Gravitational attraction of solids of revolution: Part 2: General expressions

A general integral expression is formulated for the gravitational attraction due to any solid of revolution based on the attraction of vertical, semi-infinite, circular, cylindrical shells. The expression accommodates solids with radial variation of density. For solids with constant density, further generalization to arbitrary orientation is made through coordinate transformation that considers both vertical and radial components of attraction. Special solutions for solids with simple geometry are listed. Practical applications are demonstrated by forward gravity modelling the effects of volcanic islands (cylindrical core bounded by an outer exponentially trending surface) and inclined finite-length cylinders. Corresponding expressions for the magnetic case are discussed in terms of using Poisson's relation.