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The periastron shift and the Lense-Thirring effect of bound orbital motion in a general axially symmetric space-time given by Pleba\'nski and Demia\'nski are analyzed.
Explanation of the perihelion motion of Mercury from the general theory of relativity
A. Einstein · 1915
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Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitations-theorie
J. Lense and H. Thirring · 1918
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Theory of relativistic trajectories in a gravitational field of Schwarzschild
Y. Hagihara · 1931
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Gravitational field of a spinning mass as an example of algebraically special metrics
R.P. Kerr · 1963
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Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
M. Abramowitz and I.A. Stegun · 1964
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A singularity-free empty universe
C.W. Misner and A.H. Taub · 1969
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Lie Theory and the Lauricella Functions F D F_{D}
W. Miller · 1972
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Rotating, charged, and uniformly accelerating mass in general relativity
J. Plebański and M. Demiański · 1976
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The Mathematical Theory of Black Holes
S. Chandrasekhar · 1983
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Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra
D. Lynden-Bell and M. Nouri-Zonoz · 1998
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Celestial mechanics in Kerr spacetime
W. Schmidt · 2002
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Perturbative approach to an orbital evolution around a supermassive black hole
Y. Mino · 2003
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Solar quadrupole moment and purely relativistic gravitation contributions to Mercury’s perihelion Advance
S. Pireaux, J.-P. Rozelot, and S. Godier · 2003
Cited alongside, same era.
Standard clocks, orbital precession and the cosmological constant
A.W. Kerr, J.C. Hauck, and B. Mashhoon · 2003
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Compact calculation of the perihelion precession of mercury in general relativity, the cosmological constant and Jacobis inversion problem
G.V. Kraniotis and S.B. Whitehouse · 2003
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Rotating black hole orbit functionals in the frequency domain
S. Drasco and S.A. Hughes · 2004
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Geodesic geometry of black holes
Analytic solutions of the geodesic equation in axially symmetric space–times
E. Hackmann, V. Kagramanova, J. Kunz, and C. Lämmerzahl · 2009
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Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
R. Fujita and W. Hikida · 2009
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Motion in General Relativity. Investigation of spherically and axially symmetric spacetimes through geodesics
V. Kagramanova · 2009
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Fast computation of complete elliptic integrals and Jacobian elliptic functions
T. Fukushima · 2009
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Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-time
E. Hackmann, V. Kagramanova, J. Kunz, and C. Lämmerzahl · 2010
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Analytic treatment of complete and incomplete geodesics in Taub–NUT space–times
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G. Slezáková · 2006
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The Confrontation between General Relativity and Experiment
C.M. Will · 2006
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Conformal Killing-Yano tensors for the Plebański-Demiański family of solutions
D. Kubizňák and P. Krtouš · 2007
Cited alongside, same era.
Periapsis and gravitomagnetic precessions of stellar orbits in Kerr and Kerr-de Sitter black hole spacetimes
G.V. Kraniotis · 2007
Cited alongside, same era.
Complete analytic solution of the geodesic equation in Schwarzschild–(anti) de Sitter space–times
E. Hackmann and C. Lämmerzahl · 2008
Cited alongside, same era.
Geodesic equation in Schwarzschild–(anti-)de Sitter space–times: Analytical solutions and applications
E. Hackmann and C. Lämmerzahl · 2008
Cited alongside, same era.
The metric (1) originates from [ 20 ] with t → t + 2 n φ t\to t+2n\varphi , θ → π − θ \theta\to\pi-\theta
Cited in the paper.
V. Kagramanova, J. Kunz, E. Hackmann, and C. Lämmerzahl · 2010
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Geodesic equations in black hole space-times with cosmological constant
E. Hackmann · 2010
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Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: Analytical solutions
S. Grunau and V. Kagramanova · 2011
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Analytical Solutions of the Equations of Motion in Kerr-Newman Spacetime
H. Xu · 2011
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The values for peri- and apoapsis are taken from 01/12/2010 to 01/12/2011 in 1 day time steps; the values for the inclination from 01/12/2001 to 01/12/2011 in 10 days time steps
http://ssd.jpl.nasa.gov/?horizons · 2011
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