A new geometric formulation is given for the problem of determining position and orientation of a satellite scanner from error-prone ground control point observations in linear pushbroom imagery. The pushbroom satellite resection problem is significantly more complicated than that of the conventional frame camera because of irregular platform motion throughout the image capture period. Enough ephemeris data are typically available to reconstruct satellite trajectory and hence the interior orientation of the pushbroom imagery. The new approach to resection relies on the use of reconstructed scanner interior orientation to determine the relative orientations of a bundle of image rays. The absolute position and orientation which allows this bundle to minimize its distance from a corresponding set of ground control points may then be found. The interior orientation is represented as a kinematic chain of screw motions, implemented as dual-number quaternions. The motor algebra is used in the analysis since it provides a means of line, point, and motion manipulation. Its moment operator provides a metric of distance between the image ray and the ground control point.