Celestial Mechanics and Dynamical Astronomy

, Volume 123, Issue 3, pp 263–277

Mercury’s resonant rotation from secular orbital elements

Original Article

DOI: 10.1007/s10569-015-9633-4

Cite this article as:
Stark, A., Oberst, J. & Hussmann, H. Celest Mech Dyn Astr (2015) 123: 263. doi:10.1007/s10569-015-9633-4

Abstract

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.

Keywords

Mercury Spin-orbit coupling Laplace plane MESSENGER Ephemeris Secular elements 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

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