Open Access
Original Articles
Equations of Motion for Two-Body Problem According to an Observer Inside the Gravitational Field
Kostadin Trenčevskikostatre@pmf.ukim.mkFaculty of Natural Sciences and Mathematics, STS. Cyril and Methodius UniversityP.O.Box 162Skopje, R. MacedoniaView full profile → , Emilija Celakoskaemilija.celakoska@mf.edu.mkFaculty of Mechanical Engineering, STS. Cyril And Methodius UniversityP.O.Box 464Skopje, R. MacedoniaView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2011.10698596
- Pages:
- 115–135
Abstract
In this paper we consider equations of motion for 2-body problem according to an observer close to one of the gravitational bodies. The influence of the Thomas precession of the observer’s frame has an important role. The equations of motion are based on a nonlinear connection modified by the action of an orthogonal tensor which synchronizes the 4-velocities of the considered two bodies. Finally we present periastron shift according to an observer inside the gravitational field, using the orthonormal coordinates. This is different approach than that used in General Relativity where the periastron shift is only given as observed far from the massive bodies.
Keywords
References
Celakoska, E.G. and Trenčevski, K.2007 . The Strong Equivalence Principle in a Nonholonomic Extension of the General Relativity . Phys. Macedonica, 56 : 11 – 21 . Celakoska, E.G. and Trenčevski, K.2007 . Transition between 4-velocities using a tensor . Int. J. Pure Appl. Math, 41 ( 8 ) : 1143 – 1152 . Landau, L.D. and Lifshitz, E.M.1988 . The Classical Theory of Fields, Moscow: Nauka . (in Russian) Lawden, D.F.1976 . Tensor Calculus and Relativity, London: Chapman and Hall . Misner, C.W., Thorne, K.S. and Wheeler, J.A.1973 . Gravitation, San Francisco: W.H. Freeman and Company . Thomas, L.H.1927 . The kinematics of an electron with an axis . Philos. Magazine, 3 : 1 – 22 . Trenčevski, K. and Balan, V.2005 . Shrinking of rotational configurations and associated inertial forces . J. Calcutta Math. Soc., 1 ( 3–4 ) : 165 – 180 . Trenčevski, K. and Celakoska, E.G.October 5–7, 2008 2008 . “ On the equations of motion in Minkowski space ” . In Proc. of the International Conference Differential Geometry - Dynamical Systems - DGDS2007, Edited by: Udriste, C.October 5–7, 2008 , 211 – 220 . Bucharest-Romania: Balkan Society of Geometers . In: Trenčevski, K. and Celakoska, E.G.2009 . “ General formulae to frequency shifts using a parallel transport of a 4-wave vector in flat Minkowski space ” . In Proc. of the World Congress of EngineeringVol. 2 , 1003 – 1009 . London2009 Trenčevski, K. and Celakoska, E.2008 . “ A New Approach to the Frame Dragging Effect ” . In Proc. of the International Scientific Conference 6–10.06.2007, Fac. of Math. and Nat. Sci Vol. 1 , 71 – 75 . Blagoevgrad: Southwest Univ. Neofit Rilski . Trencevski, K. and Celakoska, E.2011 . Geodetic precession and frame dragging observed far from the massive bodies and close to the gyroscope . Cent. Eur. J. Phys., 9 ( 3 ) : 654 – 661 . Trencevski, K., Celakoska, E. and Balan, V.2011 . Research of Gravitation in Flat Minkowski Space . Internat. J. Theoret. Phys., 50 ( 1 ) : 1 – 26 . Trencevski, K., Celakoska, E. and Balan, V.2006 . On a parameterization of the Poincare group . Int. J. Pure Appl. Math, 30 ( 1 ) : 109 – 117 . Trenčevski, K.1993 . One model of gravitation and mechanics . Tensor, 53 : 70 – 83 . Trenčevski, K.2005 . Time dependent gravitational potential in the universe and some consequences . Gen. Relativity Gravitation, 37 ( 3 ) : 507 – 519 . Trenčevski, K.2006 . “ Change of the orbital period of the binary pulsars ” . In Trends in Pulsar Research, Edited by: Lowry, J.A.145 – 161 . New York: Nova Science Publishers . in: Trenčevski, K.Violation of the strong equivalence principle . Proc. of Conf. ”Contemporary Geometry and Related Topics” . , pp. 475 – 489 . in: Will, C.M.1993 . Theory and Experiment in Gravitational Physics, New York: Cambridge University Press .
Views: 6Downloads: 5Citations: 0
