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


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.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. Adelberger, E.G., et al.: Annu. Rev. Nucl. Part. Sci. 53, 77 (2003)

    ADS  Article  Google Scholar 

  2. Brownstein, J.R., Moffat, J.W.: Class. Quantum Gravity 23, 3427 (2006)

    ADS  Article  Google Scholar 

  3. Chan, H.M.: Observational evidence of the yukawa potential interacting dark matter. arXiv:1304.4004v1 [astro-ph.CO] (2013)

  4. D’Olivo, J.C., Ryan, M.P. Jr.: Class. Quantum Gravity 4, L13 (1987)

    Article  Google Scholar 

  5. Goldstein, H., Poole, C., Safko, J.: Classical Mechanics 3rd edn. pp. 83–86. Addison–Wesley, Reading (2002)

    Google Scholar 

  6. Haranas, I., Mioc, V.: Poynting-Robertson effect in non-singular gravitational potential. Astrophys. Space Sci. 331, 289 (2011)

    ADS  Article  MATH  Google Scholar 

  7. Haranas, I., Ragos, O.: Yukawa-type effects in satellite dynamics. Astrophys. Space Sci. (2010). doi:10.1007/s10509-010-0440-9

    MATH  Google Scholar 

  8. Haranas, I., Ragos, O., Mioc, V.: Yukawa-type potential effects in the anomalistic period of celestial bodies. Astrophys. Space Sci. (2010). doi:10.1007/s10509-010-0497-5

    MATH  Google Scholar 

  9. Haranas, Kotsireas I, I., Gomez, Fullana J M, G., Gkigkitzis, I.: Yukawa effects in the mean motion of an orbiting body. Astrophys. Space Sci., 361–365 (2016)

  10. Iorio, L.: Phys. Lett. A 298(5–6), 315 (2002)

    ADS  Article  Google Scholar 

  11. Iorio, L.: J. High Energy Phys. 10, 041 (2007)

    ADS  Article  Google Scholar 

  12. Moffat, J.W.: A modified gravity and its consequences for the solar system. arXiv:gr-qc/0608074v2 (2006)

  13. Montenbruck, O., Gill, E.: Satellite Orbits: Models, Methods and Applications. Springer, New York (2000)

    Google Scholar 

  14. Mukherjee, R., Sounda, S.: arXiv:1705.02244v1 [physics-plasma-ph] (2017)

  15. Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge Univ. Press, Cambridge (1999)

    Google Scholar 

  16. Phillips, A.C.: The Physics of Stars. Wiley and Son, New York (1999)

    Google Scholar 

  17. Piazza, F., Marinoni, C.: Phys. Rev. Lett. 91, 14 (2003)

    Article  Google Scholar 

  18. Stacey, F.D.: Physics of the Earth, 2nd edn., pp. 17–19. Wiley, New York (1977)

    Google Scholar 

  19. Talmadge, Berthias, J.-P., Hellings, R.W., Standish, E.M.: Model-independent constraints on possible modifications of Newtonian gravity. Phys. Rev. Lett. 61, 1159 (1988)

    ADS  Article  Google Scholar 

  20. Vallado, D.A., McClain, W.D.: Fundamentals of Astrodynamics and Applications, 3rd edn. Microcosm Press/Kluwer Academic Publishers, New York (2007)

    Google Scholar 

  21. Will, C.M.: Bounding of the graviton using gravitational-wave observations of inspiralling compact binaries.

  22. Wyatt, S.P., Whipple, F.L.: The Poynting-Robertson effect on meteor orbits. Astrophys. J. 111, 134–141 (1950)

    ADS  Article  Google Scholar 

Download references


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

Author information



Corresponding author

Correspondence to Ioannis Haranas.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Haranas, I., Ragos, O., Gkigkitzis, I. et al. The Poynting-Robertson effect in the Newtonian potential with a Yukawa correction. Astrophys Space Sci 363, 3 (2018).

Download citation


  • Celestial mechanics
  • Orbital and rotational dynamics
  • Classical field theories