The geodetic precession as a 3D Schouten precession and a gravitational Thomas precession

2014 ◽  
Vol 92 (10) ◽  
pp. 1082-1093
Author(s):  
E.P.J. (Paul) de Haas
Keyword(s):  
B Physics ◽  
Parallel Transport ◽  
Free Fall ◽  
De Sitter ◽  
Thomas Precession ◽  
Gravity Probe B ◽  
Curved Space ◽  
Geodetic Precession ◽  
The Status ◽  
Gravity Probe

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. The Schiff treatment included Thomas precession 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 special and general relativity courses.

scholarly journals Is There Still Something Left That Gravity Probe B Can Measure?

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 85
Author(s):  
Lorenzo Iorio
Keyword(s):  
Equations Of Motion ◽  
Parallel Transport ◽  
Analytical Calculation ◽  
Spin Precession ◽  
Gravity Probe B ◽  
Orbital Phase ◽  
Orbital Configuration ◽  
General Relativistic ◽  
Gravity Probe ◽  
Mass Quadrupole

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment J 2 of its primary without any restriction on either the gyro’s orbital configuration and the orientation in space of the symmetry axis k ^ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin’s declination δ which may be as large as ≲30–40 milliarcseconds per year mas yr − 1 , depending on the initial orbital phase f 0 . Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector S and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin’s declination rate amounts to σ δ ˙ GP − B = 18.3 mas yr − 1 . We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary’s angular momentum J . In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.

scholarly journals Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Kostadin Trenčevski ◽  
Emilija Celakoska
Keyword(s):  
Coordinate System ◽  
Gravity Probe B ◽  
Frame Dragging ◽  
Geodetic Precession ◽  
Gravity Probe

AbstractTotal 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.

SATELLITE TEST OF THE EQUIVALENCE PRINCIPLE: OVERVIEW AND PROGRESS

2007 ◽  
Vol 16 (12a) ◽  
pp. 2215-2225 ◽  
Author(s):  
JEFFERY J. KOLODZIEJCZAK ◽  
JOHN MESTER
Keyword(s):  
Present State ◽  
Equivalence Principle ◽  
Free Fall ◽  
Development Plan ◽  
Current Status ◽  
Technology Readiness ◽  
Gravity Probe B ◽  
Universality Of Free Fall ◽  
Recent Advances ◽  
Gravity Probe

STEP, the Satellite Test of the Equivalence Principle, is reviewed and the current status of the project is discussed. This space-based experiment will test the universality of free fall and is designed to advance the present state of knowledge by over five orders of magnitude. The international STEP collaboration is pursuing a development plan to improve and verify the technology readiness of key systems. We discuss recent advances with an emphasis on accelerometer fabrication and tests. Critical technologies successfully demonstrated in flight by the Gravity Probe B mission also contribute to progress.

The Gravity Probe-B star-tracking telescope

2003 ◽  
Vol 32 (7) ◽  
pp. 1401-1405 ◽  
Author(s):  
D.-H. Gwo ◽  
S. Wang ◽  
K.A. Bower ◽  
D.E. Davidson ◽  
P. Ehrensberger ◽  
...  
Keyword(s):  
Gravity Probe B ◽  
Star Tracking ◽  
Gravity Probe

The Gravity Probe B Data Analysis Filtering Approach

2009 ◽  
Vol 148 (1-4) ◽  
pp. 411-427 ◽  
Author(s):  
M. Heifetz ◽  
W. Bencze ◽  
T. Holmes ◽  
A. Silbergleit ◽  
V. Solomonik
Keyword(s):  
Data Analysis ◽  
Gravity Probe B ◽  
Gravity Probe ◽  
Filtering Approach

scholarly journals VLBI FOR GRAVITY PROBE B . IV. A NEW ASTROMETRIC ANALYSIS TECHNIQUE AND A COMPARISON WITH RESULTS FROM OTHER TECHNIQUES

2012 ◽  
Vol 201 (1) ◽  
pp. 4 ◽  
Author(s):  
D. E. Lebach ◽  
N. Bartel ◽  
M. F. Bietenholz ◽  
R. M. Campbell ◽  
D. Gordon ◽  
...  
Keyword(s):  
Gravity Probe B ◽  
Analysis Technique ◽  
Gravity Probe

Local Scale Covariance and Its Radical Implications for Cosmology

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 76
Author(s):  
Yehonatan Knoll
Keyword(s):  
Local Scale ◽  
Covariant Theory ◽  
De Sitter ◽  
Cosmological Redshift ◽  
Physical Limit ◽  
Scale Covariance ◽  
The Status ◽  
Scale Motion ◽  
Fundamental Equations ◽  
Conceptual Foundations

Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of `scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to `move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times; (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.

scholarly journals Gravity Probe B data analysis: II. Science data and their handling prior to the final analysis

2015 ◽  
Vol 32 (22) ◽  
pp. 224019 ◽  
Author(s):  
A S Silbergleit ◽  
J W Conklin ◽  
M I Heifetz ◽  
T Holmes ◽  
J Li ◽  
...  
Keyword(s):  
Data Analysis ◽  
Final Analysis ◽  
Science Data ◽  
Gravity Probe B ◽  
Gravity Probe
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