Manoeuvrable, responsive satellite constellations that respond to real time events could provide data on demand for time-critical tasks, such as disaster monitoring and relief efforts. The authors demonstrate the feasibility of such a system by expanding on a fully analytical method for designing responsive spacecraft manoeuvres using low thrust propulsion. These manoeuvres are perceived as a graph that enables efficient exploration and optimised selection of favourable routes that achieve mission goals while highlighting resilience and redundancy in the mission’s execution. A case study is presented that considers four satellites required to provide flyovers of two targets, with an associated graph of 10839 possible manoeuvres. Investigation of the graph highlights that a good, but not minimum time, solution can allow the system to perform well, while also providing greater resilience to changes in mission priorities and errors in execution. This analytical approach enables operators to trade-off between a loss of time by using only one satellite versus the disruption of moving multiple satellites for a potentially faster response. The impact of varying mission capabilities, such as using fewer satellites, smaller swath width or less propellant, can be evaluated by reducing the graph without recalculating manoeuvre options.