The position and velocity errors of a near-circular orbit due to geopotential uncertainty are developed in Fourier series. Current satellite gravity models generate position uncertainties of up to 50 m along-track for close satellites (~1000 km altitude) in shallow resonance (periods less than 5 days, from coefficients of order 13-14). Smaller radial errors are due to resonance and to first-order terms poorly seen in current satellite geopotentials. Correlation of errors is strong by order and the same degree parity. Application of the development is made to (1) the prediction of errors for a future altimeter satellite, (2) the capability of earth-based tracking of a close Mars orbiter in resolving that planet's gravity potential, and (3) improvement of the resolution of the low-degree geopotential from the Geopotential Research Mission using tracking data from the Global Positioning System. ¿ American Geophysical Union