CEAS Space Journal

, Volume 5, Issue 1–2, pp 19–37 | Cite as

Preliminary applications of the nonsymmetric Kaluza–Klein (Jordan–Thiry) theory to Pioneer 10 and 11 spacecraft anomalous acceleration

Original Paper


The nonsymmetric Kaluza–Klein (Jordan–Thiry) theory leads to a model of a modified acceleration that can fit an anomalous acceleration experienced by the Pioneer 10 and 11 spacecraft. A mysterious connection between an anomalous acceleration and a Hubble constant is solved in the theory.


An anomalous acceleration Pioneer 10 and 11 Spacecraft Nonsymmetric Kaluza–Klein (Jordan–Thiry) theory Hubble constant Cosmological constant 


  1. 1.
    Anderson, J.D. et al.: Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys. Rev. Lett. 81, 2858 (1998)CrossRefGoogle Scholar
  2. 2.
    Anderson, J.D. et al.: Study of the anomalous acceleration of Pioneer 10 and 11. Phys. Rev. D 65, 082004 (2002)CrossRefGoogle Scholar
  3. 3.
    Nieto, M.M., Anderson, J.D.: Using early data to illuminate the Pioneer anomaly. Class. Quantum Gravity 22, 5343 (2005)MATHCrossRefGoogle Scholar
  4. 4.
    Turyshev S.G., Toth V.T.: The Pioneer anomaly. Living Rev. Relativ. 13, 4. arXiv: gr-qc/1001.3686v2; http://www.livingreviews.org/lrr-2010-4 (2010)
  5. 5.
    Kalinowski M.W.: Nonsymmetric Fields Theory and its Applications. World Scientific, Singapore (1990)Google Scholar
  6. 6.
    Kalinowski, M.W.: Nonsymmetric Kaluza–Klein (Jordan–Thiry) Theory in the electromagnetic case. Int. J. Theor. Phys. 31, 611 (1992)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Hlavatý, V.: Geometry of Einstein’s unified field theory. P. Noordhoff Ltd., Groningen (1957)Google Scholar
  8. 8.
    Kalinowski, M.W.: Nonsymmetric Kaluza–Klein (Jordan–Thiry) theory in a general nonabelian case. Int. J. Theor. Phys. 30, 281 (1991)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Kalinowski, M.W.: Can we get a confinement from extra dimensions. In: Ajduk, Z., Pokorski, S., Wróblewski, A.K. (eds.) Physics of Elementary Interactions. World Scientific, Singapore (1991)Google Scholar
  10. 10.
    Moffat, J.W.: Generalized theory of gravitation and its physical consequences. In: de Sabbata, V. (ed.) Proceeding of the VII International School of Gravitation and Cosmology. World Scientific Publishing Co., Erice, p. 127 (1982)Google Scholar
  11. 11.
    Kalinowski, M.W.: Scalar fields in the nonsymmetric Kaluza–Klein (Jordan–Thiry) theory. arXiv: hep-th/0307242v9, 7 May (2004)Google Scholar
  12. 12.
    Stix, M.: On the time scale of energy transport in the Sun. Sol. Phys. 212, 3 (2003)CrossRefGoogle Scholar
  13. 13.
    Spergel, D.N. et al.: Three-year Wilkinson microwave anisotropy probe (WMAP) observations: implications for cosmology. Astrophys. J. Suppl. Ser. 170, p. 377 (2007)Google Scholar
  14. 14.
    Sandage, A. et al.: The Hubble constant: a summary of the Hubble Space Telescope Program for the luminosity calibration of type Ia Supernovae by means of Cepheids. Astrophys. J. 653, 843 (2006)CrossRefGoogle Scholar
  15. 15.
    Planck collaboration, Ade, P.A.R., et al.: Planck 2013 results. XVI. In: Cosmological Parameters. arXiv: 1303.5076 v1 [astro-ph.CO], 20 March (2013)Google Scholar
  16. 16.
    Tully, R.B., Fisher, J.R.: A new method of determining distances to galaxies. Astronom. Astrophys. 54, 661 (1977)Google Scholar
