Abstract
We first discuss the exact solution of the timelike geodesic and the perihelion precession in the Schwarzschild gravitational field without cosmological constant ʌ. Results for the perihelion precession of Mercury and values of perihelion and aphelion are listed for different values of the invariant parameters. By use of Jacobi’s inversion theorem the influence of the cosmological constant is taken into account and the modified results are presented for different values of ʌ.
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References
A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften,(1915) 831.
G. V. Kraniotis, S. B. Whitehouse Compact calculation of the perihelion precession of Mercury in general relativity, the cosmological constant and Jacobi’s inversion problem, Classical and Quantum Gravity 20, (2003) 4817–4835.
C. M. Will, Theory and experiment in gravitational physics Cambridge University Press, Revised edition, (1993)
S. Newcomb, em Tables of Mercury. Astr. Pap.Am. Ephem., 6, part 2, Washington (1895–1898).
S. Pireaux, J.-P. Rozelot, [arXiv:astro-ph/0109032], Astrophys.Space Sci. 284 (2003) 1159–1194.
B. W. Petley, Nature 303, 373 (1983)
E. D. Groom et al, Eur.Phys.J.C.15 1, K. Hagiwara et al Phys.Rev.D 66 (2002) 010001.
G. V. Kraniotis and S. B. Whitehouse, General relativity, the cosmological constant and modular forms, Class. Quantum Grav.19 (2002)5073–5100, [arXiv:grqc/0105022]
J Horn, Math.Ann. 34 (1889), 544–600; L. Fuchs Crelle’s Journal. f. Math. 71 (1870) 91–127.
ESA science missions see http://sci.esa.int/home/bepicolombo/
J. Lense, H. Thirring, Phys.Zeitsch.19, (1918) 156
K. Schwarzschild, Sitzungsberichte der Königlichen Preussischen Akademie der Wissenschaften (Berlin) 1916,189–196
N. H. Abel, Remarques sur quelques propriétés générales d’une certaine sorte de fonctions transcendantes Crelle’s Journal f. Math. 3 (1828) 313–323.
C. G. J. Jacobi, Crelle’s Journal.f. Math. 9 (1832)394, Crelle’s Journal.f. Math. 13 (1835)55; C. G. J. Jacobi, Ueber die vierfach periodischen Functionen zweier variablen Ostwald’s klassiker der exakten Wissenschaften, Nr.64, Wilhelm Engelmann in Leipzig (1834)1–41.
A. Göpel, Entwurf einer Theorie der Abel’schen Transcendenten erster Ordnung Crelle’s Journal.f. Math. 35 (1847) 277–312.
G. Rosenhain, Crelle’s Journal.f. Math. 40 (1850)319
K. Weierstraß Zur Theorie der Abelschen Functionen, Crelle’s Journal.f. Math.47 (1854)289
B. Riemann, Theorie der Abelschen Functionen, Crelle’s Journal.f. Math.54 (1857)115
H. F. Baker Abelian functions: Abel’s Theorem and the allied theory of theta functions Cambridge University Press, 1995 edition.
F. Richelot, Crelle’s Journal f. Math 12 (1834) 181
S. Perlmutter et al. Astrophys.J. 517(1999),565; A.V. Filippenko et al, Astron.J. 116(1998)1009
G. V. Kraniotis, Precise relativistic orbits in Kerr and Kerr-(anti) de Sitter spacetimes, Class. Quantum Grav.21 (2004) 4743–4769
A Treatise on the Analytical Dynamics of Particles & Rigid Bodies, E. Whittaker, Cambridge University Press, 1947
H. Ohanian & R. Ruffini, Gravitation & Spacetime, Norton and Company, New York, 1994.
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Kraniotis, G. (2006). Precise Theory of Orbits in General Relativity, the Cosmological Constant and the Perihelion Precession of Mercury. In: Klapdor-Kleingrothaus, H.V., Arnowitt, R. (eds) Dark Matter in Astro- and Particle Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26373-X_37
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DOI: https://doi.org/10.1007/3-540-26373-X_37
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