Transformation between orbital parameters in different coordinate systems of the general relativistic schwarzschild problem

1973 ◽  
Vol 296 (4) ◽  
pp. 275-286
Author(s):  
R.M. Georgevic ◽  
J.D. Anderson
Keyword(s):  
Coordinate Systems ◽  
Orbital Parameters ◽  
General Relativistic ◽  
Schwarzschild Problem

scholarly journals Recent Observations of PSR B1534+12

2001 ◽  
Vol 205 ◽  
pp. 408-409
Author(s):  
I.H. Stairs ◽  
S.E. Thorsett ◽  
J.H. Taylor ◽  
Z. Arzoumanian
Keyword(s):  
General Relativity ◽  
Neutron Star ◽  
Spin Axis ◽  
Pulse Profile ◽  
High Quality ◽  
Orbital Parameters ◽  
General Relativistic ◽  
Star Binary

We present the results of recent Arecibo observations of the relativistic double-neutron-star binary PSR B1534+12. The timing solution includes measurements of five post-Keplerian orbital parameters, whose values agree well with the predictions of general relativity. The observations show that the pulse profile is evolving secularly at both 1400 MHz and 430 MHz. This effect is similar to that seen in PSR B1913+16, and is almost certainly due to general relativistic precession of the pulsar's spin axis. We also present high-quality polarimetric profiles at both observing frequencies.

scholarly journals Time Ephemeris and General Relativistic Scale Factor

2009 ◽  
Vol 5 (H15) ◽  
pp. 219-219
Author(s):  
Toshio Fukushima
Keyword(s):  
Scale Factor ◽  
Harmonic Series ◽  
Coordinate Transformations ◽  
Coordinate Systems ◽  
General Relativistic ◽  
The Mean ◽  
Rms Error ◽  
Time Average ◽  
The Difference ◽  
Wrong Sign

AbstractTime ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 2009). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffel et al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such as LC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate of LC as 1.4808268457(10) × 10−8, which was incorrect by around 2 × 10−16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale of LC is 1.48082686741(200) × 10−8 Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part of LC for TE405 as 1.4808268559(6) × 10−8 (Harada and Fukushima 2003). This leads to the value of LC as LC = 1.48082686732(110) × 10−8. If we combine this with the constant defining the mean rate of TCG-TT, LG = 6.969290134 × 10−10 (IAU 2001), we estimate the numerical value of another general relativistic scale factor LB = 1.55051976763(110) × 10−8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. As a compact realization of the time ephemeris, we prepared HF2002, a Fortran routine to compute approximate harmonic series of TE405 with the RMS error of 0.446 ns for the period 1600 to 2200 (Harada and Fukushima 2003). It is included in the IERS Convention 2003 (McCarthy and Petit 2003) and available from the IERS web site; http://tai.bipm.org/iers/conv2003/conv2003_c10.html.

scholarly journals Coordinate systems in the general relativistic framework

1986 ◽  
Vol 114 ◽  
pp. 145-168 ◽  
Author(s):  
T. Fukushima ◽  
M.-K Fujimoto ◽  
H. Kinoshita ◽  
S. Aoki
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference Frames ◽  
Special Theory ◽  
Newtonian Mechanics ◽  
Theory Of Relativity ◽  
Coordinate Systems ◽  
Relativistic Extension ◽  
General Relativistic ◽  
Relativistic Framework

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, 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 coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

scholarly journals Astronomical Constraints on Some Long-Range Models of Modified Gravity

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Lorenzo Iorio
Keyword(s):  
Long Range ◽  
Modified Gravity ◽  
The Other ◽  
Newtonian Potential ◽  
Orbital Parameters ◽  
Curvature Invariants ◽  
General Relativistic ◽  
Braneworld Model ◽  
Analytical Expressions ◽  
Working Out

We use the corrections to the Newton-Einstein secular precessions of the longitudes of the perihelia of the inner planets, phenomenologically estimated E.V. Pitjeva by fitting almost one century of data with the EPM2004 ephemerides, to constrain some long-range models of modified gravity recently put forth to address the dark energy and dark matter problems. They are the four-dimensional ones obtained with the addition of inverse powers and logarithm of some curvature invariants, and the DGP multidimensional braneworld model. After working out the analytical expressions of the secular perihelion precessions induced by the corrections to the Newtonian potential of such models, we compare them to the estimated extra-rates of perihelia by taking their ratio for different pairs of planets instead of using one perihelion at a time for each planet separately, as done so far in literature. The curvature invariants-based models are ruled out, even by rescaling by a factor 10 the errors in the estimated planetary orbital parameters. Less neat is the situation for the DGP model. Only the general relativistic Lense-Thirring effect, not included, as the other exotic models considered here, by Pitjeva in the EPM force models, passes such a test.

scholarly journals BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES

2008 ◽  
Vol 17 (01) ◽  
pp. 135-163 ◽  
Author(s):  
PETARPA BOONSERM ◽  
MATT VISSER
Keyword(s):  
Perfect Fluid ◽  
Functional Form ◽  
Polar Coordinates ◽  
Coordinate Systems ◽  
Large Classes ◽  
Isotropic Coordinates ◽  
General Relativistic ◽  
Algorithmic Techniques ◽  
Isothermal Coordinates ◽  
Fluid Spheres

In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.

scholarly journals Time ephemeris and general relativistic scale factor

2009 ◽  
Vol 5 (S261) ◽  
pp. 89-94
Author(s):  
Toshio Fukushima
Keyword(s):  
Scale Factor ◽  
Harmonic Series ◽  
Coordinate Transformations ◽  
Coordinate Systems ◽  
General Relativistic ◽  
The Mean ◽  
Rms Error ◽  
Time Average ◽  
The Difference ◽  
Wrong Sign

AbstractTime ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 1995). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffelet al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such asLC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate ofLCas 1.4808268457(10) × 10−8, which was incorrect by around 2 × 10−16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale ofLCis 1.48082686741(200) × 10−8Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part ofLCfor TE405 as 1.4808268559(6) × 10−8(Harada and Fukushima 2003). This leads to the value ofLCasLC= 1.48082686732(110) × 10−8. If we combine this with the constant defining the mean rate of TCG-TT,LG= 6.969290134 × 10−10(IAU 2001), we estimate the numerical value of another general relativistic scale factorLB= 1.55051976763(110) × 10−8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. The former is a natural limitation caused by the finite length of numerical planetary ephemerides and the latter is due to the uncertainty of masses of some heavy asteroids. As a compact realization of the time ephemeris, we prepared HF2002, a Fortran routine to compute approximate harmonic series of TE405 with the RMS error of 0.446 ns for the period 1600 to 2200 (Harada and Fukushima 2003). It is included in the IERS Convention 2003 (McCarthy and Petit 2003) and available from the IERS web site;http://tai.bipm.org/iers/conv2003/conv2003_c10.html.

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.

Sign in / Sign up

Export Citation Format

Share Document