  17. 17.
    Freedman, W., et al.: Final results from the Hubble Space Telescope Key Project to measure the Hubble constant. Astrophys. J. 553, 47 (2001)CrossRefGoogle Scholar
  18. 18.
    Kelson, D.D., et al.: The Hubble Space Telescope Key Project on the extragalactic distance scale. XXVII. A derivation of the Hubble constant using the fundamental plane and \(D_n-\sigma\) relations in Leo I, Virgo, and Fornax. Astrophys. J. 29:768 (2000)Google Scholar
  19. 19.
    Tonry, J.L. et al.: The SBF survey of galaxy distances. IV. SBF magnitudes, colors, and distances. Astrophys. J. 546, 681 (2001)CrossRefGoogle Scholar
  20. 20.
    Milgrom, M.: MOND—theoretical aspects. New Astron. Rev. 46, 741 (2002)CrossRefGoogle Scholar
  21. 21.
    Rievers, B., Bremer, S., List, M., Lämmerzahl, C., Dittus, H.: Thermal dissipation force modeling with preliminary results for Pioneer 10/11. Acta Astronaut. 66, 467 (2009)CrossRefGoogle Scholar
  22. 22.
    Rievers, B., Lämmerzahl, C., List, M., Bremer, S., Dittus, H.: New powerful thermal modelling for high-precision gravity missions with applications to Pioneer 10/11. New J. Phys. 11, 113032 (2009)CrossRefGoogle Scholar
  23. 23.
    Bertolami, O., Francisco, F., Gil, P.S.J., Páramos, J.: Estimating radiative momentum transfer through a thermal analysis of the Pioneer anomaly. Space Sci. Rev. 151, 75 (2010)CrossRefGoogle Scholar
  24. 24.
    Bertolami, O., Francisco, F., Gil, P.S.J., Páramos, J.: Thermal analysis of the Pioneer anomaly: a method to estimate radiative momentum transfer. Phys. Rev. D 78, 103001-1 (2008)Google Scholar
  25. 25.
    Bertolami, O., Francisco, F., Gil, P.S.J., Páramos, J.: Modeling of thermal perturbations using ray tracing method with preliminary results for a test case model of Pioneer 10/11 radioisotopic thermal generators. Space Sci. Rev. 151, 123 (2010)CrossRefGoogle Scholar
  26. 26.
    Francisco, F., Bertolami, O., Gil, P.S.J., Páramos, J.: Modelling the reflective thermal contribution to the acceleration of the Pioneer spacecraft. Phys. Lett. B 711, 337 (2012)CrossRefGoogle Scholar
  27. 27.
    Iorio, L., Giudice, G.: What do the orbital motions of the outer planets of the Solar System tell us about the Pioneer anomaly? New Astron. 11, 600 (2006)CrossRefGoogle Scholar
  28. 28.
    Fienga, A., Laskar, J., Kuchynka, P., Le Poncin-Lafitte, Ch., Manche, H., Gastineau, M.: Gravity tests with INPOP planetary ephemerides. In: Klioner, S.A., Seidelman, P.K., Soffel, M.K. (eds.) Relativity in Fundamental Astronomy. Proceedings of the IAU Symposium 261, p. 159 (2010)Google Scholar
  29. 29.
    Standish, E.M.: Testing alternate gravitational theories. In: Klioner S.A., Seidelman P.K., Soffel M.K. (eds.) Relativity in Fundamental Astronomy. Proceedings of the IAU Symposium 261, 179 (2010)Google Scholar
  30. 30.
    Page, G.L., Dixon, D.S., Wallin, J.F.: Can minor planets be used to assess gravity in the outer Solar System? Astrophys. J. 642, 606 (2006)CrossRefGoogle Scholar
  31. 31.
    Iorio, L.: Can the Pioneer anomaly be of gravitational origin? A~phenomenological answer. Found. Phys. 37, 897 (2007)MATHCrossRefGoogle Scholar
  32. 32.
    Iorio, L.: Impact of the Pioneer/Rindler-type acceleration on the Oort cloud. Mon. Not. R. Astron. Soc. 419, 2226 (2012)CrossRefGoogle Scholar
