I found an Article on this very subject that I really liked entitled "Shakespeare and Astrology." It discusses stars and planets in Shakespeare and how they worked in that time period.
Just to give a basis for looking into stars here is a quote that shows how much allusion to the stars is used in Shakespeare's plays: "In all of Shakespeare's 37 plays there are more than a hundred allusions to astrology, and many of his characters' actions are said to be favored or hindered by the stars. The signs of the zodiac are mentioned in six of Shakespeare's plays, and the planets may even be blamed for disasters, especially as they wander from their spheres"
According to this article stars were often seen almost as fate, where they controlled everything that happened. Planets as well played an important role as they were seen as the agents between humans and the stars. Stars and Planets were often personified as people, "the heavenly spheres had eternal souls."
Often Shakespeare characters believed that what star or constellation they were born under would determine their fate. I thought this was funny - but as I was searching around I actually found a site that will look up what star you were born under.
Another article I found on stars and constellations is called, "Shakespeare's Astrology," by Frank Piechoski. It goes into more depth about the role of the planets (which included the sun and moon) in an Elizabethan's life. As it states, "Each planet has its own particular astrological qualities and correlates with different parts of the body, areas of life and even places or objects. The planet Venus, for example rules the throat, artistic endeavor, jewelers, gardens and copper." This article also goes through and examines some specific quotes from plays which show how either Shakespeare or his characters use/engage this belief in stars and planets.
Bibliography
Piechoski, Frank. "Shakespeare's Astrology." Starcats' Anima Mundi Copyright © 1998-2000. Web.
"Shakespeare and Astrology." Copyright 2001, BSM Consulting. Web.
