To answer your question, Copernicus made sure he did not face many social consequences as a result of challenging Aristotle's model by:
- approaching the science from a mathematical perspective.
- keeping the work unpublished.
- sharing/discussing the work with supporters only.
- publishing the work at the end of his life, seeing the finished book as he was dying.
Copernicus' book De revolutionibus orbium coelestium (On the Revolution of Heavenly Bodies") was published in 1543, two months before he died. It took nearly 100 years for the ideas to take their place in 'modern astronomy'.
Evidence exists that the work can be traced back to as early as 1514, but publication of the book was delayed so that he wouldn't suffer social consequences. In fact the newly published book was first presented to him on his deathbed, removing the chance for retribution.
The "Copernican Revolution" happened as a result of Copernicus' work - but not during his lifetime. His work was only shared with those who supported his ideas, and those who could provide constructive criticism. Indeed it was these friends who convinced him to publish the work in the first place. People were generally interested in his ideas and were excited to see where they might lead.