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)

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.