Server-based computing in space has been recently proposed due to potential benefits in terms of capability, latency, security, sustainability, and cost. Despite this, there has been no work asking the question: how should we architect systems for server-based computing in space when considering overall cost. This paper presents a Total Cost of Ownership (TCO)-based approach to architecture of server-based computing systems for space (Space Microdatacenters - SμDC) for processing data produced by low Earth orbit (LEO)-based Earth observation (EO) satellites. We show that power of compute is the primary factor in determining SμDC TCO, though the dependence is sublinear. Second, the impact of compute mass, monetary cost, and communication on TCO is relatively insignificant. Third, architectures with the highest $\frac{\text { FLOPs }}{{\mathrm {W}}}$ provide much higher performance per TCO ${\$}$ even if they have poor $\frac{\mathrm{FLOPs}}{\$}$. We leverage these insights to advocate extreme heterogeneity designs for SμDCs. These designs reduce SμDC TCO by 116× in spite of poor $\frac{\mathrm{FLOPs}}{\$}$ characteristics. We also show that (a) collaborative compute constellations — constellations in which EO satellites are also equipped with compute hardware — further improve SμDC TCO by 1.31 to 1.74×, (b) a distributed architecture reduces TCO by 10% over a monolithic architecture, and (c) low monetary cost of compute can be leveraged to provide near zero cost compute overprovisioning which improves an SμDC’s availability significantly and supports graceful degradation. Overall, this is the first paper on cost-aware architecture and optimization of a SμDC.