  Computing gravity field of a mass body is a core routine to image anomalous
density structures in the Earth. In this study, we report the existence of
analytical routines to accurately compute the gravity potential and gravity
field of a general polyhedral mass body. The density contrasts in the
polyhedral body can be general polynomial functions up to arbitrary
non-negative orders and also can vary in both horizontal and vertical
directions. The newly derived analytical expressions of gravity fields are also
singularity-free which means that observation sites can have arbitrary
geometric relationships with polyhedral mass bodies. One synthetic prismatic
body with different density contrasts is used to verify the accuracies of our
new closed-form solutions. Excellent agreements are obtained among our
solutions and other published solutions. Our work is the first-of-its kind to
completely answer the fundamental question on existence of analytic solutions
of gravitational field for general mass bodies. It may put an end of searching
closed-form solutions in gravity surveying.
