The rapid expansion of artificial intelligence is driving sharp increases in data-center energy consumption, water use, and land demand, affecting terrestrial infrastructure and environments. In this paper, I examine orbital AI data centers powered by Dyson swarm–like solar satellite constellations. These systems would place large-scale AI compute platforms in Earth orbit, supplying them with locally harvested solar energy instead of terrestrial grids. Operating in space offers continuous high-intensity solar power and passive radiative cooling in vacuum, eliminating water-intensive cooling, cutting carbon emissions, and freeing AI growth from Earth’s environmental limits. I assess technical feasibility through modular satellite architectures, solar power generation and storage, radiative thermal management, high-bandwidth optical communications, orbital mechanics, and launch logistics enabled by reusable heavy-lift vehicles such as Starship. I compare orbital and terrestrial data centers in terms of energy efficiency, water consumption, land use, life-cycle emissions, and long-term cost per unit of computation. I also address strategic and geopolitical issues, including spectrum allocation, orbital congestion and debris risks, regulatory challenges from recent FCC filings, and potential concentration of orbital compute capacity. Finally, I explore business models and impacts on cloud services, AI training economics, and competition among technology and aerospace leaders. I conclude that large-scale orbital AI data centers are unlikely to replace terrestrial infrastructure in the near term (2026–2040). However, pilot deployments in the 2030s could mark a structural inflection point. If technical, regulatory, and orbital-sustainability challenges are met, Dyson swarm–powered orbital systems could sustain AI growth with far lower environmental impact, reshaping the relationship between energy, computation, and planetary boundaries.