Consistent post-Newtonian theory for nutation/precession in a realistic Earth model

• Applicant: Professor Dr. Michael H. Soffel
• Subject Area: Geophysics and Geodesy
• Term: from 2006 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5471782

• Final Report Year: 2015

Final Report Abstract

The objective of project P3 was to establish a consistent post-Newtonian theory for precession and nutation with an accuracy level of 1 µas for a realistic Earth model. In the first 3 years of the funding period our model of rigidly rotating multipoles was developed. We could demonstrate that our numerical model can reproduce one of the best models of rigid Earth rotation, in the Newtonian limit within the full accuracy of the latter. Further, effects from the post-Newtonian contributions to the torque have been studied in detail. It was shown, that such effects on nutation generally are very small: the main effect is a correction to the 18.6 year nutation term with an amplitude of 0.6 µas in longitude and obliquity. Also effects from geodetic precession/nutation have been derived numerically in detail. Differences to values that have been published before by other authors have been worked out and explained by an inconsistent treatment in other papers. Therefore, within the first funding period we were able to finalize the best currently available theory of rigid Earth rotation, that is able to handle correctly all important relativistic effects. In the second funding phase our model was extended towards a realistic Earth. To reach this ambitious objective we had to check the consistency and the correct relativistic interpretation of various quantities. Furthermore we could extend our numerical Earth model, which is now able to treat all relevant effects in a consistent manner. In detail this meant the extension of the Earth into different layers and the inclusion of data coming from the various sub-systems (atmosphere, ocean and continental hydrology) of the Earth. A parameter fit of the whole model to the latest IAU precession/nutation theory was done. The results obtained up to this point represent a considerable step to a complete numerical modeling of Earth rotation. The findings of the project can and will be used to improve further investigations into this direction. In addition to the planned working packages we could derive a complete relativistic model for the observations of large ring laser gyroscopes. The findings of this work provided important input also to other projects within the research unit.

Publications

• (2009): Consistent modelling of the geodetic precession in Earth rotation, VII Hotine-Marussi Symposium, Rome 6-10 July 2009, IAG Series, Springer, Vol. 137
  Gerlach, E., Klioner, S., Soffel, M.
  
• (2009): Relativistic aspects of rotational motion of celestial bodies. In: Relativity in Fundamental Astronomy, Proc. of the IAU Symposium 261, S. Klioner, K. Seidelmann, M. Soffel (eds.) Cambridge University Press, Cambridge
  Klioner, S.A., Gerlach, E., Soffel, M.
  
• (2010): About the MacCullagh Relations in Relativity, In: New Challenges for reference systems and numerical standards in astronomy, N. Capitaine (ed.), Proc. of Les Journées 2010, Paris, 255-257
  Soffel, M.H., Klioner, S.A., Gerlach, E.
  
• (2011): Relativity and Large Ring-Laser Gyroscopes, In: Earth rotation, reference systems, and celestial mechanics: Synergies of geodesy and astronomy, N. Capitaine (ed.), Proc. of Les Journées 2011, Paris, 35-37
  Soffel, M., Tian, W.
  
• (2014): On tidal tilt corrections to large ring laser gyroscope observations, Geophysical Journal International, Vol. 196
  Tian, W.
  (See online at https://doi.org/10.1093/gji/ggt415)