For thousands of years, arches have been used as durable structures that are easy to build and that rely on gravity for their inherent stability. Since then, many researchers and engineers have studied their stability either when subjected to gravity or inertial loading. Currently, given the Insight mission to Mars and the ambitious Artemis program to the Moon, it has become apparent that there will soon be the need to design and build the first resilient extraterrestrial structures and arches represent an ideal option for such structures. This paper focuses on the stability of parabolic arches with different embrace angles subjected to different levels of equivalent inertial loading in low-gravity conditions. The results are contrasted with the well-studied circular arches. More specifically, this investigation employs variational principles to identify the imminent mechanisms and numerical methods based on the limit thrust line concept in order to estimate the minimum required thickness of parabolic arches for a given loading and in different gravitational fields. The paper shows that although parabolic arches can be much more efficient than their circular counterparts for gravitational-only loading, this is not the case for different combinations of inertial loading and embrace angles where the opposite can be true. It highlights the dominant effect of low-gravity conditions on the minimum thickness requirements for both types of arches and considers the effect of a potential additional infill for radiation shielding. Furthermore, this study reveals a self-similar behaviour, introduces a “universal” inertial loading and showcases, through the use of master curves, the areas where the parabolic arches are more efficient than their circular counterparts and those where the opposite is true. These areas can be used for the preliminary design of such structures. Additionally, the paper identifies hidden patterns associated with the developed mechanisms between the two different geometries for the different gravitational fields. Finally, it presents a case study where the need to optimise the structural form of extraterrestrial structures becomes evident.