×
Vîlcu, Alina-Daniela

Geodesic effect near an elliptical orbit. (English) Zbl 1243.83020

J. Appl. Math. 2012, Article ID 240459, 8 p. (2012).
Summary: Using a differential geometric treatment, we analytically derive the expression for De Sitter (geodesic) precession in the elliptical motion of the Earth through the gravitational field of the Sun with Schwarzschild’s metric. The expression obtained in this paper in a simple way, using a classical approach, agrees with that given in B. M. Barker and R. F. O’Connell (1970, 1975) in a different setting, using the tools of Newtonian mechanics and the Euler-Lagrange equations.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
70H03 Lagrange’s equations
70F15 Celestial mechanics
85A05 Galactic and stellar dynamics
83C57 Black holes

Keywords:

precession
PDF BibTeX XML Cite
\textit{A.-D. Vîlcu}, J. Appl. Math. 2012, Article ID 240459, 8 p. (2012; Zbl 1243.83020)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] W. De Sitter, “On Einstein’s theory of gravitation, and its astronomical consequences,” Montly Notices, Royal Astronomical Society, vol. 77, pp. 155-184, 1916.
[2] J. A. Schouten, “On the arising of a Precession-motion owing to the non-Euclidian linear element,” Proceeding of Royal Academy of Amsterdam, vol. 21, pp. 533-539, 1918.
[3] A. D. Fokker, “The geodesic precession: a consequence of Einstein’s theory of gravitation,” Proceeding of Royal Academy of Amsterdam, vol. 23, pp. 729-738, 1920.
[4] J. Chazy, La Théorie de la Relativité et la Méchanique Céleste, Tomes I et II, Gauthier-Villars, Paris, France, 1928-1930. · JFM 54.0939.04
[5] B. M. Barker and R. F. O’Connell, “Derivation of the equations of motion of a gyroscope from the quantum theory of gravitation,” Physical Review D, vol. 2, no. 8, pp. 1428-1435, 1970.
[6] V. A. Brumberg, Essential Relativistic Celestial Mechanics, Adam Hilger, London, UK, 1991. · Zbl 0749.70013
[7] B. M. Barker and R. F. O’Connell, “Gravitational two-body problem with arbitrary masses, spins, and quadrupole moments,” Physical Review D, vol. 12, no. 2, pp. 329-335, 1975.
[8] J. H. Chen and Y. J. Wang, “Geodetic precession in Schwarzschild spacetime surrounded by quintessence,” Chinese Physics Letters, vol. 24, no. 11, pp. 3063-3065, 2007.
[9] S. Chen and J. Jing, “Geodetic precession and strong gravitational lensing in dynamical Chern-Simons-modified gravity,” Classical and Quantum Gravity, vol. 27, no. 22, p. 16, 2010. · Zbl 1204.83064
[10] I. I. Haranas and M. Harney, “Geodetic precession of the spin in a non-singular gravitational potential,” Progress in Physics, vol. 1, pp. 75-80, 2008. · Zbl 1153.83003
[11] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation, W. H. Freeman, San Francisco, Calif, USA, 1973.
[12] B. O’Neill, Semi-Riemannian Geometry. With Applications to Relativity, vol. 103 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1983. · Zbl 0531.53051
[13] S. N. Gupta, “Einstein’s and other theories of gravitation,” Reviews of Modern Physics, vol. 29, pp. 334-336, 1957. · Zbl 0079.41804
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.