Simplification of Geopotential Perturbing Force Acting on A Satellite

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

doi:10.2478/v10018-009-0006-7

Cited by 7 publications

(3 citation statements)

References 9 publications

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“…We simulated a three-month orbit of GOCE using the strategy used by Eshagh et al (2009) with an orbit integration step size of 5 s corresponding to a spatial resolution of 38.5 km. GOCE is flying over Fennoscandia with maximum and minimum altitude of 256 km and 231 km, respectively.…”

Section: Recovery From On-orbit T Rrmentioning

confidence: 99%

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

Eshagh

2011

Advances in Space Research

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Section: Recovery From On-orbit T Rrmentioning

confidence: 99%

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

Eshagh

2011

Advances in Space Research

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“…In the paper of Eshagh et al (2009), non-singular expressions are constructed for the geopotential derivatives of the first order in the quasi-inertial reference frame. It is possible to transform these expressions to TRF.…”

Section: First-order Derivativesmentioning

confidence: 99%

Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

Petrovskaya

Vershkov

2011

J Geod

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This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84 (3): [165][166][167][168][169][170][171][172][173][174][175][176][177][178] 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients C n,m and S n,m . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first-and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first-and second-order derivatives in terms of the geopotential coefficients. These equations are M. S. Petrovskaya (B) · A. N. Vershkov Central (Pulkovo) Astronomical Observatory of the Russian Academy of Sciences, converted into recurrent relations from which the coefficients C n,m and S n,m are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission.Keywords Terrestrial reference frame · Gravitational gradients of the first and second orders · Transformation of the gradients into geopotential models

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“…Su (2000), Wolf (2000), Eshagh (2003Eshagh ( , 2005Eshagh ( , 2009a, Najafi-Alamdari (2006 and2007) and Somodi and Földvary (2011). Eshagh et al (2009) simplified the mathematical formulae of equations of motion of satellites and applied them for a study on the orbit integration of GOCE, the gravity field recovery and climate experiment (GRACE) (Tapley et al 2005) and the Challenging Minisatellite Payload (CHAMP) (Reigber et al 1999 and missions. In all methods for orbit determination, the acceleration of the satellite should be computed before the integration process using the force models.…”

Section: Introductionmentioning

confidence: 99%

From Tensor to Vector of Gravitation

Eshagh

2014

Artificial Satellites

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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.

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Simplification of Geopotential Perturbing Force Acting on A Satellite

Cited by 7 publications

References 9 publications

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

Inversion of satellite gradiometry data using statistically modified integral formulas for local gravity field recovery

Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame

From Tensor to Vector of Gravitation

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