Skip to main content
Log in

Quantification of tidal parameters from Solar System data

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

Tidal dissipation is the main driver of orbital evolution of natural satellites and a key point to understand the exoplanetary system configurations. Despite its importance, its quantification from observations still remains difficult for most objects of our own Solar System. In this work, we overview the method that has been used to determine, directly from observations, the tidal parameters, with emphasis on the Love number \(k_2\) and the tidal quality factor Q. Up-to-date values of these tidal parameters are summarized. Last, an assessment on the possible determination of the tidal ratio \(k_2/Q\) of Uranus and Neptune is done. This may be particularly relevant for coming astrometric campaigns and future space missions focused on these systems.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Archinal, B.A., et al.: Report of the IAU working group on cartographic coordinates and rotational elements: 2009. Celest. Mech. Dyn. Astron. 109, 101–135 (2011)

    Article  ADS  MATH  Google Scholar 

  • Arlot, J.-E., Emelyanov, N.V.: The NSDB natural satellites astrometric database. Astron. Astrophys. 503, 631–638 (2009)

    Article  ADS  Google Scholar 

  • Crida, A., Charnoz, S.: Formation of regular satellites from ancient massive rings in the solar system. Science 338, 1196 (2012)

    Article  ADS  Google Scholar 

  • Cuk, M.: Recent Origin of Titan’s Orbital Eccentricity. American Astronomical Society, DDA meeting vol. 45, p. 301.01 (2014)

  • Gavrilov, S.V., Zharkov, V.N.: Love numbers of the giant planets. Icarus 32, 443–449 (1977)

    Article  ADS  Google Scholar 

  • Goldreich, P., Soter, S.: Q in the solar system. Icarus 5, 375–389 (1966)

    Article  ADS  Google Scholar 

  • Iess, L., et al.: The tides of Titan. Science 337, 457–459 (2012)

    Article  ADS  Google Scholar 

  • Jacobson, R.A.: The orbits of the Neptunian satellites and the orientation of the pole of Neptune. Astron. J. 137, 4322–4329 (2009)

    Article  ADS  Google Scholar 

  • Jacobson, R.A., Lainey, V.: Martian satellite orbits and ephemerides. Planet. Space Sci. 102, 35–44 (2014)

    Article  ADS  Google Scholar 

  • Konopliv, A.S., Yoder, C.F.: Venusian \(k_2\) tidal Love number from Magellan and PVO tracking data. Geophys. Res. Lett. 23, 1857–1860 (1996)

    Article  ADS  Google Scholar 

  • Konopliv, A.S., et al.: Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters. Icarus 211, 401–428 (2011)

    Article  ADS  Google Scholar 

  • Konopliv, A.S., et al.: The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission. J. Geophys. Res. (Planets) 118, 1415–1434 (2013)

    Article  ADS  Google Scholar 

  • Lainey, V.: A new dynamical model for the Uranian satellites. Planet. Space Sci. 56, 1766–1772 (2008)

    Article  ADS  Google Scholar 

  • Lainey, V., Tobie, G.: New constraints on Io’s and Jupiter’s tidal dissipation. Icarus 179, 485–489 (2005)

    Article  ADS  Google Scholar 

  • Lainey, V., et al.: Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature 459, 957–959 (2009)

    Article  ADS  Google Scholar 

  • Lainey, V., et al.: New constraints on Saturn’s interior from Cassini astrometric data (2015). arXiv:1510.05870

  • Lemoine, F.G., et al.: High-degree gravity models from GRAIL primary mission data. J. Geophys. Res. (Planets) 118, 1676–1698 (2013)

    Article  ADS  Google Scholar 

  • Love, A.E.H.: Some Problems of Geodynamics. Cambridge University Press, Cambridge (1911)

    MATH  Google Scholar 

  • Matson, D.L., et al.: Heat flow from Io. J. Geophys. Res. 86, 1664–1672 (1981)

    Article  ADS  Google Scholar 

  • Mazarico, E., et al.: The gravity field, orientation, and ephemeris of Mercury from MESSENGER observations after three years in orbit. J. Geophys. Res. (Planets) 119, 2417 (2014)

    Article  ADS  Google Scholar 

  • Moyer, T.D.: Mathematical formulation of the double-precision orbit determination program (DPDOP). Technical report 32-1527, National Aeronautics and Space Administration (1971)

  • Moyer, T.D.: Formulation for Observed and Computed Values of Deep Space Network Observables, p. 576. Wiley, Hoboken (2003)

    Book  Google Scholar 

  • Pavlis, D.E., et al.: GEODYN II System Description, vol. 1–5, Contractor Report. SGT Inc., Greenbelt, MD (2013)

  • Peters, C.F.: Numerical integration of the satellites of the outer planets. Astron. Astrophys. 104, 37–41 (1981)

    ADS  MathSciNet  MATH  Google Scholar 

  • Petit, G., Luzum, B.: IERS conventions. IERS Technical Note No. 36 (2010)

  • Ray, R.D., et al.: Detection of tidal dissipation in the solid Earth by satellite tracking and altimetry. Nature 381, 595–597 (1996)

    Article  ADS  Google Scholar 

  • Ray, R.D., et al.: Constraints on energy dissipation in the Earth’s body tide from satellite tracking and altimetry. Geophys. J. Int. 144, 471–480 (2001)

    Article  ADS  Google Scholar 

  • Robert, V., et al.: A new astrometric reduction of photographic plates using the DAMIAN digitizer: improving the dynamics of the Jovian system. Mon. Not. R. Astron. Soc. 415, 701–708 (2011)

    Article  ADS  Google Scholar 

  • Robert, V., et al.: A new astrometric measurement and reduction of USNO photographic observations of Phobos and Deimos: 1967–1997. Astron. Astrophys. 582, A36 (2015)

    Article  ADS  Google Scholar 

  • Sharpless, B.P.: Secular accelerations in the longitudes of the satellites of Mars. Astron. J. 51, 185–186 (1945)

    Article  ADS  Google Scholar 

  • Spencer, J.R., et al.: Cassini encounters Enceladus: background and the discovery of a south polar hot spot. Science 311, 1401–1405 (2006)

    Article  ADS  Google Scholar 

  • Veiga, C.H., et al.: Positions of Uranus and its main satellites. Astron. J. 125, 2714–2720 (2003)

    Article  ADS  Google Scholar 

  • Wahr, J.M.: Body tides on an elliptical, rotating, elastic and oceanless earth. Geophys. J. R. Astron. Soc. 64, 677–703 (1981)

    Article  ADS  MATH  Google Scholar 

  • Williams, J.G., et al.: Lunar interior properties from the GRAIL mission. J. Geophys. Res. (Planets) 119, 1546–1578 (2014)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

V. L. is grateful to P. Rosenblatt, J. C. Marty and B. Noyelles for fruitful discussions. This work has been supported by the International Space Science Institute (ISSI), the Scientific Council of the Paris Observatory and the PNP (INSU/CNES).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Valéry Lainey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lainey, V. Quantification of tidal parameters from Solar System data. Celest Mech Dyn Astr 126, 145–156 (2016). https://doi.org/10.1007/s10569-016-9695-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-016-9695-y

Keywords

Navigation