The linear perturbations of the radius of a satellite orbit due to the geopotential are derived. From these, estimates are made of the radial orbit error just to geopotential errors from current models employing only conventional satellite-tracking data. The estimates show that about an order of magnitude improvement in the satellite geopotential will be necessary to utilize the full accuracy of independent satellite altimeter measurements. The linear perturbations are used to show that (1) a substantial improvement in the low-degree geopotential is possible from the indirect use of Seasat altimetry at track crossovers, and (2) a separation of ''permanent'' sea topography and geoid may be possible from direct crossovers, and (2) a separation of ''permanent'' sea topography and geoid may be possible from direct use of the heights along the track.