Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Ardalan, Alireza A.; Karimi, Roohollah

doi:10.1007/s10569-013-9523-6

Cited by 7 publications

(2 citation statements)

References 40 publications

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“…Numerical values of the first five parameters are listed in Table 1. The semi-major and semi-minor axes a 0 and b 0 define the best-fitting oblate spheroids (Ardalan and Karimi, 2014;Preusker et al, 2016).…”

Section: Gravitational Field Of a Homogeneous Spheroidal Shellmentioning

confidence: 99%

Spheroidal forward modelling of the gravitational fields of 1 Ceres and the Moon

Šprlák

Han

Featherstone

2020

Icarus

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A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectrum from the volumetric bulk density and geometry of a gravitating body. We discretise the volume integral and formulate a new and efficient numerical algorithm for the spheroidal forward modelling. We provide complete sets of recursions for calculating the associated Legendre functions of the first kind and their integrals in the Supplementary Material. We also develop a computer program that implements the numerical algorithm and we test its performance. For this purpose, we consider synthetic gravitational fields of 1 Ceres (a significantly flattened asteroid) and of the Moon (a nearly spherical body). These tests prove high numerical accuracy and applicability of the spheroidal forward modelling up to degree and order 2519. We finally apply our spheroidal forward modelling and its simpler spherical counterpart for computing global gravitational field models up to degree and order 2519 generated by realistic topographic mass distributions of 1 Ceres and of the Moon. These models are compared in the spatial and spectral domains to manifest an enhanced applicability of the spheroidal approach with respect to the spherical one. In particular, we show an extended convergence space when using the spheroidal forward modelling and the corresponding harmonic representation for the oblate 1 Ceres.

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Section: Gravitational Field Of a Homogeneous Spheroidal Shellmentioning

confidence: 99%

Spheroidal forward modelling of the gravitational fields of 1 Ceres and the Moon

Šprlák

Han

Featherstone

2020

Icarus

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“…Throughout these numerical experiments, the normal gravitational field of the Moon was generated by an equipotential spheroid. It is defined by four parameters: the major semi-axis a = 1737325.0 m, the minor semi-axis b = 1736789.0 m, the planetocentric gravitational constant GM = 4902.8×10 9 m 3 s −2 , and the angular velocity ω = 2.6617×10 −6 rad s −1 as determined by Ardalan and Karimi (2014).…”

Section: Numerical Experimentsmentioning

confidence: 99%

Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field

Šprlák

Han

Featherstone

2020

Advances in Space Research

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We present an integral-based approach for high-resolution regional recovery of the gravitational field in this article. We derive rigorous remove-compute-restore integral estimators relating the line-of-sight gravitational acceleration to an arbitrary order radial derivative of the gravitational potential. The integral estimators are composed of three terms, i.e., the truncated integration, the low-frequency line-of-sight gravitational acceleration, and the high-frequency truncation error (effect of the distant zones). We test the accuracy of the integral transformations and of the integral estimators in a closed-loop simulation over the Montes Jura region on the nearside of the Moon. In this way, we determine optimal sizes of integration radii and grid discretisation. In addition, we investigate the performance of the regional integral inversion with synthetic and realistic GRAIL observations. We demonstrate that the regional inversion results of the disturbing gravitational potential and its first order radial derivative in the Montes Jura mountain range are less contaminated by high-frequency noise than the global spherical harmonic models.

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Definition of Physical Height Systems for Telluric Planets and Moons

et al. 2018

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Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Cited by 7 publications

References 40 publications

Spheroidal forward modelling of the gravitational fields of 1 Ceres and the Moon

Spheroidal forward modelling of the gravitational fields of 1 Ceres and the Moon

Integral inversion of GRAIL inter-satellite gravitational accelerations for regional recovery of the lunar gravitational field

Definition of Physical Height Systems for Telluric Planets and Moons

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