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Solving the dark-matter problem through dynamic interactions


Owing to the renewed interest in dark matter after the upgrade of the large hadron collider and its dedication to dark-matter research, it is timely to reassess the whole problem. Considering dark matter is one way to reconcile the discrepancy between the velocity of matter in the outer regions of galaxies and the observed galactic mass. Thus far, no credible candidate for dark matter has been identified. Here, we develop a model accounting for observations by rotations and interactions between rotating objects analogous to magnetic fields and interactions with moving charges. The magnitude of these fields is described by a fundamental constant on the order of 10−41kg−1. The same interactions can be observed in the solar system, where they lead to small changes in planetary orbits.


  1. 1.

    H. I. Ewen and E. M. Purcell, Observation of a line in the galactic radio spectrum: radiation from galactic hydrogen at 1420 Mc./sec., Nature 168, 356 (1951)

  2. 2.

    Vera C. Rubin and W. Kent Ford Jr., Rotation of the Andromeda Nebula from a spectroscopic survey of emission regions, Astrophys. J. 159, 379 (1970)

  3. 3.

    H. J. Rood, Clusters of galaxies, Rep. Prog. Phys. 44(10), 1077 (1981)

  4. 4.

    K. G. Begeman, A. H. Broeils, and R. H. Sanders, Extended rotation curves of spiral galaxies - Dark haloes and modified dynamics, Mon. Not. R. Astron. Soc. 249, 523 (1991)

  5. 5.

    See, for example, the dark matter focus on the NASA website: what-is-dark-energy/

  6. 6.

    X.-J. Bi, P.-F. Yin, and Q. Yuan, Status of dark matter detection, Front. Phys. 8(6), 794 (2013)

  7. 7.

    M. Milgrom, A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, Astrophys. J. 270, 365 (1983)

  8. 8.

    M. Milgrom, A modification of the Newtonian dynamics - Implications for galaxies, Astrophys. J. 270, 371 (1983)

  9. 9.

    J. D. Jackson, Classical Electrodynamics, 3rd Ed., NJ: Wiley, 1998

  10. 10.

    S. Torres-Flores, B. Epinat, P. Amram, H. Plana, C. Mendes de Oliveira, GHASP: An H-kinematic survey of spiral and irregular galaxies - IX: The near-infrared, stellar and baryonic Tully–Fisher relations, Mon. Not. R. Astron. Soc. 416, 1936 (2011)

  11. 11.

    See the NASA website at:

  12. 12.

    For the calculations we assumed circular orbits, with rM = 5.79 × 1010m and ωM = 1.32 × 10−7s−1 for Mercury, and rE = 1.50 × 1011m and ωE = 3.17 × 10−8s−1 for Earth.

  13. 13.

    G. M. Clemence, The relativity effect in planetary motions, Rev. Mod. Phys. 19, 361 (1947)

  14. 14.

    For the calculations of Venus we assumed a circular orbit with rV = 1.08 × 1011m and ωV = 5.15 × 10−8s−1.

  15. 15.

    Jean Chazy, La Theorie de la relativite et la Mechanique celeste, Gauthier Villars, Paris, 1928, p. 230

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Correspondence to Werner A. Hofer.

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Hofer, W.A. Solving the dark-matter problem through dynamic interactions. Front. Phys. 10, 109502 (2015).

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  • galactic rotation curves
  • dark matter
  • solar system
  • perihelion of Mercury
  • nodes of Venus