At last count (last I heard anyway), Jupiter has 62 moons, while Saturn has 35. Mars has 2 moons.

However, the majority of the moons of Jupiter and Saturn, and all of Mar's moons are little more than captured asteroids. They're not even spherical.

Tradition aside, should these satellites be counted as moons?
Or should the term "moon" be restricted to bodies large enough to become spherical under their own gravity, aka big and round.

And if not, what exactly would the lower cut off limit be for determining if something is a moon, or just a satellite body? Surely a rock the size of a baseball cannot be called a moon...

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AFAIK, there is no precise definition, but IMO there is room for the smaller irregular-shaped moons to be called moons. Probably the biggest criteria to be called a moon is that it is an object in a stable orbit around a planet, which brings us to another definitional connundrum. What is a planet?

I would argue that Titan is more a planet than Pluto or Mercury.

Well, just like a moon is an object orbiting a planet, a planet must be orbiting the sun. So, Titan doesn't qualify.

So what do you call an object in stable orbit around a moon?

By who's definition? IIRC, there is no formal definition as yet.

Tomba: I don't think there would be a stable orbit like that.

???? Doesn't a dictionary qualify? http://dictionary.reference.com/search?q=moon

I don't believe you can have a stable orbit around a moon, the gravitational attraction of the parent planet would drag on it every time it orbitted nearest to said planet. That field would drag it out of any hope for a stable orbit, unless it somehow, miraculously, stabilized into a figure 8 orbit without tearing itself apart.

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But he that sows lies in the end shall not lack of a harvest, and soon he may rest from toil indeed while others reap and sow in his stead. -J.R.R. Tolkien, The Silmarillion

One weakness with the current definition of moon is that there is no guidance for a small chunk of rock or ice. When is an object a moon versus just another particle in a ring?

There have been numerous spacecraft that have orbited our Moon, though admittedly I'm not sure what sort of adjustments they had to make to maintain their orbits.

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I guess that apart from a stable orbit aruond a planet, it also has to 'fly' on its own, not in a larger group in approximately the same orbit. Thus you exclude rings. As for minimum size, that's harder to decide...

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Interesting, as I understand it a few of Saturn's and Jupiter's moons are co-orbital.

http://www.solarviews.com/eng/janus.htm

Take Janus and Epimethius for example.

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Russ: The Dictionary is certainly source to consider, when determining how a word is used in common parlance. However, as anyone with any science or technical background can verify, it is not an authoritative source for professional jargon.

So, if we are applying the common man's definitions, you are quite correct. However, since this is an Astronomy forum, I assumed we were talking in terms of the jargon of Astronomers. Astronomers have no formal definition of planet. It is a topic that is actually in hot debate in recent years with the discoveries on Titan and extra-solar planets, particularly the planets that roam free from any star.

I am not sure if there is a formal definition of "Moon", but my suspicion is that it is as nebulous as "planet". I will have to look it up.

That's what I feared... Allright, my definition doesn't work! There goes my chance to make it in the science history books: "The generally agreed on definition of what is a moon and what isn't, informally called 'Fram's definition'... ".

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LOL, this discussion came up related to Cassini over the possibility of finding new shepard moons in the rings. Its probably this mission that will start to put a hard line between what's a moon and what's orbital debris.

I suppose my own personal take on it would be, any object in orbit around a planet which is individually identifiable as separate and distinct from other bodies orbiting a planet.

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Honestly, I doubt any universal definition will ever be satisfactory to everyone involved. People interested in celestial mechanics will always insit that a moon orbits a planet, and a planet orbits a star. However, people more interested in the composition of the planet will look at Titan, and be hard pressed not to call it a planet.

Edit: As to the size limit for a moon, I propose that we set the minimum at a size where a human could walk/jump on the surface without risk of flying off into space, and without noticably altering the orbit of the "moon". I am not sure whether all of the currently identified moons would meet this size limit.

If this were necessarily true, one could make the same argument for the Earth/moon/sun system. Every time the Moon's orbit brings it directly between us and the sun, it is closest to the sun and thus experiences more gravitational pull in that direction. However as we all know, the gravitational attraction of the sun has never yanked the moon out of its orbit around the Earth. Without doing the math involved it is simple enough to say that there is a certain critical distance, after which the gravitational pull of the sun would outpull the gravity of the Earth. Anything within this point is not pulled away from the Earth because the Earth pulls harder.

There must therefore be a region of space around the moon where its gravitational pull is greater than that of the Earth. If there was not, then the rockets we fired to the moon would never have been able to land there, and would have fallen back to the Earth instead. This region of space is likely rather small, and the chances of our Moon capturing a satellite that would orbit within this critical distance are equally small, nevertheless there do exist stable orbits around the Moon (and thus any moon of any planet), its just that a configuration happening naturally is unlikely.

I'd suggest the minimum size be set at the diameter of the Death Star. After all, we know that it's the size of a "small moon", and that's good enough for me.

Yes, size is the big source of ambiguity. The definition just says "larger than an asteroid or comet," but what does that really mean? My criteria would probably include a gravity field strong enough to make it roughly spherical (which would exclude many moons, including Mars's).

A better word (and often used by astronomers) may be satellite, for which size is irrelevant.
I suspect astronomers simply don't care, which is why you rarely see any controversy over the issue. Planet, asteroid, minor planet? Not that important. Moon or just a satellite? Not that important either.

But you won't ever see moon and planet being interchanged.

This is all well and good, but how big is this "moon around a moon" we're talking about? Yes, a satellite can be made to orbit in a stable and reasonably circular orbit, 50 miles from the moon - but are you suggesting we call a 30m rock at that same distance another moon? Any "moon around a moon" of reasonable size would be larger, orbit much further away, and thus be perturbed quite a lot by its neighboring planet.