Analytical solution of Newton's Integral in terms of polar spherical coordinates

Abstract

In association with precise modelling of the Earth's gravity field, analytical integration can be used as an alternative to numerical integration, particularly for the intermediate neighbourhood of the computation point. Accordingly, closed analytical formulae for the gravitational potential and attraction are derived after expressing Newton's integral in terms of polar spherical coordinates. As the elemental volume for the integration element is defined by finite changes of the polar spherical coordinates, the actual mass density distribution is discretized so that each integration element is represented by a constant value of density. © Springer-Verlag Berlin Heidelberg 2007.