The orbit accuracies needed to support the global crustal dynamics project and recent satellite altimeter missions have placed unique demands on both the data precision and the analysis systems. These include requirements for accurate and well-distributed observations, improved computational techniques and substantial enhancements in the force models which describe the satellite's motion. For example, the satellite altimeter mission (TOPEX), whose objectives will be (1) to measure the time variable ocean surface topography and (2) to demonstrate the ability to map the general ocean circulation, requires that the radial component of the satellite's orbit be known with a root-sum-square absolute error of 13 cm for the three-year mission lifetime. The primary force model error, which limits the contemporary orbit computation accuracy, is the inaccuracy in the values assigned to the spherical harmonic coefficients used to model the earth's gravity field. This investigation describes the effects of gravity model errors on previous satellite altimeter missions and looks at the projected effects of current geopotential model errors on future satellite altimeter missions. The investigation demonstrates that (1) the radial orbit error, represented in a geographic sense, will contain a regionally dependent mean and variability, (2) historically, it has not been possible to use conventional ground-based tracking to remove these effects, and (3) the regionally correlated component can lead to bias in mean ocean surfaces created by minimizing altimeter differences at ground track crossover points. This last effect has been a primary limitation in using satellite altimetry to obtain the long-wavelength components of the ocean surface topography. The magnitude of the regionally correlated error can be reduced only by improvement in the knowledge of the gravity field. The conclusion reached in this investigation is that an order of magnitude improvement in the accuracy of the earth's gravity field model is required to realize the full potential of the proposed TOPEX altimeter measurements.