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The utilisation of the Very Low Earth Orbit (VLEO) region offers significant application specific, technological, operational, and cost benefits. However, attaining sustained and economically viable VLEO flight is challenging, primarily due to the significant, barely predictable and dynamically changing drag caused by the residual atmosphere, which leads to a rapid deterioration of any spacecraft's orbit unless mitigated by a combination of active and passive techniques. This article addresses one passive method by optimising satellite shapes in order to achieve a minimisation of the atmospheric drag force and thus extension of operational lifetime. Contrary to previous investigations in the field, a constant internal volume is maintained to account for the placement of satellite instruments and payload inside the structure. Moreover, the satellite geometry is not varied heuristically but optimised via a numerical 2D profile optimisation specifically developed for this purpose. From the resulting optimal satellite profiles, 3D satellite bodies are derived, which are then verified via the Direct Simulation Monte Carlo method within the open-source particle code PICLas. In addition, rather unconventional designs, i.e. ring geometries, which are based on the assumption of fully specular particle reflections, are proposed and assessed. The optimised satellite geometries offer pure passive lifetime extensions of up to 46 $\%$ compared to a GOCE like reference body, while the above-mentioned ring geometries achieve passive lifetime extensions of more than 3000 $\%$. Finally, the article presents design recommendations for VLEO satellites in dependence of different surface properties.