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3 Artificial Satellites : Journal of Planetary Geodesy

3 Eshagh M.

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From tensor to vector of gravitation

100%

Eshagh M.

tom Vol. 49, No. 2

63--80

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.

The effect of polar gaps on the solutions of gradiometric boundary value problems

100%

Eshagh M.

Artificial Satellites : Journal of Planetary Geodesy

2008

tom Vol. 43, No. 3

97--108

The lack of satellite gravity gradiometric data, due to inclined orbit, in the Polar Regions influences the geopotential coefficients obtained from the solutions of gradiometric boundary value problems. This paper investigates the polar gaps effect on these solutions and it presents that the near zero-, first- and second-order geopotential coefficients are weakly determined by the vertical-vertical, vertical-horizontal and horizontal solutions, respectively. Also it shows that the vertical-horizontal solution is more sensitive to the lack of data than the other solutions.

Spatially restricted integrals in gradiometric boundary value problemsSpatially restricted integrals in gradiometric boundary value problems

75%

Eshagh M.

Artificial Satellites : Journal of Planetary Geodesy

2009

tom Vol. 44, No. 4

131--148

The spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth’s gravity field locally from the satellite gravity gradiometry data.