In this paper we report upon the cloud-based solution that we designed and implemented for space situational awareness. We begin by introducing the background to the work and to the area of space situational awareness. This concerns tracking the hundreds of thousands of known objects in near-Earth orbits, and determining where it is necessary for satellite operators to conduct collision-avoidance manoeuvres to protect their satellites. We also discuss active debris removal, which would be necessary to stabilise the debris population at current levels. We examine the strengths that cloud-based solutions offer in general and how these specifically fit to the challenges of space situational awareness, before describing the architecture we designed for this problem. We demonstrate the feasibility of solving the space situational awareness problem with a cloud-based architecture and note that as time goes on and debris levels rise due to future collisions, the inherent scalability offered by a cloud-based solution will be invaluable.