As satellite constellations for communications rise in importance in both academic and industrial circles, we face the challenge of adapting Software-Defined Networks (SDN) and Multi-access Edge Computing (MEC), initially designed for static terrestrial networks, for the dynamic nature of Non-Terrestrial Networks (NTN). This paper presents MeteorNet, a continuous time emulation framework grounded in realistic orbital propagators, Mininet, and Docker virtualization, designed to develop and test space mission software. Our solution adapts link characteristics according to constellation orbits and Earth dynamics using Linux network interfaces. We provide the results of a tested networking scenario detailing how network usage measurements and output data analysis can be used to examine the behavior of routing protocols within the framework. This work underscores the necessity for appropriate network management and transport protocol adaptations for effective communication in emerging satellite constellations.