  33. 33.
    Page, G.L., Wallin, J.F., Dixon, D.S.: How well do we know the orbits of the outer planets? The Astrophys. J. 697, 1226 (2009)CrossRefGoogle Scholar
  34. 34.
    Page, G.L.: Exploring the weak limit of gravity at Solar System scales. Publ. Astron. Soc. Pac. 122, 259 (2010)CrossRefGoogle Scholar
  35. 35.
    Wallin, J.F., Dixon, D.S., Page, G.L.: Testing gravity in the outer Solar System: results from trans-Neptunian objects. Astrophys. J. 666, 1296 (2007)CrossRefGoogle Scholar
  36. 36.
    Tangen, K.: Could the Pioneer anomaly have a gravitational origin? Phys. Rev. D 76, id. 042005 (2007)Google Scholar
  37. 37.
    Varieschi, G.U.: Conformal cosmology and the Pioneer anomaly. Phys. Res. Int. 2012, art. ID 469095 (2012).Google Scholar
  38. 38.
    Mbelek, J.P., Mosquera Cuesta, H.J., Navello, M., Salim, J.M.: Nonlinear electrodynamics and the Pioneer 10/11 space-craft anomaly. arXiV: astro-ph/0608538 v. 3 (2006)Google Scholar
  39. 39.
    Nizony, M., Lachièze-Rey, M.: Cosmological effects in the local static frame. Astron. Astrophys. 434, 45 (2005)CrossRefGoogle Scholar
  40. 40.
    Lachièze-Rey, M.: Cosmology in the Solar System: the Pioneer effect is not cosmological. Class. Quantum Gravity 24, 2735 (2007)MATHCrossRefGoogle Scholar
  41. 41.
    Iorio, L.: The Lense-Thirring effect and the Pioneer anomaly: solar system tests. In: Kleinert, H., Jantzen, R.T., Ruffini, R. (eds.) Proceedings of the 11th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, p. 2558. World Scientific,Singapore (2008)Google Scholar
  42. 42.
    Iorio, L.: Orbital effects of a time-dependent Pioneer-like anomalous acceleration. Modern Phys. Lett. A 27, id.~1250071 (2012)Google Scholar
  43. 43.
    Iorio, L.: Does the Neptunian system of satellites challenge a gravitational origin for the Pioneer anomaly. Mon. Not. R. Astron. Soc. 405, 2615 (2010)Google Scholar
  44. 44.
    Iorio, L.: Can the Pioneer anomaly be induced by velocity-dependent forces? Tests in the outer regions of the Solar System with planetary dynamics. Int. J. Mod. Phys. D 18, 947 (2009)MATHCrossRefGoogle Scholar
  45. 45.
    Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies with an Introduction to the Problem of Three Bodies. Cambridge University Press, Cambridge (1952)Google Scholar
  46. 46.
    Sterne T.E.: An Introduction to Celestial Mechanics. Interscience Publishers, Inc., New York (1960)Google Scholar
  47. 47.
    Misner, W.C., Thorne, S.K., Wheeler, J.A.: Gravitation, W. H. Freeman and Comp., San Francisco (1971)Google Scholar
  48. 48.
    Iorio, L.: The recently determined anomalous perihelion precession of Saturn. Astron. J. 137, 3615 (2009)CrossRefGoogle Scholar
  49. 49.
    Iorio, L., Lichtenegger, H.I.M., Ruggiero, M., Corda, Ch.: Phenomenology of the Lense–Thirring effect in the Solar System. Astrophys. Space Sci. 331, 351 (2011)MATHCrossRefGoogle Scholar
  50. 50.
    Iorio, L.: Is it possible to measure the Lense–Thirring effect on the orbits of the planets in the gravitational field of the Sun? Astron. Astrophys. 431, 385 (2005)CrossRefGoogle Scholar
  51. 51.
    Iorio, L.: On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging. Astron. Astrophys. 433, 385 (2005)CrossRefGoogle Scholar
  52. 52.
