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I want the answer to incorporate apparent magnitudes of those moons, power of his telescope, light pollution of that time, successful recreation of the scenario of watching Galilean moons using that telescope recently, possibilities of extraordinary eye sight, etc.

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    $\begingroup$ A simple Wiki's search may suffices: Galilean moons: Discovery. $\endgroup$ Mar 29, 2018 at 12:15
  • $\begingroup$ Usually I don't consider Wikipedia a good source for these kind of information. $\endgroup$ Mar 30, 2018 at 15:45
  • $\begingroup$ There are good and bad papers in Wikipedia. Good papers give reference to sources. About Galileo, a good source is the book of Drake, "Galileo at work". $\endgroup$ Mar 30, 2018 at 17:22

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There can be no doubt that he has seen them, for the simple reason that he determined their periods and configuration correctly, and published them. Therefore the other things (magnification of his telescope, light pollution etc.) are irrelevant for the answer. You can easily see them yourself using an 8x binocular.

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  • $\begingroup$ Our Astronomy instructor said Galileo's original telescope doesn't suffices the needs to watch those moons. I guess it's wrong. $\endgroup$ Mar 30, 2018 at 15:42
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    $\begingroup$ @aquire: It is definitely wrong. We don't have Galileo's telescope to investigate it. But we have his publications on the subject which imply that he definitely saw these satellites and was able to measure their parameters correctly. $\endgroup$ Mar 30, 2018 at 17:19
  • $\begingroup$ Are there any successful recreations of his telescope? $\endgroup$ Mar 30, 2018 at 17:58
  • $\begingroup$ @aquire: I suppose there are. But I do not know how successful they are, and have no ready references. With information available on the web, you can try to make one yourself, using lenses from eyeglasses. I actually made one when I was a child:-) $\endgroup$ Mar 30, 2018 at 18:21
  • $\begingroup$ @aquire: here is the first site which came in my search: popsci.com/build-diy-replica-galileos-telescope, scitechantiques.com/Adler $\endgroup$ Mar 30, 2018 at 18:25

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