Excerpts from:
Peter D. Usher
Mercury Magazine Vol. 26, No. 1, pp. 20-23, 1997.
. . . Degree being vizarded,
Th' unworthiest shows as fairly in the mask.
The Heavens themseves, the Planets, and this centre
Observe degree, priority, and place . . .
The Ptolemaic model . . . was still the accepted paradigm in Shakespeare's day, although the heliocentric model was gaining ground.
. . . Shakespeare's plays and poems give the impression that he neglected the advances in astronomy that had occurred before his birth and continued in his lifetime . . .
The astronomer Cecilia Payne-Gaposchkin has suggested that Shakespeare may have referred to heliocentricism in Hamlet. In her 1970 textbook, she noted that the 16th-century astronomer Rheticus, who played an early and prominent role in promoting the publication of De revolutionibus, was from Wittenberg, where Tycho Brahe was a student -- as was Hamlet.
Moreover, as Leslie Hotson has pointed out, Hamlet's chums Rosencrantz and Guildenstern have the names of [ancestors] of [Tycho] Brahe. . . . Shakespeare . . . appears to have taken their names from an engraved portrait sent to England. . . .
In the Bulletin of the AAS, I suggested that Hamlet's complaint that "Denmark's a prison" and his proclamation: "I could be bounded in a nutshell and count myself a king of infinite space" may be comparing competing models of cosmic space that existed at the time. On the one hand, the Ptolemaic and Copernican models encase humanity in a cosmic nutshell; on the other, the visionary extension of the Copernican model by Shakespeare's contemporary Thomas Digges liberate us from that prison to live in infinite space.
So the evidence is mounting that Shakespeare did not completely ignore the astronomical revolutions of the 16th century. . . .