    Iorio, L.: Constraining the angular momentum of the Sun with planetary orbital motions and general relativity. Sol. Phys. 281, 815 (2012)CrossRefGoogle Scholar
  53. 53.
    Iorio, L.: General relativistic spin-orbit and spin-spin effects on the motion of rotating particles in an external gravitational field. Gen. Relativ. Gravit. 44, 719 (2012)MathSciNetMATHCrossRefGoogle Scholar
  54. 54.
    Avalos-Vargas, A., Ares de Parga, G.: The precession of the orbit of a charged body interacting with a massive charged body in general relativity. Eur. Phys. J. Plus 127, art. id. 155 (2012)Google Scholar
  55. 55.
    Iorio, L.: Constraining the electric charges of some astronomical bodies in Reissner–Nordström spacetimes and generic r −2-type power-law potentials from orbital motions. General Relativ. Gravit. 44, 1753 (2012)MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Avalos-Vargas, A., Ares de Parga, G.: The precession of the orbit of a test neutral body interacting with a massive charged body. Eur. Phys. J. Plus 126, art. id. 117 (2011)Google Scholar
  57. 57.
    Iorio, L.: Astronomical constraints on some long-range models of modified gravity. Adv. High Energy Phys. 2007, art. id. 090731 (2007)Google Scholar
  58. 58.
    Adkins G.S., McDonnell, J.: Orbital precession due to central-force perturbations. Phys. Rev. D 75, id. 082001 (2007)Google Scholar
  59. 59.
    Schmidt H.-J.: Perihelion precession for modified Newtonian gravity. Phys. Rev. D 78, id. 023512 (2008)Google Scholar
  60. 60.
    Chashchina O.I., Silagadze Z.K.: Remark on orbital precession due to central-force perturbations. Phys. Rev. D 77, id. 107502 (2008)Google Scholar
  61. 61.
    Sanders, R.H.: Solar System constrains on multifield theories of modified dynamics. Mon. Not. R. Astron. Soc. 370, 1519 (2006)CrossRefGoogle Scholar
  62. 62.
    Sereno, M., Jetzer, P.h.: Dark matter versus modifications of the gravitational inverse-square law: results from planetary motion in the Solar System. Mon. Not. R. Astron. Soc. 371, 626 (2006)CrossRefGoogle Scholar
  63. 63.
    Weinberg, S.: Cosmology. Oxford University Press, Oxford (2008)Google Scholar
  64. 64.
    Hobson M.P., Efstathiou G.P., Lasenby, A.N.: General relativity. In: An Introduction for Physicists. Cambridge University Press, Cambridge (2007)Google Scholar
  65. 65.
    Adkins, G.S., McDonnell, J., Fell, R.N.: Cosmological perturbations on local systems. Phys. Rev. D 75, id. 064011 (2007)Google Scholar
  66. 66.
    Iorio, L.: Local cosmological effects of the order of H in the orbital motion of a binary system. Mon. Not. R. Astron. Soc. 429, 915 (2013)CrossRefGoogle Scholar
  67. 67.
    Cooperstock, F.I., Faraoni, V., Vollick, D.N.: The influence of the cosmological expansion on local systems. Astrophys. J. 503, 61 (1998)CrossRefGoogle Scholar
  68. 68.
    Carrera, M., Giulini, D.: Influence of global cosmological expansion on local dynamics and kinematics. Rev. Mod. Phys. 82, 169 (2008)CrossRefGoogle Scholar
  69. 69.
    Kopeikin, S.M.: Celestial ephemerides in an expanding universe. Phys. Rev. D 86, id. 064004 (2012)Google Scholar
  70. 70.
    Sereno, M., Jetzer, Ph.: Evolution of gravitational orbits in the expanding universe. Phys. Rev. D 75, id. 064031 (2007)Google Scholar
  71. 71.
