AHC/WI: Tighter space race

What if the Soviets were able to keep a better pace with the US in the moon race? USA still lands on the moon first, but the Russians own program comes close and maybe even performs a lunar orbit at some point.

Can the Soviets do it, and if so, would the Space Race continue after the moon landings, or would the Soviets give up after being beaten to the moon?
 
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