Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

The exterior gravitation of a constant-density polyhedron is derived analytically in closed form. Expressions for potential, attraction, and gravity gradient matrix involve one logarithm term per edge and one arctangent term per face, The Laplacian can be used to determine whether a field point is inside or outside the polyhedron, This polyhedral method is well suited to evaluating the gravitational field of an irregularly shaped body such as an asteroid or comet, Conventional harmonic and mascon potential and attraction expressions suffer large errors when evaluated close to a polyhedral model of asteroid 4769 Castalia.