Robotic Astronomical Observatories (RAOs) have provided very good results in different research projects in astrophysics/astronomy. Their applications in the detection, tracking, and identification of near-Earth objects have contributed to the identification of potentially dangerous objects for our security, such as near-Earth Objects (NEOs), near-Earth Asteroids (NEAs), meteors, and comets, whose trajectory changes can cause an impact on our planet. If advances in astrometry techniques (measuring the position and trajectory of Earth-orbiting objects) and photometry (variation in light curves) are considered together with the new sensors that work in the optical and near-infrared spectral ranges, a new observatory system that allows for the detection of nearby satellite objects in different spectral ranges and with better-defined optics can be developed. The present paper describes the design of a new observatory applied to the surveillance and tracking of satellites and other debris objects, the Satellite Robotic Observatory (SRO). Starting from general constraints from astronomy observatories, the design process has been determined, considering the main objectives, the necessary sensors, and several technical improvements that have contributed to a final configuration proposed for the SRO. The result is the design of a portable observatory model that can host at least two sensors to track and monitor satellite objects simultaneously.