A Heliocentric Theory. By 1532 Copernicus had mostly completed a detailed astronomical manuscript he had been working on for 16 years. He had resisted publishing it for fear of the ensuing controversy and out of hope for more data.
The heliocentric model was generally rejected by the ancient philosophers for three main reasons: If the Earth is rotating about its axis, and orbiting around the Sun, then the Earth must be in motion. However, we cannot ``feel'' this motion. Nor does this motion give rise to any obvious observational consequences.
After the collapse it become a "democratic" nation so US saw it as less of a enemy. Also, it become a lot weaker so it wasn't as big of a rival or threat to the USA. Allowing it to trade and work together on major projects.