Analysis of the data from the SEASAT altimeter, a 10-cm precision instrument, requires accurate knowledge of the radial position of the spacecraft for oceanographic applications such as the study of tides and ocean circulation as well as for geodetic applications. Initial orbit determinations using the best available geodetic and force models gave radial errors approaching 5 m. The dominant source of this radial error was the gravity field model. Improvements in the gravity modeling were made by successively incorporating the SEASAT laser and Unified S Band ground tracking data, the GEOS 3 altimeter data, and finally, the SEASAT altimeter data. With the most recent model (a set of spherical harmonic coefficients complete to degree and order 36), SEASAT ephemerides have been computed for an orbital arc length of 12 days with an rms radial accuracy of about 70 cm.