Precise Theory of Orbits in General Relativity, the Cosmological Constant and the Perihelion Precession of Mercury

  • G.V. Kraniotis
Conference paper


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.


Cosmological Constant Modular Form Theta Function Precise Theory Geodesic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Einstein, Sitzungsberichte der Preussischen Akademie der Wissenschaften,(1915) 831.Google Scholar
  2. 2.
    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.MathSciNetCrossRefADSMATHGoogle Scholar
  3. 3.
    C. M. Will, Theory and experiment in gravitational physics Cambridge University Press, Revised edition, (1993)Google Scholar
  4. 4.
    S. Newcomb, em Tables of Mercury. Astr. Pap.Am. Ephem., 6, part 2, Washington (1895–1898).Google Scholar
  5. 5.
    S. Pireaux, J.-P. Rozelot, [arXiv:astro-ph/0109032], Astrophys.Space Sci. 284 (2003) 1159–1194.CrossRefADSGoogle Scholar
  6. 6.
    B. W. Petley, Nature 303, 373 (1983)CrossRefADSGoogle Scholar
  7. 7.
    E. D. Groom et al, Eur.Phys.J.C.15 1, K. Hagiwara et al Phys.Rev.D 66 (2002) 010001.Google Scholar
  8. 8.
    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]MathSciNetCrossRefADSMATHGoogle Scholar
  9. 9.
    J Horn, Math.Ann. 34 (1889), 544–600; L. Fuchs Crelle’s Journal. f. Math. 71 (1870) 91–127.MathSciNetCrossRefGoogle Scholar
  10. 10.
    ESA science missions see Scholar
  11. 11.
    J. Lense, H. Thirring, Phys.Zeitsch.19, (1918) 156Google Scholar
  12. 12.
    K. Schwarzschild, Sitzungsberichte der Königlichen Preussischen Akademie der Wissenschaften (Berlin) 1916,189–196Google Scholar
  13. 13.
    N. H. Abel, Remarques sur quelques propriétés générales d’une certaine sorte de fonctions transcendantes Crelle’s Journal f. Math. 3 (1828) 313–323.MATHGoogle Scholar
  14. 14.
    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.MATHGoogle Scholar
  15. 15.
    A. Göpel, Entwurf einer Theorie der Abel’schen Transcendenten erster Ordnung Crelle’s Journal.f. Math. 35 (1847) 277–312.MATHGoogle Scholar
  16. 16.
    G. Rosenhain, Crelle’s Journal.f. Math. 40 (1850)319MATHGoogle Scholar
  17. 17.
    K. Weierstraß Zur Theorie der Abelschen Functionen, Crelle’s Journal.f. Math.47 (1854)289MATHGoogle Scholar
  18. 18.
    B. Riemann, Theorie der Abelschen Functionen, Crelle’s Journal.f. Math.54 (1857)115MATHGoogle Scholar
  19. 19.
    H. F. Baker Abelian functions: Abel’s Theorem and the allied theory of theta functions Cambridge University Press, 1995 edition.Google Scholar
  20. 20.
    F. Richelot, Crelle’s Journal f. Math 12 (1834) 181MATHGoogle Scholar
  21. 21.
    S. Perlmutter et al. Astrophys.J. 517(1999),565; A.V. Filippenko et al, Astron.J. 116(1998)1009CrossRefADSGoogle Scholar
  22. 22.
    G. V. Kraniotis, Precise relativistic orbits in Kerr and Kerr-(anti) de Sitter spacetimes, Class. Quantum Grav.21 (2004) 4743–4769MATHMathSciNetCrossRefADSGoogle Scholar
  23. 23.
    A Treatise on the Analytical Dynamics of Particles & Rigid Bodies, E. Whittaker, Cambridge University Press, 1947Google Scholar
  24. 24.
    H. Ohanian & R. Ruffini, Gravitation & Spacetime, Norton and Company, New York, 1994.MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • G.V. Kraniotis
    • 1
  1. 1.Physics DepartmentTexas A&M UniversityCollege StationUSA

Personalised recommendations