Searching for the Center of Gravity in a Spherical Gravitational Field
Chris Rorres, University of Pennsylvania

Abstract:
The center of gravity of a body is most commonly defined as the intersection of its lines of suspension, a definition dating from antiquity. While these suspension lines all pass through a unique point in a uniform gravitational field, this is not the case in a nonuniform gravitational field. In this talk I show that for a spherically symmetric gravitational field the suspension lines determine certain "surfaces of gravity" that can be used to replace the concept of a center of gravity.  For example, the figure shows various surfaces of gravity of a one-euro coin located on the surface of the earth. All of these surfaces of gravity are centered about the geometric center of the coin, which is its center of gravity in a uniform gravitational field. Their sizes are compared to that of a water molecule.