We present inverse-theory techniques for the determination of the trajectory of a fireball using seismic network data. Assuming that the speed of sound (c) in air is constant and known and that the trajectory is a straight line, the unknowns are the velocity of the fireball (v), and the following parameters related to the trajectory: the two horizontal coordinates of the end point and the corresponding arrival time (t0), the azimuth of its horizontal projection, and the angle with the vertical. As the computation of travel times for a given set of parameters is nonlinear, the inverse problem is solved by use of a standard linearization technique with the resulting linear system of equations solved using damped least squares and the generalized inverse. These two approaches are applied to data from a fireball observed in northeast Arkansas in November 2003 and recorded by stations of the University of Memphis seismic network. We find that v and t0 are essentially unconstrained, with the computed values depending on the initial value of v (and the assigned value of c). However, the two angles that define the trajectory are well constrained. Inversion of realistic synthetic data confirm our observations, which are also supported by analytical considerations. The results obtained for the Arkansas data were used to predict the direction of the ground motion in the horizontal plane, which is in good agreement with the observations. Although this is not the main point of the article, we also noted that the observed ground motion is prograde, which we were able to reproduce with synthetic seismograms.