Space situational awareness (SSA) is vital for international safety and security, and the future of space travel. By improving SSA data-sharing we improve global SSA. Computational ontology may provide one means toward that goal. This paper develops the ontology of the SSA domain and takes steps in the creation of the space situational awareness ontology. Ontology objectives, requirements and desiderata are outlined; and both the SSA domain and the discipline of ontology are described. The purposes of the ontology include: exploring the potential for ontology development and engineering to (i) represent SSA data, general domain knowledge, objects and relationships (ii) annotate and express the meaning of that data, and (iii) foster SSA data-exchange and integration among SSA actors, orbital debris databases, space object catalogs and other SSA data repositories. By improving SSA via data- and knowledge-sharing, we can (iv) expand our scientific knowledge of the space environment, (v) advance our capacity for planetary defense from near-Earth objects, and (vi) ensure the future of safe space flight for generations to come.