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New model of precession, valid in time interval 400 thousand years. (English) Zbl 1313.70009

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 2–5, 2012. In honor of the 60th birthday of Michal Křížek. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-60-8/pbk). 290-299 (2012).
Under the influence of the gravitational field of the Sun and the Moon, the axis of rotation of the Earth exhibits a complicated motion which is called precession-nutation. Precession is the long periodic part of this motion, with period around 26 thousands years. At present, a model based on polynomial expansions in time is used by IAU. This model has high accuracy in an interval of a few centuries around a reference point J2000.0 but quickly deviates from reality outside this interval.
In the present proceeding contribution, the author briefly summarizes his results on a model of precession valid on the scale of several thousand centuries published elsewhere. This approach is based on using very long period terms fitted to a numerical integration of the problem. The accuracy of various models is also compared. The presented new model has similar accuracy as the IAU model in the interval of a couple of centuries around J2000.0. However, it is much more accurate for larger intervals, with reasonable accuracy in the interval \(\pm\) 200 thousands years around J2000.0.
For the entire collection see [Zbl 1277.00031].

MSC:

70F15 Celestial mechanics
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65L70 Error bounds for numerical methods for ordinary differential equations
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