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Galileo Galilei believed that stars were distant suns whose sizes, measuredvia his telescope, were a direct indication of distance -- fainter stars(appearing smaller in the telescope) were farther away than brighter ones.Galileo argued in his Dialogue that telescopic observation of a chancealignment of a faint (distant) and bright (closer) star would reveal annualparallax, if such double stars could be found. This would provide support bothfor Galileo's ideas concerning the nature of stars and for the motion of theEarth. However, Galileo actually made observations of such double stars, wellbefore publication of the Dialogue. We show that the results of theseobservations, and the likely results of observations of any double star thatwas a viable subject for Galileo's telescope, would undermine Galileo's ideas,not support them. We argue that such observations would lead either to the morecorrect conclusion that stars were sun-like bodies of varying sizes which couldbe physically grouped, or to the less correct conclusion that stars are notsun-like bodies, and even to the idea that the Earth did not move. Lastly, wecontrast these conclusions to those reached through applying Galileo's ideas toobservations of visible stars as a whole.

Regarding the Potential Impact of Double Star Observations on Conceptions of the Universe of Stars in the Early 17th Century