Forecasting the disturbed polar motion of the Earth within a short time interval
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractModeling the fundamental components of the Earth’s rotation parameters for solving navigation problems.
Develop a few-parameters model for forecasting the movement trajectory of Earth's pole within short time intervals for some navigation problems.
Theoretical modeling of the vibrational-rotational motion of the deformable Earth, appropriate observations and measurements are carried out by using the approximate methods of nonlinear mechanics, combining with numerical experiment. Oscillating process described by model of the Earth's pole is based on the considering gravitational-tidal torques from the Sun and the Moon.
The numerical simulation for the model is made, providing a set of basic functions and the estimation of the unknown coefficients. The calculations were carried out by setting up the filtering algorithm of the International Earth Rotation and Reference Systems Service's (IERS) data observations with the least squares method. The length of interpolation's interval, or in the other words the number of the measurements processed, depends on the total estimation’s error for the given set of based functions in attempt to minimize the error.
Using the mathematical model of the Earth's polar motion, which is constructed by applying celestial mechanics’ methods, an interpolation and forecast of the trajectory of the Earth’s pole are obtained. Intervals of interpolation vary between 30 and 60 days and forecast based on such interpolations is made for short time intervals, from 15 to 40 days. The comparison between the constructed model for different time intervals and the IERS-provided observations is made. The value of the standard deviation of the theoretical curve from the experimental one, obtained by using IERS data observations during the respective time intervals of the filtering algorithm, the interval settings, proves the sufficient accuracy of the constructed model. When being placed into the real environment with the up-to-date IERS observations’ data the higher accuracy for the short-term forecast is achieved by taking into an account structural properties of the few-parameters model. One of the main perspective applications of the mathematical models of the Earth’s motion is to improve the orbital-rotating parameters of a flyby because for the modern the space technology and telecommunication systems the accuracy of the coordinate-time support is of a great importance.
The forecast of the fundamental components of Earth’s rotation parameters at a short time interval (up to 40 days) allows much more accurate estimation of the parameters of the satellite's orbit, which in turn provides a significant increase of the accuracy of the forecast of satellites’ ephemeris calculated for the following days.
Keywords:fluctuation, earth’s pole, alteration of latitude, prediction, gravitation tide
- IERS Frankfurt am Mein, 2010,Technical Note no. 36, ftp://hpiers.obspm.fr/eop-pc/eop/eopc04/.
- Munk W., Makdonald G. Vrashhenie Zemli (The Rotation of the Earth), Moscow, Mir, 1964, 384 p.
- Moritz H., Mueller A. Vrashhenie Zemli: teorija i nabljudenija (Earth rotation: Theory and Observation), Kiev, Naukova dumka, 1992, 512 p.
- Akulenko L.D., Kumakshev S.A., Markov Ju.G., Ryhlova L.V. Astronomicheskij zhurnal, 2002, vol. 79, no. 10, pp. 952 – 960.
- Akulenko L.D., Kumakshev S.A., Markov Ju.G., Ryhlova L.V. Astronomicheskij zhurnal, 2006, vol. 83, no. 4, pp. 376 – 384.
- Akulenko L.D., Klimov D.M., Markov Ju.G. Pokuchaev V.N. Kosmonavtika i raketostroenie, 2012, vol. 4, pp. 100-107.
- Akulenko L.D., Markov Ju.G., Perepelkin V.V. Doklady akademii nauk, 2009, vol. 425, no 2, pp. 1-6.
- Gubanov V.S. Obobshhennyj metod naimen'shih kvadratov: Teorija i primenenie v astrometrii (Generalized least squares method: Theory and application in astronomy), St. Petersburg, Nauka, 1997, 318 p.