◽  
pp. 35-42
Author(s):  
T. E. Corbin
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Fundamental System ◽  
The Earth ◽  
Naval Observatory ◽  
Solar System Objects ◽  
The Individual ◽  
Systematic Reduction ◽  
Zero Points ◽  
The U.S

The fundamental system is currently based on the Dynamical Reference Frame as defined by the motions of the Earth and other Solar System objects. The link to this frame has traditionally been made by the observation of these objects and of stars in absolute transit circle programs. The zero points of the link are applied to quasi-absolute catalogs, and these are combined with the absolute catalogs to define the fundamental system. The individual positions and motions of the fundamental stars are then strengthened by incorporating differential catalogs reduced to the fundamental system. The system can be extended to higher densities and fainter magnitudes by further systematic reduction and combination of differential catalogs. The fundamental system itself, however, can only be extended through a planned series of observations resulting in absolute stellar positions over a range of epochs. A new fundamental catalog being compiled at the U.S. Naval Observatory is discussed and compared with the existing standard, the FK5.

Sign in / Sign up

Export Citation Format

Share Document