ABSTRACT

Physical geodesy is the branch of science that relates the internal distribution of mass within the Earth to its corresponding gravity field. Under ideal circumstances, there would be no hills, valleys, mountains, or oceans on the Earth, and the distribution of mass within the Earth would be uniform. Given those conditions, the plumb line (the vertical) would be coincident with the ellipsoid normal and there would be no difference between the ellipsoid and the geoid. But, the geoid is an equipotential surface that is always perpendicular to the local plumb line and the direction of the plumb line is dictated by the vector sum of forces acting on the plumb bob; for example, gravity is the sum of gravitational attraction and centrifugal force, as shown in Figure 8.1. The centrifugal force component is very predictable and can be computed. But, due to the Earth’s topography and due to variations of density within the Earth, gravitational attraction varies from point to point and, although the difference is generally quite small, the resulting vertical is rarely coincident with the ellipsoid normal. That being the case, the geoid is not parallel to the ellipsoid, and separation between the two surfaces varies with location. Ongoing geodetic research continues to improve knowledge of the relationship between the ellipsoid and the geoid. Evidence of continuing progress and improvement in geoid modeling in the United States is seen in the publication of various geoid models (dated 1990, 1993, 1996, 1999, 2003, and so on).