Advertisement

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
  • 79 Downloads

Abstract

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.

Keywords

Celestial mechanics Orbital and rotational dynamics Classical field theories 

Notes

Acknowledgement

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

References

  1. Adelberger, E.G., et al.: Annu. Rev. Nucl. Part. Sci. 53, 77 (2003) ADSCrossRefGoogle Scholar
  2. Brownstein, J.R., Moffat, J.W.: Class. Quantum Gravity 23, 3427 (2006) ADSCrossRefGoogle 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) CrossRefGoogle 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) ADSCrossRefMATHGoogle Scholar
  7. Haranas, I., Ragos, O.: Yukawa-type effects in satellite dynamics. Astrophys. Space Sci. (2010). doi: 10.1007/s10509-010-0440-9 MATHGoogle 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 MATHGoogle 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) Google Scholar
  10. Iorio, L.: Phys. Lett. A 298(5–6), 315 (2002) ADSCrossRefGoogle Scholar
  11. Iorio, L.: J. High Energy Phys. 10, 041 (2007) ADSCrossRefGoogle 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) CrossRefMATHGoogle 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) MATHGoogle 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) CrossRefGoogle 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) ADSCrossRefGoogle Scholar
  20. Vallado, D.A., McClain, W.D.: Fundamentals of Astrodynamics and Applications, 3rd edn. Microcosm Press/Kluwer Academic Publishers, New York (2007) MATHGoogle Scholar
  21. Will, C.M.: Bounding of the graviton using gravitational-wave observations of inspiralling compact binaries. https://cds.cern.ch/record/333219/files/9709011.pdf
  22. Wyatt, S.P., Whipple, F.L.: The Poynting-Robertson effect on meteor orbits. Astrophys. J. 111, 134–141 (1950) ADSCrossRefGoogle Scholar

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

Personalised recommendations