We have been making dual dome enclosures which are useful to track artificial space objects at SSNT (Space Science and Technology Lab.) Kyung Hee University. We verified the safety of the dome enclosures using basic design and structure analyses before manufacturing them, and then performed an optimization analysis for economic and safe systems. The dome enclosure has a fully-open type structure to smoothly operate a telescope made in the style of altazimuth mount with very fast tracking. It is also designed to be safe against extreme weather conditions. The general structure of the observatory system consists of the dual dome enclosures at the top of a container. For the structural analyses, we consider the following two methods: (1) gravitational sustain analysis - how the structure supporting the dome withstand the weight of the dome, and (2) wind load analysis that considers the effect of the wind velocity at the region where the observatory is located. The result of overall deformation is found to be less than 0.551mm and the result of equivalent stress is found to be 20.293Mpa, indicating that the dual dome system is reasonably designed. This means structurally to be safe.