Effective calculation of gravity effects of uniform triangle polyhedra

Uniform tetrahedra are commonly used elementary bodies for gravity calculations from which arbitrary polyhedra can be composed. A simple derivation of the gravity effect is presented for the apex P of the tetrahedron expanded from P to an arbitrarily oriented plane triangle. Integration of its potential effect in a rotated coordinate system applies vector algebra and renders the anomalous potential depending on the distance of P over the triangle plain and a function of the triangle coordinates. Partial differentiation by moving P infinitesimally in z-direction leads to two terms, a simple and a complex one; they can be understood as describing the same difference from two points of view: leaving P at the apex of the changed polyhedron or moving P off the unchanged polyhedron. Both views imply the same shape change and the sum over the polyhedron is thus numerically equal. Hence we need to calculate only the one of the terms of the differential which is simpler. The calculation of the gravity effect is numerically simplified and more stable. This has been tested for many models and is demonstrated by two examples.