Given you take a (non-amateur) refractor telescope, what are aperture and magnification required to recognize phases of the four Galilean moons?
What did Galileo see: http://www.astro.umontreal.ca/~paulchar/grps/site/images/galileo.4.html
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1$\begingroup$ Because Jupiter is much farther from the Sun than the Earth, it hardly shows any phase other than 100%. (astronomy.com/magazine/ask-astro/2017/02/jupiters-illumination says a minimum of 99%.) With the moons being much smaller, I doubt that any amateur scope will show anything other than 100% phase on the Galilean moons. $\endgroup$– JohnHoltzAug 6, 2018 at 20:01
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$\begingroup$ @JohnHoltz if you take a moment to look at the link in the OP's question, you will discover what the OP is referring to re what Galileo saw. That would have taken you less time than to write your comment which now seems unhelpful. $\endgroup$– uhohAug 10, 2018 at 12:24
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1$\begingroup$ Thanks @uhoh. I do not know what J.Doe intended to ask, but I do know that phase indicates the amount of illumination. Once J.Doe clarifies what is intended, then someone can provide the proper answer. Otherwise, anyone reading the question and understanding the terminology of phase would not find the answer on the referenced website; that is, did Galileo see the phases of Jupiter's moons? If not, what size scope is required to see their phase? Since our Moon exhibits phases, it may be natural to assume that other moons do too. There, 35 characters remaining. $\endgroup$– JohnHoltzAug 11, 2018 at 17:26
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$\begingroup$ @JohnHoltz I was certain the question was about observing the orbital phases of the Galilean moons, but after re-reading the Q a few more times and then reading through Revealed Through Reason: The Phases of the Jovian Moons a few times, and reminding myself that this is Astronomy SE, I've realized my previous comment is wrong and uncalled for, sorry about that. I think an answer along the lines of your comments would in fact be correct. $\endgroup$– uhohAug 12, 2018 at 0:54
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1$\begingroup$ @Mike yes full, quarter.. $\endgroup$– J. DoeAug 19, 2018 at 5:42
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2 Answers
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From Earth the resolution of is limited by the atmosphere. Turbulence in the atmosphere make it impossible to resolve the moons of Jupiter to more than a few pixels wide.
Amateur refractor telescopes tend to be small and less powerful than reflector telescopes. I'm not aware of any amateur refactor telescope that could resolve a moon of Jupiter to more than a point of light. The eye is unable to resolve an object that is less than about 60 arcseconds and it would need to be closer to 1000 arcseconds before many surface details became visible. The Moon, for comparison, is 1800 arcseconds.
Professional equipment can partially overcome the atmosphere by using adaptive optics, but this is not a feature that is generally available to amateurs.
Jupiter and its moons orbit outside the orbit of Earth, so from our point of view Jupiter is never partially lit less than 99%. The moons are sometimes eclipsed by Jupiter, but they too are never partially lit less than 99%. With amateur equipment, Jupiter and its moons are never anything other than "full".
Even with the Hubble telescope, the resolution is not sufficient to identify phases of the moons.
What Galileo saw was Jupiter, resolved as a disc and 4 moons orbiting it which appeared to him as "stars" (he called them the Medicean stars). The four moons were not always visible, sometimes a moon was hidden in the shadow of Jupiter, or behind Jupiter from our point of view. At other times a moon would be too close to Jupiter to be visible, or outside the field of view of his telescope.
What he realised was that these were bodies in orbit around Jupiter, and that they obeyed the same rule for orbits that Kepler had proposed for the planets.
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Galileo saw Jupiter and its moons, now called the Galilean moons in his honor. They include Io, Europa, Ganymede, and Callisto.
When he took those "images", that period of time was around early January in 1610. During that time, Galileo was testing his 30x magnification telescope (Source).
However in terms of the phases of the Galilean moons, it would definitely require a stronger telescope.
How about some math...
There's a really complicated formula for this here - Website.
In order to see the moons themselves, you can put in the diamter of one of the moons in as R for a rough estimate. I'm going to use Io.
Io's diameter is 3642.58921 km. Its distance is 628287897.6 km.
We insert that into the website/calculator... Getting 0.0003321805004 degrees or 1.19585 arcsecs.
However, since you are referring to a refracting telescope, there definitely is a limit on how much resolution you can get due to blurring as the telescope gets larger and larger lenses are bound to break easily.
The largest refracting telescopes are less than a meter long. We can use diffraction limit to see the limit of their size and viewing before they start diffracting - Diffraction limit.
We can use the wavelength of green, or approximately 530 nm or 5.3e-5 cm as a rough estimate. The largest telescopes are 1 m or 100 cm. We then get 0.000000647 or 6.466e-7 rad. We convert this to arcsecs and get 0.13337082 arcsecs.
That means that Io is clearly visible, but a large telescope is definitely necessary. I would somewhat recommend not doing so, since a singular decent sized telescope probably wouldn't be strong enough...
Edit - 8/19/18 - made a mistake on the calculation, it is actually possible to see Io's phases, but would be rather difficult. Credit to Mike G for pointing it out.
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1$\begingroup$ I get an angular diameter of 1.2 arcsec for Io with Jupiter at opposition. $\endgroup$– Mike GAug 19, 2018 at 3:38
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1$\begingroup$ Oh oops! I just rechecked my work, and I got 1.2 arcsecs as well. Sorry for the mistake - thanks for pointing it out. I'll edit my post. Looks like it is possible. Again, I apologize for the confusion! $\endgroup$ Aug 19, 2018 at 3:43