Mathematical models of geopotential gradients

The present work investigates several alternatives to the usual method of expressing the gravitational potential of the earth at an exterior point as a summation of spherical harmonics. Alternative representations considered are point masses, density layers, and Taylor's series. These representations are examined in terms of the goodness of fit to test data and conservation of computer time and/or core storage. The Taylor series representation provides the most compact representation and is highly conservative of computer time. The point mass and density layer models are competitive with it and with each other. The trade-off is an order of magnitude difference in computer time requirements versus a factor of two improvement in accuracy. In orbit computation applications using a numerical integration scheme such as Runge-Kutta or Cowell's method, the necessity to recompute the gravity vector component several times in one integration step makes the Taylor series model quite attractive.