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1

Selected Accelerations and Orbital Elements of the GOCE Satellite in the Time Domain

Bobojć A.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2009

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nr 12

104-117

EN

The work contains the results of the GOCE satellite orbit simulation. The GOCE satellite orbit was presented in the aspect of the temporary changes in selected accelerations and in selected keplerian elements. The satellite accelerations due to: the geopotential, the Earth tides and the ocean tides (the radial component for both), the gravitation of the Moon and the gravitation of the Sun, were presented in function of time. The showed changes in orbital elements include the semi-major axis, eccentricity, inclination, argument of perigee and right ascension of ascending node. For the orbit determination the Cowell numerical integration method of the eighth order was used. The geopotential was described by means of the EGM96 model. The mentioned temporary changes in the selected accelerations and orbital elements were described. Most of them contain the characteristic periodic components, which are close to the satellite orbital period, the Earth's rotation period and the Moon's synodic period.

PL

Praca zawiera wyniki symulacji orbity satelity GOCE. Orbitę satelity GOCE przedstawiono w aspekcie zmian czasowych wybranych przyśpieszeń i elementów keplerowskich. Przyśpieszenia satelity spowodowane przez: geopotencjał, pływy skorupy, pływy oceaniczne (składowa radialna dla obu), grawitację Słońca i grawitację Księżyca, przedstawiono w funkcji czasu. Pokazane zmiany w elementach orbity obejmują półoś wielką, mimośród, nachylenie, argument perygeum i rektascensję węzła wstępującego. Do wyznaczenia orbity użyto całkowania numerycznego metodą Cowella ósmego rzędu. Geopotencjał opisano modelem EGM96. Opisano wspomniane zmiany czasowe wybranych przyśpieszeń i elementów orbity. Większość z nich zawiera charakterystyczne składowe okresowe, które są zbliżone do okresu orbitalnego satelity, okresu rotacji Ziemi oraz okresu synodycznego Księżyca.

2

Simplification of geopotential perturbing force acting on a satellite

Eshagh M., Abdollahzadeh M., Najafi-Alamdari M.

Artificial Satellites : Journal of Planetary Geodesy

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2008

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Vol. 43, No. 2

45--64

EN

One of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with respect to the other perturbing forces. The equation of motion of satellites is a secondorder vector differential equation. These equations are further simplified and developed in this study based on the geopotential force. This new expression is much simpler than the traditional one as it does not derivatives of the associated Legendre functions and the transformations are included in the equations. The maximum degree and order of the geopotential harmonic expansion must be selected prior to the orbit integration purposes. The values of the maximum degree and order of these coefficients depend directly on the satellite’s altitude. In this article, behaviour of orbital elements of recent geopotential satellites, such as CHAMP, GRACE and GOCE is considered with respect to the different degree and order of geopotential coefficients. In this case, the maximum degree 116, 109 and 175 were derived for the Earth gravitational field in short arc orbit integration of the CHAMP, GRACE and GOCE, respectively considering millimeter level in perturbations.

3

On accuracy of current geopotential models estimated through comparison of quasi-geoid models and GPS/levelling data

Novak P., Kostelecky J., Klokocnik J.

Reports on Geodesy

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2006

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z. 1/76

245-251

EN

Gravity-dedicated satellite missions CHAMP and GRACE provide accurate data that can be inverted into geopotential coefficients forming global geopotential models (GGM). Through an estimation process, mean square errors of these coefficients can be elvaluated. In most cases, even the entire variance-covariance matrices are computed. However, these errors are only formaI and do not represent weIl the actual accuracy of estimated coefficients, thus also of various gravity field parameters synthesized from these coefficients. For this reason validation procedures for the new GGMs are being sought since the classical validation methocts reached their limits. This article discusses the validation procedure of the GGM through its comparison with idependent data estimated at selected GPS/leveIling stations over the area of Central Europe. Due to a different spectral content of height anomalies synthesized from the GGM and of those derived from combination of ellipsoidal and normal heights at selected points of the European Vertical Reference Network, the GGM-based low-frequency height anomaly is completed for a missing higth-frequency component based on high resolution and high accuracy ground gravity and elevation data. The methodology is also applied on a set of GPS/leveIling stations in the Czech Republic. In accordance with previous validation tests of GGMs based on data of crossover altimetry, obtained results indicate that the current GGMs estimated from single/dual-sateIlite data seem to have significant problems namely with low-order and degree coefficients.