The geodetic precession as a 3-D Schouten precession and a gravitational Thomas precession (original) (raw)
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The geodesic precession as a 3-D Schouten precession plus a
The Gravity Probe B (GP-B) experiment measured the geodetic precession due to parallel transport in a curved space-time metric, as predicted by de Sitter, Fokker and Schiff. Schiff included the Thomas precession in his treatment and argued that it should be zero in a free fall orbit. We review the existing interpretations regarding the relation between the Thomas precession and the geodetic precession for a gyroscope in a free fall orbit. Schiff and Parker had contradictory views on the status of the Thomas precession in a free fall orbit, a contradiction that continues to exist in the literature. In the second part of this paper we derive the geodetic precession as a global Thomas Precession by use of the Equivalent Principle and some elements of hyperbolic geometry, a derivation that allows the treatment of GP-B physics in between SR and GR courses.
The three-fold theoretical basis of the Gravity Probe B gyro precession calculation
Eprint Arxiv 1405 5511, 2014
The Gravity Probe B (GP-B) experiment is complete and the results are in agreement with the predictions of general relativity (GR) for both the geodetic precession, 6.6 arcsec/yr to about 0.3%, and the Lense-Thirring precession, 39 marcsec to about 19%. This note is concerned with the theoretical basis for the predictions. The predictions depend on three elements of gravity theory, firstly that macroscopic gravity is described by a metric theory such as general relativity, secondly that the Lense-Thirring metric provides an approximate description of the gravitational field of the spinning earth, and thirdly that the spin axis of a gyroscope is parallel displaced in spacetime, which gives its equation of motion. We look at each of these three elements to show how each is solidly based on previous experiments and well-tested theory. The agreement of GP-B with theory strengthens our belief that all three elements are correct and increases our confidence in applying GR to astrophysical phenomena. Conversely, if GP-B had not verified the predictions a major theoretical quandary would have occurred.
Gyroscope precession and general relativity
American Journal of Physics, 2001
Precession of a gyroscope in the presence of a gravitational field is of considerable interest, on account of the soon to be launched satellite test and because of its connection to Mach's principle. Nevertheless, this topic is not generally covered in the curriculum because of the mathematical sophistication required. We examine some of the simple physics involved and argue that by examining simple graviton-elementary particle couplings one can easily understand this phenomenon.
Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope
Central European Journal of Physics, 2011
Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.
Gravitational Thomas Precession - A Gravitomagnetic Effect ?
Gravitational Thomas Precession ( GTP ) is the name given to the Thomas Precession when the acceleration is caused by a gravitational force field. In continuation of our discussion on the idea of a GTP, in this note by way of considering the motion of a planet around the Sun, the GTP is shown to be a gravitomagnetic effect that a planet might experience while moving through a gravitational field (say that of the Sun). The contribution of the GTP to the perihelion advance of Mercury is again estimated at 21.49 arc-seconds per century confirming and clarifying our earlier results.
Foundations of Physics, 1997
Gyrogroup theol 3' and its applications is introduced and explored, exposing the jascinating inteugay between Thomas precession o/' special relatirity theory and hyperbolic geometJ 7. The abstract Thomas precession, called Thomas gyration, gives rise to grouplike ot?jeets called gyrogroups [ A. A. U~gar, Am. J. Phys. 59, 824 (1991) ] the under(ring axioms of which are presented. The prefix gyro extensively used in terms like gyrogroups, gyroassociative and gyrocommutative laws, gyroautomolThisms, and gyrosemidirect produets, stems fi'om their underlying abstract Thomas gyration. Thomas gw'ation is tailor made for hyperbolic geometry. In a similar way that commutative groups underlie vector spaces, gyrocommutative gyrogroups underlie gyrot'ector spaces. Gyrovector s7~aces, in turn, provide a most natural setting)'or hyperbolic geometry in full analogy with vector spaces that provide the setting/br Euclidean geometry. As such, their applicability to relativistic" physics and its s7)acetime geomet~2p is' obvious. 1. INTRODUCTION. HYPERBOLIC GEOMETRY BECOMES COORDINATE BY MEANS OF THOMAS PRECESSION Thomas precession of special theory of relativity (STR) has reached a milestone in 1988 following the discovery of the mathematical regularity that it storesjl 2) Resulting links with hyperbolic geometry now follow, giving rise to coordinate hyperbolic geometry analogous to coordinate Euclidean geometry in the sense indicated by Eqs. (1.3) and (1.4) below. Links between hyperbolic geometry and Thomas precession are not unexpected/3) Unexpectedly, however, the recent exposition of the symmetries concealed in Thomas precession places it centrally in the foundations of hyperbolic geometry.
Thomas precession in post-Newtonian gravitoelectromagnetism
Physical review, 1994
The well-known Thomas precession effect is discussed in the context of the post-Newtonian approximation to general relativity using the language of gravitoelectromagnetism (3-plus-1 splitting of gravitational theory). Preliminary discussion anchors the post-Newtonian coordinate system and choice of gravitational variables in the mathematical structure of fully nonlinear general relativity, linking the post-Newtonian gravitoelectric and gravitomagnetic fields to kinematical properties of the associated observer congruence. The transformation laws for these fields under a change of post-Newtonian coordinate system are derived first within the post-Newtonian theory and then by taking the limit of their fully nonlinear form to reveal the interpretation of the various terms in the post-Newtonian case. These transformation laws are then used to make a case for the existence of a gravitational analogue of the ordinary Thomas precession of the spin of a gyroscope.
Is there a Gravitational Thomas Precession ?
Gravitational Thomas Precession ( GTP ) is the name given to Thomas Precession when the acceleration is caused by a gravitational force field. The contribution of the GTP to the the anomalous perihelion advance of the orbit of Mercury is here estimated aṫ ω GT P = 21 · 49 1 + ( L · S ) L 2 arcsec/century ,where L and S respectively represents the orbital angular momentum and the spin angular momentum of Mercury .This effect seems to be of some serious concern for the General Relativity.
Gödel spacetime: Planar geodesics and gyroscope precession
Physical Review D
We study elliptic-like geodesic motion on hyperplanes orthogonal to the cylindrical symmetry axes of the Gödel spacetime by using an eccentricity-semi-latus rectum parametrization which is familiar from the Newtonian description of a two-body system. We compute several quantities which summarize the main features of the motion, namely the coordinate time and proper time periods of the radial motion, the frequency of the azimuthal motion, the full variation of the azimuthal angle over a period, etc. Exact as well as approximate (i.e., Taylor-expanded in the limit of small eccentricity) analytic expressions of all these quantities are obtained. Finally, we consider their application to the gyroscope precession frequency along these orbits, generalizing the existing results for the circular case.
Gravity Probe-B, a Gyro Test of General Relativity in a Satellite
Automatic Control in Aerospace 1992, 1993
Gravity Probe-B is the relativity gyroscope experiment being developed by NASA and Stanford University to test two extraordinary, unverified predictions of Albert Einstein's general theory of relativity. The experiment will check very precisely, tiny changes in the directions of spin of fo~r gyroscopes contained in an Earth satellite orbiting at 400-mile altitude directly over the poles. So free are the gyroscopes from disturbance that they will pr?vide an almost perfect space-time reference system. They wlII measure how space and time are warped by the presence of the Earth, and, more profoundly, how the Earth's rotation drags space-time around with it. These effects, though small for the Earth, have far-reaching implications for the nature of matter and the structure of the Universe.