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  • Access by Xinjiang University

Could the Pioneer anomaly have a gravitational origin?

Kjell Tangen*

  • DNV, 1322 Høvik, Norway

  • *kjell.tangen@dnv.com

Phys. Rev. D 76, 042005 – Published 23 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.042005

Abstract

If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity over long distances or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Following the general assumption that the Pioneer spacecraft move geodesically in a spherically symmetric space-time metric, we derive the metric disturbance that is needed in order to account for the Pioneer anomaly. We then analyze the residual effects on the astronomical observables of the three outer planets that would arise from this metric disturbance, given an arbitrary metric theory of gravity. Providing a method for comparing the computed residuals with actual residuals, our results imply that the presence of a perturbation to the gravitational field necessary to induce the Pioneer anomaly is in conflict with available data for the planets Uranus and Pluto, but not for Neptune. We therefore conclude that the motion of the Pioneer spacecraft must be nongeodesic. Since our results are model-independent within the class of metric theories of gravity, they can be applied to rule out any model of the Pioneer anomaly that implies that the Pioneer spacecraft move geodesically in a perturbed space-time metric, regardless of the origin of this metric disturbance.

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References (35)

  1. J. D. Anderson et al., Phys. Rev. Lett. 81, 2858 (1998).
  2. J. D. Anderson et al., Phys. Rev. D 65, 082004 (2002).
  3. S. G. Turyshev, M. M. Nieto, and J. D. Anderson, EAS Publ. Ser. 20, 243 (2006).
  4. S. G. Turyshev, M. M. Nieto, and J. D. Anderson, in Proceedings of the XXII Texas Symposium on Relativistic Astrophysics, Stanford, 2004, econf C041213, 0310 (2004).
  5. C. B. Markwardt, arXiv:gr-qc/0208046.
  6. L. K. Scheffer, Phys. Rev. D 67, 084021 (2003).
  7. Ø. Olsen, Astron. Astrophys. 463, 393 (2007).
  8. M. M. Nieto, S. G. Turyshev, and J. D. Anderson, Phys. Lett. B 613, 11 (2005).
  9. M. M. Nieto, Phys. Rev. D 72, 083004 (2005).
  10. O. Bertolami and J. Páramos, Phys. Rev. D 71, 023521 (2005).
  11. O. Bertolami and J. Páramos, Classical Quantum Gravity 21, 3309 (2004).
  12. M. Milgrom, Astrophys. J. 270, 365 (1983).
  13. J. Bekenstein and J. Magueijo, arXiv:astro-ph/0602266.
  14. S. Reynaud and M. T. Jaekel, Int. J. Mod. Phys. A 20, 2294 (2005).
  15. M. T. Jaekel and S. Reynaud, Mod. Phys. Lett. A 20, 1047 (2005).
  16. It should be noted that, by gravitational, we here mean any physical interaction mediated indirectly through the space-time metric, regardless of the nature of its source or how the metric couples to the source. A gravitational theory in this context means any metric theory of gravity, and gravitational sources would include not only matter or radiation, but also exotic sources, like dark energy, scalar fields, as well as the four-dimensional effects of higher-dimensional models, such as the brane-world models.

  17. E. M. Standish, Report No. IOM 312.F-98-048, 1998, http://iau-comm4.jpl.nasa.gov.
  18. E. V. Pitjeva, Solar System Research 39, 176 (2005).
  19. G. L. Page, D. S. Dixon, and J. F. Wallin, arXiv:astro-ph/0504367.
  20. D. Izzo and A. Rathke, arXiv:astro-ph/0504634.
  21. L. Iorio and G. Giudice, New Astron. Rev. 11, 600 (2006).
  22. C. Talmadge, J. P. Berthias, R. W. Hellings, and E. M. Standish, Phys. Rev. Lett. 61, 1159 (1988).
  23. C. M. Will, Living Rev. Relativity 4, 4 (2001), http://www.livingreviews.org/lrr-2001-4.
  24. O. Bertolami, J. Paramos, and S. G. Turyshev, arXiv:gr-qc/0602016.
  25. H. Goldstein, Classical Mechanics (Addison-Wesley, Reading, 1950).
  26. The validity of this approach has been checked by comparing analytical and numerical solutions to the perturbation equations.

  27. C. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W. H. Freeman and Company, San Francisco, 1973).
  28. S. M. Carrol, Spacetime and Geometry. An Introduction to General Relativity (Addison Wesley, San Francisco, 2004).
  29. For the Pluto data set, a few data points with r.a. or dec. of 10 arc sec or more were deleted. These residuals were more than 10 times the a priori measurement accuracy, and were therefore deemed to be due to invalid measurements.

  30. We fit solutions to the unperturbed equations of motion to solutions of the perturbed equations of motion. This is a simplification compared to the way the real ephemeris is constructed by fitting to real observations. However, we expect this simplification to have no impact on the end result, i.e., the best-fit solution will provide the best fit regardless of the reference frame in which the fit was made.

  31. The reason why we choose to work from the basic equations of motion and not to use a perturbative approach like the Gaussian equations is to be able to generalize the approach to any metric theory of gravity.

  32. The reason for using the argument of latitude as a model parameter instead of the true anomaly is just formal; that the former is a coordinate that is relative to a point that in our idealized models is fixed (the ascending node, i.e., the point where the object ascends through the ecliptic), whereas the true anomaly is measured relative to the a point that moves—the periapsis.

  33. M. T. Jaekel and S. Reynaud, Classical Quantum Gravity 22, 2135 (2005).
  34. J. D. Bekenstein, Phys. Rev. D 70, 083509 (2004).
  35. D. A. Vallado, Fundamentals of Astrodynamics and Applications (Microcosm Press and Kluwer Academic Publishers, El Segundo, 2001).

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