    Kopeikin, S.M.: Post-Newtonian celestial dynamics in cosmology: field equations. Phys. Rev. D 87, id. 044029 (2013)Google Scholar
  72. 72.
    Adkins, G.S., McDonnell, J.: Orbital precession due to central-force perturbations. Phys. Rev. D 75, id. 082001 (2007)Google Scholar
  73. 73.
    Iorio, L.: Solar System motions and the cosmological constant: a new approach. Adv. Astron. 2008, art. id. 268647 (2008)Google Scholar
  74. 74.
    Iorio, L.: Can Solar System observations tell us something about the cosmological constant? Int. J. Mod. Phys. D 15, 473 (2006)MathSciNetMATHCrossRefGoogle Scholar
  75. 75.
    Islam, J.N.: The cosmological constant and classical tests of general relativity. Phys. Lett. A 97, 239 (1983)MathSciNetCrossRefGoogle Scholar
  76. 76.
    Jetzer, P.h., Sereno, M.: Two-body problem with the cosmological constant and observational constraints. Phys. Rev. D 73, 044015 (2006)CrossRefGoogle Scholar
  77. 77.
    Arakida, H.: Note on the perihelion/periastron advance due to cosmological constant. Int. J. Theor. Phys. 52, 1408 (2013)CrossRefGoogle Scholar
  78. 78.
    Kerr, A.W., Hauck, J.C., Mashhoon, B.: Standard clocks, orbital precession and the cosmological constant. Class. Quantum Gravity 20, 2727 (2003)MathSciNetMATHCrossRefGoogle Scholar
  79. 79.
    Arakida, H., Kasai, M.: Effect of the cosmological constant on the bending of light and the cosmological lens equation. Phys. Rev. D 85, id. 023006 (2012)Google Scholar
  80. 80.
    Biressa, T., de Freits Pacheco, J.A.: The cosmological constant and the gravitational light bending. Gen. Relativ. Gravit. 43, 2649 (2011)MATHCrossRefGoogle Scholar
  81. 81.
    Ishak, M., Rindler, W.: The relevance of the cosmological constant for lensing. Gen. Relativ. Gravit. 42, 2247 (2010)MathSciNetMATHCrossRefGoogle Scholar
  82. 82.
    Lake, K.: Bending of light and the cosmological constant. Phys. Rev. D 65, id. 087301 (2002)Google Scholar
  83. 83.
    Rindler, W., Ishak, M.: Contribution of the cosmological constant to the relativistic bending of light revisited. Phys. Rev. D 76, id. 043006 (2007)Google Scholar
  84. 84.
    Calura, M., Fortini, P., Montanari, E.: Post-Newtonian Lagrangian planetary equations. Phys. Rev. D 56, 4782 (1997)CrossRefGoogle Scholar
  85. 85.
    Calura, M., Montanari, E., Fortini, P.: Lagrangian planetary equations in Schwarzschild spacetime. Class. Quantum Gravity 15, 3121 (1998)MathSciNetMATHCrossRefGoogle Scholar
  86. 86.
    Pitjeva, E.V., Pitjev, N.P.: Changes in the Sun’s mass and gravitational constant estimated using modern observations of planets and spacecraft. Sol. Syst. Res. 46, 78 (2012)CrossRefGoogle Scholar
  87. 87.
    Burgess, C.P., Cloutier, J.: Astrophysical evidence for a weak new force?. Phys. Rev. D 38, 2944 (1988)CrossRefGoogle Scholar
  88. 88.
    Talmadge, C., Berthias, J.-.P., Hellings, R.W., Standish, E.M.: Model-independent constraints on possible modifications of Newtonian gravity. Phys. Rev. Lett. 61, 1159 (1988)CrossRefGoogle Scholar
  89. 89.
    Sereno, M., Jetzer, P.h.: Dark matter versus modifications of the gravitational inverse-square law: results from planetary motion in the Solar System. Mon. Not. R. Astron. Soc. 371, 626 (2006)CrossRefGoogle Scholar
  90. 90.
    Moffat J.W.: Scalar tensor vector gravity theory. J. Cosmol. Astropart. Phys. 2006(03), id. 004 (2006)Google Scholar
