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 a nalytically in closed form. Expressions for potential, attraction, and gravity gradient matrix involve one logarithm term per edge and one a rctangent term per face. The Laplacian can be used to determine whethe r a field point is inside or outside the polyhedron. This polyhedral m ethod is well suited to evaluating the gravitational field of an irreg ularly shaped body such as an asteroid or comet. Conventional harmonic and mascon potential and attraction expressions suffer large errors w hen evaluated close to a polyhedral model of asteroid 4769 Castalia.