The Poynting-Robertson effect in the Newtonian potential with a Yukawa correction

  • Ioannis Haranas
  • Omiros Ragos
  • Ioannis Gkigkitzis
  • Ilias Kotsireas
  • Connor Martz
  • Sheldon Van Middekoop
Original Article


We consider a Yukawa-type gravitational potential combined with the Poynting-Robertson effect. Dust particles originating within the asteroid belt and moving on circular and elliptic trajectories are studied and expressions for the time rate of change of their orbital radii and semimajor axes, respectively, are obtained. These expressions are written in terms of basic particle parameters, namely their density and diameter. Then, they are applied to produce expressions for the time required by the dust particles to reach the orbit of Earth. For the Yukawa gravitational potential, dust particles of diameter \(10^{ - 3}\) m in circular orbits require times of the order of \(8.557 \times 10^{6}\) yr and for elliptic orbits of eccentricities \(e =0.1, 0.5\) require times of \(9.396 \times 10^{6}\) and \(2.129 \times 10^{6}\) yr respectively to reach Earth’s orbit. Finally, various cases of the Yukawa potential are studied and the corresponding particle times to reach Earth’s are derived per case along with numerical results for circular and various elliptical orbits.


Celestial mechanics Orbital and rotational dynamics Classical field theories 



The authors would like to thank an anonymous reviewer whose useful comments help improve this manuscript considerably.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Ioannis Haranas
    • 1
  • Omiros Ragos
    • 2
  • Ioannis Gkigkitzis
    • 3
  • Ilias Kotsireas
    • 1
  • Connor Martz
    • 1
  • Sheldon Van Middekoop
    • 1
  1. 1.Department of Physics and Computer ScienceWilfrid Laurier University Science BuildingWaterlooCanada
  2. 2.Department of Mathematics, Faculty of SciencesUniversity of PatrasPatrasGreece
  3. 3.Departments of MathematicsEast Carolina UniversityGreenvilleUSA

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