  91. 91.
    Reynaud, S., Jaekel, M.-.T.: Testing the Newton law at long distances. Int. J. Mod. Phys. A 20, 2294 (2005)MATHCrossRefGoogle Scholar
  92. 92.
    Iorio, L.: Constraints on a Yukawa gravitational potential from laser data of LAGEOS satellites. Phys. Lett. A 298, 315 (2002)CrossRefGoogle Scholar
  93. 93.
    Iorio, L.: Constraints on the range λ of Yukawa-like modifications to the Newtonian inverse-square law of gravitation from Solar System planetary motions. J. High Energy Phys. 2007(10), id. 041 (2007)Google Scholar
  94. 94.
    Iorio, L.: Putting Yukawa-like modified gravity (MOG) on the test in the Solar System. Sch. Res. Exch. 2008, art. id. 238385 (2008)Google Scholar
  95. 95.
    Sanders, R.H.: Solar System constraints on multifield theories of modified dynamics. Mon. Not. R. Astron. Soc. 370, 1519 (2006)CrossRefGoogle Scholar
  96. 96.
    Brownstein JR, Moffat JW (2006) Gravitational solution to the Pioneer 10/11 anomaly. Class. Quantum Gravity 23, 3427Google Scholar
  97. 97.
    Iorio, L.: On a Recently Proposed Scalar–Tensor–Vector Metric Extension of General Relativity to Explain the Pioneer Anomaly. arXiv: astro-ph/0608538 v. 3 (2006).Google Scholar
  98. 98.
    Anderson, J.D.; Morris, J.R.: Brans–Dicke theory and the Pioneer anomaly. Phys. Rev. D 86, id. 064023 (2012)Google Scholar
  99. 99.
    Turyshev, S.G., Toth, V.K., Ellis, J., Markwardt, C.B.: Support for temporary behavior of the Pioneer anomaly from the extended Pioneer 10 and 11 Doppler data sets. Phys. Rev. Lett. 107, 081103 (2011)Google Scholar
  100. 100.
    Turyshev, S.G., Toth, V.K., Kinsella, G., Lee, S.-.C., Lok, S.M., Ellis, J.: Support for the thermal origin of the Pioneer anomaly. Phys. Rev. Lett. 108, 241101 (2012)CrossRefGoogle Scholar
  101. 101.
    Anderson, J.D., Morris, J.R.: Chameleon effect and the Pioneer anomaly. Phys. Rev. D 85, 084017 (2012)CrossRefGoogle Scholar
  102. 102.
    Anderson, J.D., Schubert, G.: Rhea’s gravitational field and interior structure inferred from the archival data files of the 2005 Cassini flyby. Phys. Earth Planet. Inter. 178, 176 (2010)CrossRefGoogle Scholar
  103. 103.
    Rievers, B., Lämmerzal, C.: High precision thermal modelling of complex systems with application to the flyby and Pioneer anomaly. Ann. Phys. (Berlin) 523, 439 (2011)CrossRefGoogle Scholar
  104. 104.
    Illumination for computer generated pictures. Commun. ACM 18, 311 (1975)CrossRefGoogle Scholar
  105. 105.
    He, D.X., Torrance, K.E., Silion, F.X., Greenberg, D.P.: A comprehensive physical model for light reflection. Comput. Graph. 25, 175 (1991)CrossRefGoogle Scholar
  106. 106.
    Irawan, P., Marschner, S.: Specular reflection from woven cloth. ACM Trans. Graph. 31, 11 (2012)CrossRefGoogle Scholar
  107. 107.
    Exirifard, Q.: Constraints on f(R ijkl R ijkl) gravity: an evidence against the covariant resolution of the Pioneer anomaly. arXiv: 0708.0662 [gr-gc] (2007)Google Scholar
  108. 108.
    Nieto, M.M.: Analytic Gravitational-Force Calculations for Models of the Kuiper Belt, With Application to the Pioneer Anomaly. arXiv: astro-ph/0506281 v. 3 (2005).Google Scholar

Copyright information

© CEAS 2013

Authors and Affiliations

  1. 1.Faculty of PhysicsWarsaw UniversityWarsawPoland

Personalised recommendations