Slow-fast affine control systems with one fast angle are considered. An approximation based on standard averaging of the extremal is defined. When the drift of the original system is small enough, this approximation is metric, and minimum time trajectories of the original system converge towards geodesics of a Finsler metric. The asymmetry of the metric accounts for the presence of the drift on the slow part of the original dynamics. The example of the J2 effect in the two-body case in space mechanics is examined. A critical ratio between the J2 drift and the thrust level of the engine is defined in terms of the averaged metric. The qualitative behaviour of the minimum time for the real system is analyzed thanks to this ratio.