Though some encounters with potentially illicit radiological or nuclear material involve a stationary or dwell survey, many of the conceivable encounters are dynamic in nature. In the general unshielded or homogeneously shielded dynamic encounter, the mean detectable source signature strength will follow a well behaved curve with time: increasing on approach, peaking at the point-of-closest-approach, and then decreasing. Despite this well understood phenomenon, many currently available detection systems are set up to optimally detect an arbitrary step function that may or may not be representative of the anticipated dynamics of the encounter. Of course, the fact that radiation emission generally follows a Poisson process requires a signal integration time. For example, the dynamic scanning mode of many detection systems considers discrete and independent one second response data. Such a system is only optimized for a one second dwell. This approach can be improved upon. It will be shown that if the dynamics (meaning range and relative velocity) are understood, the integration period can be optimized to yield maximum signal to noise ratio. An analytical expression describing gamma radiation signature strength will be provided that may be used as the basis for studies of the effectiveness of temporally aware approaches to source detection in a dynamic encounter.