What effect did Soviet achievements in space have on American society and culture?

USA was behind in Science and Math. So the federal government dumped massive amounts of money at the high school and college level. Americans so the Cold War heat up in Space. Very far behind.

The first space shuttle had enough capablities to go to Mars.

Mars was the orginal goal!

Moon became the target because USA moved it to so.

Watch Hidden Figures and October Sky for some inspiration.