Skip to main content

Long Period Tidal Force Variations and Regularities in Orbital Motion of the Earth-Moon Binary Planet System


We have studied long period, 206 and 412 day, variations in tidal sea level corresponding to various moon phases collected from five observatories in the Northern and Southern hemispheres. Variations in sea level in the Bay of Fundy, on the eastern Canadian seaboard, with periods of variation 206 days, and 412 days, have been discovered and carefully studied by Desplanque and Mossman (Proceedings of the 4th Bay of fundy workshop Saint John, New Brunswick 2001, Atlantic Geol 40:1, 2004). The current manuscript focuses on analyzing a larger volume of observational sea level tide data as well as on rigorous mathematical analysis of tidal force variations in the Sun-Earth-Moon system. We have developed a twofold model, both conceptual and mathematical, of astronomical cycles in the Sun-Earth-Moon system to explain the observed periodicity. Based on an analytical solution of the tidal force variation in the Sun-Earth-Moon system, it is shown that the tidal force can be decomposed into two components: the Keplerian component and the Perturbed component. The Perturbed component of the tidal force variation was calculated, and it was shown that the observed periodicity, 206 and 412 days, of atmospheric and hydrosphere tides results from variations of the Perturbed component of tidal force. The amplitude of the Perturbed component of tidal force is 19 × 10−8 N/kg. It is the same order of magnitude as the amplitude of the Keplerian component of tidal force: 58 × 10−8 N/kg. It follows that the Perturbed component of the variation of a tidal force must always be taken into consideration along with the Keplerian component in geodynamical constructions involving tides.

This is a preview of subscription content, access via your institution.

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


  1. Yu.N. Avsyuk, Tidal Forces and Natural Processes (UIPE RAS, Moscow, 1996) 190 p. In Russian

  2. Yu.N. Avsyuk, Izvestia Phys. Solid Earth 37, 11 (2001)

    Google Scholar 

  3. Yu.N. Avsyuk, I.I. Suvorova, Izvestia Phys. Solid Earth 42, 7 (2006)

    Google Scholar 

  4. Yu. Barkin, J. Ferrandiz, M. Ferrandez, Earth, Moon, Mercury and Titan seismicity: Observed and expected phenomena. (Lunar and Planetary Science XXXVI, 2005), Accessed 10 September 2010

  5. C. Desplanque, D.J. Mossman, 2001. Fundamentals of fundy tides. (p.178–204), In: Chopin, T., and Wells, P.G., (eds.), 2001. Opportunities and challenges for protecting, restoring and enhancing coastal habitats in the Bay of fundy. Proceedings of the 4th Bay of fundy workshop Saint John, New Brunswick, September 19–21, 2000. Environment Canada, Dartmouth, Nova Scotia, 237p

  6. C. Desplanque, D.J. Mossman, Atlantic Geol. 40, 1 (2004)

    Google Scholar 

  7. Yu. Kosygin, L. Maslov, Geotectonics 20, 6 (1986)

    Google Scholar 

  8. D. Lammlein, Rev. Geophys. Space Phys. 16, 224 (1974)

    Google Scholar 

  9. B.W. Levin, E.V. Sasorova, Doklady Earth Sci. 434, Part 1 (2010)

  10. L. Métivier, O. de Viron, C.P. Conrad, S. Renault, M. Diament, G. Patau, Earth Planet. Sci Lett. 278, 370 (2009)

    Google Scholar 

  11. N.S. Sidorenkov, The Interaction Between Earth’s Rotation and Geophysical processes (WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2009), p. 317

    Chapter  Google Scholar 

  12. G.P. Tamrazian, Ikarus. 7, 59 (1967)

Download references


We are grateful to the Editor and reviewers of this article for their remarks, comments and patience, contributing to the considerable improvement of our work. This work was supported by RFBR grant 09-05-00426-a.

Author information



Corresponding author

Correspondence to L. A. Maslov.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Avsyuk, Y.N., Maslov, L.A. Long Period Tidal Force Variations and Regularities in Orbital Motion of the Earth-Moon Binary Planet System. Earth Moon Planets 108, 77 (2011).

Download citation


  • Earth
  • Moon
  • Sea level tides
  • Seismicity
  • Tidal force
  • Baricenter
  • Binary planet system