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Earth-viewing satellite sensors (e. g., the Landsat 4/5 Thematic Mapper) produce images with nontrivial amounts of geometric distortion due to local terrain variations. Although correction formulas are easy to derive, the high frequency of terrain variation relative to pixel size means that excessive computer time is required to process a large digital image. This paper derives approximations to the correction geometry that reduce computer time by orders of magnitude. A statistical sensitivity analysis shows that the approximations do not adversely affect the accuracy of the results even under a very demanding error budget.