Density layer models for the geopotential

Spherical harmonic representation of the geopotential suffers from convergence problems in both the mathematical and numerical senses; it also is not suitable for use with the terrestrial gravity data, which is distributed very unevenly over the surface of the earth. Of the alternative mathematical models, the simple density layer offers the most mathematical and computational simplicity and avoids the problems associated with spherical harmonics. In practice low order spherical harmonic models have been combined with a density layer for a complete model of the geopotential. Results from satellite data alone and from combinations of satellite and gravity measurements have been published already; improved models will be obtained as new data become available. Presented to the Twelfth Special Projects Branch Astrodynamics Conference, Goddard Spaceflight Center, Greenbelt, Md. 20771, USA, 26–27 October 1970.