It created heroes out of explorers and ideological WMDs out of missiles that never hit a single living being.

The cultural change is a pretty awesome thing to study and would have been an amazing thing to experience. All of a sudden you had the entire hopes and dreams of a nation pinned on the backs of the few brave and bold who were willing to go where no man had gone before.

Ever read about the role Greco-Roman mythology in their respective societies? The long and the short of it was that it connected each and every citizen in a unique yet universal way. And the space race was the modern equivalent. Here you had these heroes doing tasks that could be only deemed as godlike while coming from the same stock of men and women that roamed the streets.

A great example of this comes at the end of Forrest Gump, (which if you haven't seen is a must watch as it is one of the greatest epics ever made) where Lieutenant Dan remarks about his new prosthetic legs, "tap, tap tap", "Aluminum, just like what they use for the spaceships". That just gives a great window into how much the public integrated the space race into day to day life.