Celestial Mechanics and Dynamical Astronomy

, Volume 123, Issue 3, pp 263–277 | Cite as

Mercury’s resonant rotation from secular orbital elements

  • Alexander StarkEmail author
  • Jürgen Oberst
  • Hauke Hussmann
Original Article


We used recently produced Solar System ephemerides, which incorporate 2 years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncertainties. As Mercury is in a stable 3:2 spin-orbit resonance, these values constitute an important reference for the planet’s measured rotational parameters, which in turn strongly bear on physical interpretation of Mercury’s interior structure. In particular, we derive a mean orbital period of \((87.96934962 \pm 0.00000037)\,\hbox {days}\) and (assuming a perfect resonance) a spin rate of \((6.138506839\pm 0.000000028){}^{\circ }/\hbox {day}\). The difference between this rotation rate and the currently adopted rotation rate (Archinal et al. in Celest Mech Dyn Astron 109(2):101–135, 2011. doi: 10.1007/s10569-010-9320-4), corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet, when derived from observations of Mercury’s rotation.


Mercury Spin-orbit coupling Laplace plane MESSENGER Ephemeris Secular elements 



The authors thank Jean-Luc Margot, Benoît Noyelles, Stanton J. Peale, and Marie Yseboodt for fruitful discussions, and we also thank William M. Folkner and Charles H. Acton for providing information on the DE432 ephemeris. The reviews by two anonymous reviewers significantly improved earlier versions of this manuscript. J.O. greatly acknowledges being hosted by MIIGAiK and supported by the Russian Science Foundation under project 14-22-00197.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Alexander Stark
    • 1
    Email author
  • Jürgen Oberst
    • 1
    • 2
  • Hauke Hussmann
    • 1
  1. 1.DLR, Institute of Planetary ResearchBerlinGermany
  2. 2.Moscow State University for Geodesy and CartographyMoscowRussia

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