The gravitational effect of bodies with variable density

Pick, Miloš; Šimon, Z.

doi:10.1007/bf01642991

Cited by 3 publications

(2 citation statements)

References 1 publication

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“…The traditional orbit analysis of gravity uses a spherical harmonic formalism, such as that developed by Kaula [1966]. However, alternative direct analytical techniques have been in use for many years [e.g., Pick , 1984; Tenzer et al , 2007]. An independently derived analytic method for a spherical, axisymmteric surface cap has been modeled into the JPL MIRAGE software [ Guinn et al , 1994] to calculate the gravitational force acting on the two spacecraft following a formulation described by Sunseri [2010].…”

Section: Global Mascon and Gps Trendsmentioning

confidence: 99%

On-land ice loss and glacial isostatic adjustment at the Drake Passage: 2003–2009

Ivins¹,

Watkins²,

Yuan³

et al. 2011

J. Geophys. Res.

116

117

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Land glacier extent and volume at the northern and southern margins of the Drake Passage have been in a state of dramatic demise since the early 1990s. Here time‐varying space gravity observations from the Gravity Recovery and Climate Experiment (GRACE) are combined with Global Positioning System (GPS) bedrock uplift data to simultaneously solve for ice loss and for solid Earth glacial isostatic adjustment (GIA) to Little Ice Age (LIA) cryospheric loading. The present‐day ice loss rates are determined to be −26 ± 6 Gt/yr and −41.5 ± 9 Gt/yr in the Southern and Northern Patagonia Ice Fields (NPI+SPI) and Antarctic Peninsula (AP), respectively. These are consistent with estimates based upon thickness and flux changes. Bounds are recovered for elastic lithosphere thicknesses of 35 ≤ h ≤ 70 km and 20 ≤ h ≤ 45 km and for upper mantle viscosities of 4–8 × 1018 Pa s and 3–10 × 1019 Pa s (using a half‐space approximation) for NPI+SPI and AP, respectively, using an iterative forward model strategy. Antarctic Peninsula ice models with a prolonged LIA, extending to A.D. 1930, are favored in all χ2 fits to the GPS uplift data. This result is largely decoupled from Earth structure assumptions. The GIA corrections account for roughly 20–60% of the space‐determined secular gravity change. Collectively, the on‐land ice losses correspond to volume increases of the oceans equivalent to 0.19 ± 0.045 mm/yr of sea level rise for the last 15 years.

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Section: Global Mascon and Gps Trendsmentioning

confidence: 99%

On-land ice loss and glacial isostatic adjustment at the Drake Passage: 2003–2009

Ivins¹,

Watkins²,

Yuan³

et al. 2011

J. Geophys. Res.

116

117

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“…For the gravitational field modelling of inhomogeneous density formations, the approximation of geological structures by more general geometrical forms are often implemented. Pick (1984) summarized the expressions for computing the gravitation of various geometrical bodies. Hurbbert (1948) introduced a methodology called the line-integral approach.…”

Section: Introductionmentioning

confidence: 99%

Application of Möbius coordinate transformation in evaluating Newton's integral

Tenzer

Gladkikh

2011

Contributions to Geophysics and Geodesy

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Application of Möbius coordinate transformation in evaluating Newton's integralWe propose a numerical scheme which efficiently combines various existing methods of solving the Newton's volume integral. It utilises the analytical solution of Newton's integral for tesseroid in computing the near-zone contribution to gravitational field quantities (potential and its first radial derivative). The far-zone gravitational contribution is computed using the expressions derived based on applying Molodensky's truncation coefficients to a spectral representation of Newton's integral. The weak singularity of Newton's integral is treated analytically using formulas for the gravitational contribution of the cylindrical mass volume centered with respect to the observation point. All three solutions are defined and evaluated in the system of polar spherical coordinates. A conversion of the geographical to polar spherical coordinates of input data sets (digital terrain and density models) is based on the Möbius transformation with an enhanced integration grid resolution at vicinity of the observation point.

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Analytical Solution of Newton’s Integral in Terms of Polar Spherical Coordinates

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The gravitational effect of bodies with variable density

Cited by 3 publications

References 1 publication

On-land ice loss and glacial isostatic adjustment at the Drake Passage: 2003–2009

On-land ice loss and glacial isostatic adjustment at the Drake Passage: 2003–2009

Application of Möbius coordinate transformation in evaluating Newton's integral

Analytical Solution of Newton’s Integral in Terms of Polar Spherical Coordinates

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