The exact transformation from spherical harmonic to ellipsoidal harmonic coefficients for gravitational field modeling

2016 ◽  
Vol 125 (2) ◽  
pp. 195-222 ◽  
Author(s):  
Xuanyu Hu
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonic ◽  
Field Modeling ◽  
Ellipsoidal Harmonic

scholarly journals An oceanographer’s guide to GOCE and the geoid

2006 ◽  
Vol 3 (5) ◽  
pp. 1543-1568 ◽  
Author(s):  
C. W. Hughes ◽  
R. J. Bingham
Keyword(s):  
Gravitational Field ◽  
Measurement System ◽  
Spherical Harmonic ◽  
Gravity Data ◽  
Reference Ellipsoid ◽  
Satellite Mission ◽  
Satellite Gravity ◽  
Ocean Models ◽  
Goce Satellite ◽  
The Way

Abstract. A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. The usual spherical harmonic description of the gravitational field is described, together with the concepts required to calculate a geoid from the spherical harmonic coefficients. A brief description is given of the measurement system in the GOCE satellite mission, scheduled for launch shortly, followed by a description of a reference ellipsoid with respect to which the geoid may be calculated. Finally, a recipe is given for calculation of the geoid relative to any chosen ellipsoid, given a set of spherical harmonic coefficients and defining constants.

scholarly journals A solution of Jupiter’s gravitational field from Juno data with the orbit14 software

2019 ◽  
Vol 490 (1) ◽  
pp. 766-772 ◽  
Author(s):  
Daniele Serra ◽  
Giacomo Lari ◽  
Giacomo Tommei ◽  
Daniele Durante ◽  
Luis Gomez Casajus ◽  
...  
Keyword(s):  
Gravitational Field ◽  
Orbit Determination ◽  
Spherical Harmonic ◽  
Real Data ◽  
Jet Propulsion ◽  
Doppler Data ◽  
The University ◽  
First Time ◽  
Alternative Set ◽  
Juno Mission

ABSTRACT The latest estimation of Jupiter’s gravitational field was obtained by processing the Doppler data from two gravity orbits of NASA’s Juno mission, using the Jet Propulsion Laboratory software monte. In this work, we present the results of the analysis of the same measurements employing the orbit determination software orbit14, developed at the University of Pisa, used here for the first time with real data. We found that the estimated values of Jupiter’s spherical harmonic coefficients from the two solutions are consistent within the formal uncertainty. The analysis is complemented with a discussion on the results obtained with alternative set-ups.

scholarly journals An Oceanographer's Guide to GOCE and the Geoid

Ocean Science ◽  
2008 ◽  
Vol 4 (1) ◽  
pp. 15-29 ◽  
Author(s):  
C. W. Hughes ◽  
R. J. Bingham
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonic ◽  
Gravity Data ◽  
Reference Ellipsoid ◽  
Sea Surface ◽  
Dynamic Topography ◽  
Satellite Mission ◽  
Satellite Gravity ◽  
Ocean Models ◽  
Goce Satellite

Abstract. A review is given of the geodetic concepts necessary for oceanographers to make use of satellite gravity data to define the geoid, and to interpret the resulting product. The geoid is defined, with particular attention to subtleties related to the representation of the permanent tide, and the way in which the geoid is represented in ocean models. The usual spherical harmonic description of the gravitational field is described, together with the concepts required to calculate a geoid from the spherical harmonic coefficients. A brief description is given of the measurement system in the GOCE satellite mission, scheduled for launch shortly. Finally, a recipe is given for calculation of the ocean dynamic topography, given a map of sea surface height above a reference ellipsoid, a set of spherical harmonic coefficients for the gravitational field, and defining constants.

scholarly journals Regularized collocation for spherical harmonics gravitational field modeling

2013 ◽  
Vol 5 (1) ◽  
pp. 81-98 ◽  
Author(s):  
Valeriya Naumova ◽  
Sergei V. Pereverzyev ◽  
Pavlo Tkachenko
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonics ◽  
Field Modeling

scholarly journals The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast

2010 ◽  
Vol 40 (3) ◽  
pp. 207-223 ◽  
Author(s):  
Robert Tenzer ◽  
Ahmed Abdalla ◽  
Peter Vajda ◽  
Keyword(s):  
Gravitational Field ◽  
Lower Bound ◽  
Spherical Harmonic ◽  
Mean Value ◽  
Density Contrast ◽  
Constant Density ◽  
Height Functions ◽  
Elevation Data ◽  
Elevation Model ◽  
Harmonic Representation

The spherical harmonic representation of the gravitational field quantities generated by the ice density contrastWe derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice functions combined with the spherical height functions describe the global thickness of the continental ice sheet. The newly derived formulas are utilized in the forward modelling of the gravitational field quantities generated by the ice density contrast. The 30×30 arc-sec global elevation data from GTOPO30 are used to generate the global elevation model (GEM) coefficients. The spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness data from the CRUST 2.0 global crustal model are used to generate the global lower-bound ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m3(i.e., difference of the reference constant density of the continental upper crust 2670 kg/m3and the density of glacial ice 917 kg/m3) is adopted. The numerical examples are given for the gravitational potential and attraction generated by the ice density contrast computed globally with a low-degree spectral resolution complete to degree and order 90 of the GEM and GIM coefficients.

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