During periods of rest, hippocampal place cells feature bursts of activity called sharp-wave ripples (SWRs). Heuristic approaches to their analysis have revealed that a small fraction of SWRs appear to "simulate" trajectories through the environment - called awake hippocampal replay - while the functional role of a majority of these SWRs remains unclear. Applying a novel probabilistic approach to characterize the spatio-temporal dynamics embedded in SWRs, we instead show that almost all SWRs of foraging rodents simulate such trajectories through the environment. Furthermore, these trajectories feature momentum, that is, inertia in their velocities, that mirrors the animals' natural movement. This stands in contrast to replay events during sleep which seem to follow Brownian motion without such momentum. Lastly, interpreting the replay trajectories in the context of navigational planning revealed that similar past analyses were biased by the heuristic SWR sub-selection. Overall, our approach provides a more complete characterization of the spatio-temporal dynamics within SWRs, highlights qualitative differences between sleep and awake replay, and ought to support future, more detailed, and less biased analysis of the role of awake replay in navigational planning.