Here are some things they already knew in Shakespeare's time:
The earth revolves around the sun (1543)
the earth has a magnetic field (1600)
Galileo was already making detailed astronomical observations although he had not yet formuulated the law of falling bodies. Johannes Kepler had discovered the first two laws of planetary motion. Shakespeare would have been aware of these studies in the same way that an educated person today is aware of important scientific discoveries. His plays are full of poetic references to stars and one speech from Romeo & Juliet is considered a test of how well an actor can handle the playwright's language.
“When he shall die,
So Happy Birthday Will!
Take him and cut him out in little stars,
And he will make the face of heaven so fine
That all the world will be in love with night
And pay no worship to the garish sun.”
The illustration is from the Wiki quotes site. Don't know who created it, but it tickles me. Shakespeare would have fit right into the 21st century.