The spaceborne altimeter missions of Geos 3 (50-cm accuracy) and the future Seasat (10-cm accuracy) require precise knowledge of the radial position of the spacecraft to be most effective. Though errors in previous gravity models have produced large uncertainties in the orbital position of Geos 3, significant improvement has been obtained with new geopotential solutions, Goddard Earth Model (GEM) 9 and 10. The solution for GEM 9 was derived by combining laser data from Geos 3, Lageos, and Starlette; S band measurements on Landsat 1; and data from 26 other satellites used in previous solutions. GEM 10 is a combination solution containing a global set of surface gravity anomalies along with the data in GEM 9. Radial errors of Geos 3 for 5-day arcs have been reduced from about 5 m to 1 m on the basis of orbital intercomparisons, station navigations, and analyses employing crossover points from passes of altimetry. The use of highly accurate laser data in a constrained least squares solution has permitted GEM 9 to be a larger field than previous derived satellite models, GEM 9 having harmonics complete to 20¿20 with selected higher-degree terms. The satellite data set has approximately 840,000 observations, of which 200,000 are laser ranges taken on nine satellites equipped with retroreflectors. GEM 10 is complete to 22¿22 with selected higher-degree terms out to degree and order 30 amounting to a total of 592 coefficients. Comparisons with surface gravity and altimeter data indicate a substantial improvement in GEM 9 over previous satellite solutions; GEM 9 is in even closer agreement with surface data than the previously published GEM 6 solution which contained surface gravity. In particular, the free air gravity anomalies calculated from GEM 9 and a surface gravity solution by Rapp (1977) are in excellent agreement for the high-degree terms (13 ? l ? 22). From these terms an estimate is made of the gravity anomalies for the upper mantle. The mass constant of the earth, GM, has been estimated from the laser data as 398,600.64 ¿0.02 km3/s2, a value which is principally determined from Lageos. The speed of light used was 299,792.5 km/s. Geocentric station positions were determined for approximately 150 stations in GEM 10. These station coordinates, their mean sea level heights, and altimetry data provide an estimate for the mean radius of the earth of ae = 6,378,139 ¿ 1 m. Accuracy estimates derived for the potential coefficients have been verified with independent data sets. These produce commission errors in geoid heights of 1.9 m and 1.5 m (global rms values), respectively, for GEM 9 and 10.