Astrophysics and Space Science

, 361:365 | Cite as

Yukawa effects on the mean motion of an orbiting body

  • Ioannis Haranas
  • Ilias Kotsireas
  • Guillem Gómez
  • Màrius J. Fullana
  • Ioannis Gkigkitzis
Original Article


In today’s gravity research there exist few modified gravitational theories which among other things predict the existence of a Yukawa-type correction to the classical gravitational potential. In this paper we study the Yukawa effect on the mean motion if any in a two-body scenario, assuming the influence of the existence of a possible Yukawa correction in the gravitational force of a primary. For that, we derive an equation in order to approximate the mean motion for secondary time rate of change of the orbiting body and its total variation over one revolution, under the influence of the non-Newtonian radial acceleration. Numerical results for Mercury and the companion star of the pulsar PSR \(1913+16\) are calculated. For specific values of the parameters \(\alpha\) and \(\lambda\), as given in the bibliography we have found that there is no corresponding Yukawa effect affecting the mean motion of the planet Mercury. On the other hand it appears that there is a periodic Yukawa effect that affects the mean motion of \(\mbox{PSR}+16\) whose maximum numerical value occurs when the eccentric anomaly is equal to \(180^{\circ}\).


Yukawa potential Celestial mechanics orbital and rotational dynamics Classical field theories 



The authors would like to thanks an unknown reviewer who with his/her valuable comments help improve the manuscript considerably. Similarly, the authors would like to thanks the Dr. Krzysztof Gozdziewski, Associate Editor of Astrophysics and Space Science for providing us with extra time during the revision of this manuscript.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Ioannis Haranas
    • 1
  • Ilias Kotsireas
    • 1
  • Guillem Gómez
    • 3
  • Màrius J. Fullana
    • 3
  • Ioannis Gkigkitzis
    • 2
  1. 1.Dept. of Physics and Computer ScienceWilfrid Laurier University Science BuildingWaterlooCanada
  2. 2.Departments of MathematicsEast Carolina UniversityGreenvilleUSA
  3. 3.Institut de Matemàtica MultidisciplinàriaUniversitat Politècnica de ValènciaValenciaSpain

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