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What strength of telescope is required to observe some of the non-Galilean moons of Jupiter?

My current telescope at 50 magnification resolves the Galilean moons well, but I'm guessing it's far below what's needed to observe any of the smaller moons. Given that the largest is 5% of the size of the smallest Galilean moon (according to what I found on Wikipedia, in Moons of Jupiter), is it even possible to observe them with an amateur telescope?

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First of all, it's not magnification that determines whether you can see Jupiter's moons: it's aperture (diameter of main lens or mirror). The same is true in general in astronomy: aperture wins!

There are two problems with Jupiter's smaller moons. First, they are small, so don't reflect much light. Secondly, they are close to one of the brightest objects in the sky, so tend to be washed out by Jupiter's brilliance. So you need a large aperture to even see the tiny specks of light, and then good quality, high contrast optics that won't be overwhelmed by stray light from Jupiter.

The Galilean moons range in brightness from 4.6 to 5.6 magnitude. The next brightest moons are Amalthea (14.1) and Himalia (14.6). Stars of magnitude 14.1 to 14.6 require at least an aperture of 250mm (10-inch) to be visible, and even then they require perfectly dark skies, high magnification, and a trained eye. Amalthea orbits very close to Jupiter, 181,400 km as compared to 421,800 km for Io, so it will be completely overwhelmed by Jupiter except in the largest telescopes. Himalia orbits much farther away, 11,461,000 km, nearly 10 times farther than Callisto (1,883,000 km). As a result, Himalia is the most frequently observed non-Galilean moon. All the other moons of Jupiter are 16th magnitude or fainter, making them very difficult to see visually. Most have been discovered photographically.

My friend Alan Whitman has observed Himalia with a 400mm (16-inch) Newtonian. (RASC Observer's Handbook 2011, p.230).

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I take it Alan Whitman's observation was done in very dark ideal observing conditions as you mentioned are needed for the 14.1+ magnitude stars? –  jball Jun 5 '11 at 17:51
    
Yes, Alan observes from very dark sites in southern British Columbia and Arizona. –  Geoff Gaherty Jun 5 '11 at 20:27
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Incidentally, I have seen stars down to magnitude 15.9 with my 11-inch Schmidt-Cassegrain here in Ontario, but not that close to Jupiter. I'll have a look for Himalia when Jupiter gets back into view! –  Geoff Gaherty Jun 5 '11 at 20:33
    
Note that the first non-Galilean moon to be discovered, Amalthea, wasn't seen until 1892. It's fairly safe to assume that you won't be able to see any of them unless your telescope is at least as good as the best that was available in 1892. –  Keith Thompson Dec 22 '11 at 2:50

I think that I have seen Himalia or Amalthea on Dec, 20 in Xalapa, Veracruz, Mexico. I thought that it was a star that was very close to the limb, but about two hours later it appeared as a tiny speck on one side of Jupiter. It was a pin size dot that was not seen in my excellent meade 10" Schmidt. It was so tiny that I couldn't immagine what it was. It was definitely a shadow of a very small satelite. There is no substitute for aperture.

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