Abstract
We will investigate the influence of the inhomogeneity of the Universe, especially that of the Lemaître–Tolman–Bondi (LTB) model, on a gravitationally bound local system such as the solar system. We concentrate on the dynamical perturbation to the planetary motion and derive the leading order effect generated from the LTB model. It will be shown that there appear not only a well-known cosmological effect arisen from the homogeneous and isotropic model, such as the Robertson–Walker (RW) model, but also the additional terms due to the radial inhomogeneity of the LTB model. We will also apply the obtained results to the problem of secular increase in the astronomical unit, reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of the Universe cannot have a significant effect for explaining the observed dAU/dt = 15 ±4 [m/century].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adkins, G. S., McDonnell, J. 2007, Phys. Rev., D75, id 082001.
Anderson, J. D., Campbell, J. K., Ekelund, J. E., Ellis, J., Jordan, J. F. 2008, Phys. Rev. Lett., 100, id 091102.
Anderson, J. D., Laing, P. A., Lau, E. L., Nieto, M. M., Turyshev, S. G. 1998, Phys. Rev. Let., 81, 2858.
Arakida, H. 2009, New Astron., 14, 264.
Arakida, H. 2010, Adv. Space Res., 45, 1007.
Bondi, H. 1947, Mon. Not. R. Astron. Soc., 107, 410.
Bretagnon, P., Francou, G. 1988, Astron. Astrophys., 202, 309.
Brumberg, V., Kopeikin, S. 1989a, Nuovo Cimento, B103, 63.
Brumberg, V., Kopeikin, S. 1989b, Reference frames in astronomy and geophysics, 115.
Carrera, M., Giulini, D. 2010, Rev. Mod. Phys., 82, 169.
Cooperstock, F. I., Faraoni, V., Vollick, D. N. 1998, Astrophys. J., 503, 61.
Damour, T., Soffel, M., Xu, C. 1991, Phys. Rev., D43, 3273.
Damour, T., Soffel, M., Xu, C. 1992, Phys. Rev., D45, 1017.
Damour, T., Soffel, M., Xu, C. 1993, Phys. Rev. D47, 3124.
Damour, T., Soffel, M., Xu, C. 1994, Phys. Rev., D49, 618.
Danzmann, K. 2000, Adv. Space Res., 25, 1129.
Dodelson, S. 2003, Modern Cosmology (Academic Press).
Einstein, A., Straus, E. G. 1945, Rev. Mod. Phys., 17, 120.
Einstein, A., Straus, E. G. 1946, Rev. Mod. Phys., 18, 148.
Faraoni, V., Jacques, A. 2006, Phys. Rev., D76, id 063510.
Fienga, A., Manche, M., Laskar, J. Gastineau, M. 2008, Astron. Astrophys., 477, 315.
Gautreau, R. 1984, Phys. Rev., D29, 198.
Iguchi, H., Nakamura, T., Nakao, K. 2002, Prog. Theor. Phys., 108, 809.
Iorio, L. 2009, Astron. J., 137, 3715.
Irvine, W. M. 1965, Ann. Phys. (N.Y.), 32, 322.
Järnefelt, G. 1940a, Ann. Acad. Soc. Sci. Fennicae, A45, 3.
Järnefelt, G. 1940b, Arkiv Matem. Astron. Fys., 27, 1.
Järnefelt, G. 1942, Ann. Acad. Soc. Sci. Fennicae, A45, 12.
Kasai, M. 2007, Prog. Theor. Phys., 117, 1067.
Klioner, S. A., Soffel, M. H. 2004, Proc. of the Symposium “The Three-Dimensional Universe with Gaia”, 305.
Kodama, H., Sasaki, M. 1984, Prog. Theo. Phys. Suppl., 78, 1.
Kopeikin, S. M. 2007, AIP Conference Proc., New Trends in Astrodynamics and Applications III, 886, 268.
Krasiński, A. 1997, Inhomogeneous Cosmological Models (Cambridge Univ. Press).
