The Gravity Field of the Earth, Part 1

This chapter covers physical geodesy-the shape of the Earth and its gravity field. This is just electrostatic theory applied to the Earth. Unlike electrostatics, geodesy is a nightmare of unusual equations, unusual notation, and confusing conventions. There is no clear and concise book on the topic although Chapter 5 of Turcotte and Schubert is OK. The things that make physical geodesy messy include: • earth rotation • latitude is measured from the equator instead of the pole; • latitude is not the angle from the equator but is referred to the ellipsoid; • elevation is measured from a theoretical surface called the geoid; • spherical harmonics are defined differently from standard usage; • anomalies are defined with respect to an ellipsoid having parameters that are constantly being updated; • there are many types of anomalies related to various derivatives of the potential; and • mks units are not commonly used in the literature. In the next couple of lectures, I'll try to present this material with as much simplification as possible. Part of the reason for the mess is that prior to the launch of artificial satellites, measurements of elevation and gravitational acceleration were all done on the surface of the Earth (land or sea). Since the shape of the Earth is linked to variations in gravitational potential, measurements of acceleration were linked to position measurements both physically and in the mathematics. Satellite measurements are made in space well above the complications of the surface of the earth, so most of these problems disappear. Here are the two most important issues related to old-style geodesy. Elevation Prior to satellites and the global positioning system (GPS), elevation was measured with respect to sea level-orthometric height. Indeed, elevation is still defined in this way however, most measurements are made with GPS. The pre-satellite approach to measuring elevation is called leveling.