Rotating nonspherical masses and their effects on the precession of a gyroscope
The formula due to Lense and Thirring for the dragging of locally inertial frames is generalized, in the limit of weak stationary fields, to any arbitrary axisymmetric spinning body. We determine the multipole structure of the off-diagonal terms in the metric resulting from the mass current of the body. For a rotating mass divided into nearly spherical strata of equal density, the relativistic multipole moments are related to the deviation from spherical symmetry in a quite simple manner. We apply our results to an oblate spheroid stratified into slightly flattened ellipsoids. Thus a realistic geophysical model enables us to evaluate the contribution of the earth's nonsphericity to the Lense-Thirring procession of a gyroscope. The magnitude of this contribution does not exceed the experimental error for observations covering a span of about one year.
- Research Organization:
- Equipe de Recherche associee au C.N.R.S. no 533, Institut Henri Poincare 11, rue Pierre et Marie Curie: 75231 Paris Cedex 05, France
- OSTI ID:
- 7209595
- Journal Information:
- Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 16:4; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AXIAL SYMMETRY
CONFIGURATION
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
GRAVITATIONAL FIELDS
GYROSCOPES
METRICS
MOTION
PRECESSION
ROTATION
SPHERICAL CONFIGURATION
SYMMETRY
THIRRING MODEL