Hello Nate,
That is a very interesting question.
Here on Earth, a solar eclipse happens when our Moon passes in front of the Sun. Luckily for us, the angular or apparent size of our Moon in the sky is about the same as the angular or apparent size as the Sun. This means that the Moon can sometimes completely block out the Sun in the sky, creating a total solar eclipse. Because the Moon's distance from Earth varies along its orbit, sometimes the angular size of the Moon is actually a little bit smaller than the Sun's angular size, so a ring-shaped section of the Sun is still visible during the eclipse. We call this an annular eclipse. We can also have partial solar eclipses, where only a portion of the Sun is blocked by the Moon.
If you were on another planet in the solar system, the type of solar eclipse you could see would depend upon the Sun's angular or apparent size in the sky, the angular or apparent size of the moon (or other object) passing in front of the Sun, and the relative orbital alignments of the Sun and the object causing the eclipse. If the apparent size of the object that passes in front of the Sun is a lot smaller than the apparent size of the Sun, scientists actually would say that a transit had occurred instead of an eclipse.
The Mars rovers have taken some pictures of eclipses, or more accurately "transits" of Mars' moons Phobos and Deimos across the Sun. For more information, you can visit this web site: http://marsrovers.jpl.nas...unity/20040308a.html
The angular sizes of Mars' tiny moons are so small that they can never entirely block out the Sun for an observer on the surface of Mars, so solar "eclipses" on Mars are more properly called "transits." Scientists can learn a lot by studying eclipses on other planets. By carefully studying the timing of the transits of Phobos and Deimos across the Sun observed by the Mars rovers, improved our knowledge of the orbits of Phobos and Deimos. Scientists also used the shape of the shadows cast by Phobos and Deimos to learn more about how these two small moons are shaped.
Kris