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This was somewhat inspired by this question but is a bit different: I am interested in if there are any known systems in which the angular size of the eclipsing object is almost the same as the angular size of the object being eclipsed from the surface of a planet, as is the case for the Moon and the Sun as viewed from Earth. This is the only way that one can get "annular" eclipses, or eclipses in which the host star's corona is clearly visible. This could be the case for some moons in the solar system (which requires that they eclipse at all), and at least Phobos in particular seems to have a similar angular size to the Sun as viewed from Mars,

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but it could also be true for some known (or candidate) multiple-planet exoplanetary systems in which the periods of the two planets are not too different. Probably a perusal of the public Kepler candidate sample would be helpful here.

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The Sun's corona is not clearly visible during an annular eclipse, only during a total eclipse that blocks the entire photosphere. (The photosphere is much brighter than the corona.) The Earth-Moon-Sun geometry is coincidentally quite unusual, in that the Moon can just barely block the photosphere, leaving the corona visible all around the visible disk. An eclipse of the Sun seen from the surface of the Moon, where the Earth blocks the photosphere, could still leave part of the corona visible (but refraction through the Earth's atmosphere could cause some interesting effects). – Keith Thompson Sep 26 '13 at 20:28
I haven't crunched the numbers, but solar eclipses caused by a planet passing in front of the Sun as seen from the surface of a moon might be a good place to look. – Keith Thompson Sep 26 '13 at 20:28
@KeithThompson I should mention that the title of my question was edited by Robert Cartaino, I originally asked if other bodies have eclipses that are as "spectacular" as Earth's (which is a bit subjective), annular eclipses being one particularly impressive type of eclipse. – Guillochon Sep 26 '13 at 20:36
How are you distinguishing an annular eclipse from a transit? Must a certain portion of the Sun's disk be covered at maximum obscurity? As viewed from Mars, the Sun has an angular diameter of about 19 arcminutes, Phobos 6.5 arcminutes, Deimos 2 arcminutes. More of a transit than an eclipse, no? – barrycarter Jan 7 at 19:02

This will depend the position of the observer and (obviously) the relative sizes of the star and the eclipsing body.

For an intelligent observer standing on the surface of a planet the most obvious and likely candidate for an eclipsing body would be a moon of that planet. The nearer the planet is to the sun the larger that moon has to be, and the further the planet is away from the star the smaller the moon can be.

Finding planets around stars is hard enough, finding moons that will be orbiting quite closely around those planets across interstellar distances is even harder (I'm not going to say impossible, but it's pretty close) with current technology, so at the moment the answer is "None, that we know of".

Also don't forget that, according to current theories, the moon was formed when a large Mars sized body collided with the nascent Earth, the chances of another Earth/Moon type system is probably remote. This means that most natural satellites are likely to be Phobos sized bodies. Therefore to get an eclipse the planet would have to be further out from the star (so the star looks smaller) and that would tend to put it on the edge of the "Goldilocks" zone, making the likelihood of there being an intelligent observer somewhat rare.

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Some known exoplanets are very close to one another, with one planet appearing very large in the other planet's sky (e.g. Kepler-36). I think near-annular eclipses would be possible in these sorts of systems. – Guillochon Sep 26 '13 at 20:39

In our solar system, the answer to this depends on how you define "annular eclipse" (as opposed to transit).

I wrote to see how big planets' moons appear compared to the sun.

The full results:

Planet/moon combinations closest to annular eclipse (note these numbers are averages, not ranges):

Earth Moon 0.972 
Saturn Epimetheus 0.790 
Saturn Prometheus 0.689 
Saturn Pandora 0.588 
Uranus Perdita 0.54 
Jupiter Amalthea 0.515 
Saturn Iapetus 0.4231 
Saturn Tarqeq 0.4 
Mars Phobos 0.388 
Uranus Cupid 0.28 
Jupiter Thebe 0.249 
Uranus Mab 0.21 
Neptune Nereid 0.199 
Saturn Pan 0.197 
Jupiter Metis 0.188 
Saturn Hyperion 0.1818 
Saturn Atlas 0.15 

Note that the Earth-Moon ratio is much closer to 1 than any of the others.

If you're looking for total eclipses where the moon is only slightly larger than the Sun:

Saturn Janus 1.22 
Jupiter Callisto 1.433 
Pluto S2012P1 1.5 
Uranus Ophelia 1.64 
Uranus Cordelia 1.67 
Uranus Bianca 1.79 
Pluto S2011P1 1.9 
Uranus Desdemona 2.11 
Uranus Rosalind 2.1 
Saturn Enceladus 2.174 
Uranus Belinda 2.21 
Jupiter Europa 2.603 
Uranus Cressida 2.66 
Jupiter Ganymede 2.751 
Saturn Rhea 2.975 
Uranus Juliet 3.00 
Saturn Dione 3.057 
Saturn Tethys 3.733 
Uranus Puck 3.9 
Uranus Portia 4.22 
Saturn Titan 4.324 
Neptune Naiad 4.4 
Jupiter Io 4.83 

And, just in case you're wondering, Charon is 257 times larger in Pluto's sky than the Sun.

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