The problem there is that the Soviet Union, between the space race and the unremitting military brinksmanship of keeping up with the Unitied States, bankrupted itself, which was the real reason the Cold War ended in the first place. Any plausible AU exploring the possibilities of an extended space race would have to A) get around the economic factor, showing how such a race could have possibly continued to be financed, consuming a significant portion of a nation's GDP without tipping it over the brink and still providing material and political benefit and B: Getting around the incessant military pressure to begin reallocating those resources toward bigger and better weapons whose principles were refined and discovered due to the explosion of technical capability that the space race resulted in.
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