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1

From tensor to vector of gravitation

Eshagh M.

Artificial Satellites : Journal of Planetary Geodesy

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2014

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Vol. 49, No. 2

63--80

EN

Different gravitational force models are used for determining the satellites’ orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except Txy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from Tzz, Txz and Tyz and those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering Ty from Tyz. Larger cap sizes than 5 on is recommended for recovering Tx and Tz but smaller ones for Ty.

2

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.

3

Spectral analysis of the selected accelerations and orbital elements for the GOCE satellite orbit

Bobojć A.

Artificial Satellites : Journal of Planetary Geodesy

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2008

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Vol. 43, No. 3

109--127

EN

The work contains the results of research of the simulated GOCE satellite orbit. For the 30-day orbit determination the Cowell numerical integration of the eighth order was used and the geopotential was described by means of the EGM96 model. The selected accelerations and the Keplerian elements were computed along this orbit. These accelerations included the satellite accelerations due to: the geopotential, the Earth tides and the ocean tides (the radial component for both), the gravitation of the Moon, the gravitation of the Sun, the gravitation of the Venus and the relativity effects. The computed accelerations and Keplerian elements were treated as the input data for the DFT algorithm (Discrete Fourier Transform) to determine their spectral characteristics, i.e. the amplitude power spectral densities (PSD). Additionally, the averages and standard deviations were obtained for the aforementioned accelerations and Keplerian elements. The numerous periodic components were identified. The characteristic resonances with the satellite orbital period, with the Earth’s rotation period and with the Moon’s synodic period were described.