The stroboscopic method in nonlinear mechanics is applied to the calculations of a low constant tangential thrust spiral trajectory in a single force field. Closed-form solutions for the first approximation are derived. The oscillatory nature of the spiral is exposed; the maximum deviation of the oscillation is of the order of 2/A, where I/A is the initial thrust to local weight ratio, and the oscillations damp out as the spiral proceeds. 1581