Numerical Computation of Gravitational Field for General Three-Dimensional Objects

We developed a method to compute the Newtonian gravitational field at an arbitrary point in the three-dimensional space for general three-dimensional objects of arbitrary size, shape, and density distribution. Adopting a spherical polar coordinate system centered at the evaluation point, we numerically evaluate a volume integral representation of the gravitational potential and/or the associated acceleration vector. The utilization of the integration variables with not the global but the local symmetry in spherical polar coordinates completely removes the inherent algebraic singularities of the integral expressions. As a result, the numerical comparison with a few exact solutions reveals around 15 digits accuracy of the integrated gravitational field. This accuracy is independent on the location of the evaluation point: inside, outside, on and near the boundary of a gravitating body. Thus, the new method will be a reliable tool to compute the gravitational field of general three-dimensional objects