The space industry is quietly building toward something nobody has fully reckoned with: orbital data centers running thousands of autonomous AI workloads with no human in the loop, 550 km above the Earth. Microsoft, AWS, and a growing list of orbital computing ventures are moving cloud-scale processing off the ground and into orbit. What none of them have answered yet is the governance question -- when autonomous AI systems at orbital data center scale make wrong decisions in space, what stops those decisions before they become irreversible? We introduce Glass Box: a runtime constitutional AI verification layer that intercepts every candidate action from an onboard AI policy and evaluates it against six physics-grounded constitutional constraints and seven Linear Temporal Logic (LTL) safety invariants before a single command reaches any spacecraft subsystem. Every approved action carries a weighted explainability score E(a_t) in [0,1] and a complete constitutional audit log. We demonstrate Glass Box within Project October: a fully simulated five-layer autonomous orbital intelligence architecture for CubeSat-class spacecraft. We prove that Glass Box verification overhead is O(N_c) in the number of constitutional rules, independent of model size or spacecraft state dimension. We present a complete formal specification of the constitutional constraint grammar, seven LTL safety invariants verified by Z3 and NuSMV model checking, and a detailed worked example of Glass Box intercepting an unsafe inference request at eclipse-entry under degraded battery state. As orbital computing scales toward data center infrastructure, runtime constitutional verification is no longer a research novelty -- it is mission-critical safety infrastructure that every autonomous orbital platform will eventually require.