Krasinsky, G. A. 2007, private communication.
Krasinsky, G. A., Brumberg, V. A. 2004, Celest. Mech. Dyn. Astrn., 90, 267.
Lämmerzahl, C., Preuss, O., Dittus, H. 2008, in: Lasers, Clocks and Drag-Free Control: Exploration of Relativistic Gravity in Space (eds) Dittus, H., Lämmerzahl, C., Turyshev, S. G., (Springer, Berlin) 75.
Lemaître, G. 1933, Ann. Soc. Sci. Bruxelles, A53, 51.
Mashhoon, B., Mobed, N., Singh, D. 2007, Class. Quant. Grav., 24, 5031.
McVittie, G. C. 1933, Mon. Not. R. Astron. Soc., 93, 325.
Mukhanov, V. F., Feldman, H. A., Brandenberger, R. H. 1992, Phys. Rep., 215, 203.
Ni, W. T. 2008, Int. J. Mod. Phys., D17, 921.
Noerdlinger, P. D. 2008, arXiv:0801.3807.
Noerdlinger, P. D., Petrosian, V. 1972, Astrophys. J., 168, 1.
Partovi, M. H., Mashhoon, B. 1984, Astrophys. J., 276, 2.
Perlmutter, S. et al. 1999, Astrophys. J., 517, 565.
Pitjeva, E. V. 2005, Solar Syst. Res., 39, 176.
Pitjeva, E. V. 2009, private communication.
Plebański, J., Krasiński, A. 2006, An Introduction to General Relativity and Cosmology (Cambridge Univ. Press).
Robertson, H. P. 1928, Phil. Mag., 7, 845.
Schücking, E. 1954, Zeitschrift für Physik, 137, 595.
Sereno, M., Jetzer, P. 2007, Phys. Rev., D75, id 064031.
Shibata, M., Asada, H. 1995, Prog. Theo. Phys., 94, 11.
Soffel, M. et al. 2003, Astron. J., 126, 2687.
Soffel, M. H. 1989, Relativity in Astrometry, Celestial Mechanics and Geodesy (Berlin, Heidelberg, New York, London, Paris, Tokyo: Springer Verlag).
Standish, E. M. 2003, JPL Interoffice Memorandum, 312N, 03.
Standish, E. M. 2005, Proc. IAU Colloq., 196, 163.
Tolman, R. C. 1934, Proc. Nat. Acad. Sci., 20, 410.
Tomita, K. 1991, Prog. Theo. Phys., 85, 1041.
Tomita, K. 2000a, Astrophys. J., 529, 26.
Tomita, K. 2000b, Astrophys. J., 529, 38.
Tomita, K. 2001a, Mon. Not. R. Astron. Soc., 326, 287.
Tomita, K. 2001b, Prog. Theo. Phys., 105, 419.
Tomita, K. 2001c, Prog. Theo. Phys., 106, 929.
Turyshev, S. G., Shao, M., Nordtvedt, K. 2004, Class. Quant. Grav., 21, 2773.
Weinberg, S. 1972, Gravitation and Cosmology (New York, Chichester, Brisbane, Toronto, Singapore: John Wiley & Sons).
Will, C. M. 1993, Theory and Experiment in Gravitational Physics (Cambridge Univ. Press).
Will, C. M. 2006, Living Reviews in Relativity, http://relativity.livingreviews.org/Articles/lrr-2006-3/.
Note Added in Proof
Recently Iorio (Iorio, L. 2010, J. Cosmol. Astropart. Phys. 6, 4) investigated the influence of LTB model to the solar system dynamics and based on recent observational data, he evaluated the parameters of LTB metric in Fermi coordinate system K 1 and K 2.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arakida, H. Effect of Inhomogeneity of the Universe on a Gravitationally Bound Local System: A No-Go Result for Explaining the Secular Increase in the Astronomical Unit. J Astrophys Astron 33, 201–211 (2012). https://doi.org/10.1007/s12036-012-9142-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12036-012-9142-8