Corrections to “A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling” (Heck and Seitz, 2007) and “Optimized formulas for the gravitational field of a tesseroid” (Grombein et al., 2013)

Xiao-Le Deng,Kurt Seitz,Thomas Grombein,Wen-Bin Shen,Bernhard Heck

doi:10.1007/s00190-016-0907-8

Abstract

1 Summary A second-order approximation of the tesseroid method has been presented in the paper “A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling” (Heck and Seitz 2007) for the gravitational potential and its first radial derivative. In the paper “Optimizedformulasforthegravitationalfieldofatesseroid” (Grombein et al. 2013) this analytical approach was optimized and extended to all first- and second-order derivatives of the potential. In both papers the general expression of the Taylor series expansion contains a formal error and needs to be corrected. As will be shown, this correction or rather erratum has no impact on the published and widely used second-order tesseroid formulas.

Highlights

In both papers the general expression of the Taylor series expansion contains a formal error and needs to be corrected
The disadvantage of the tesseroid method is that no analytical solutions of the respective mass integrals exist
Heck and Seitz (2007) presented an approximation approach for calculating the gravitational potential and its first radial derivative of a spherical tesseroid based on Taylor expansion (see Eqs. (21)–(23) and (32)–(33))

Summary

Introduction

In both papers the general expression of the Taylor series expansion contains a formal error and needs to be corrected. Heck and Seitz (2007) presented an approximation approach for calculating the gravitational potential and its first radial derivative of a spherical tesseroid based on Taylor expansion The Taylor expansion of the integral kernel

Results

Conclusion