The object of their musing is Pluto, usually the farthest planet from the Sun (though this year, for the first time this decade, its elliptical orbit passes inside that of Neptune). Discovered in 1930, almost 100 years after Neptune, Pluto takes 248 years to orbit the Sun and has a diameter of just 2,300km (1,440 miles), less than that of our own Moon. Its mass is just 0.2 per cent of that of the Earth, though it can boast its own moon, Charon, with a diameter of 1,270km.
But the IAU thinks that is not sufficient to merit inclusion with a grouping that ranges up to the huge Jupiter, 318 times the mass of Earth. Instead they are thinking of either reclassifying Pluto as a "minor planet", or lumping it in with an entirely new class of objects.
The underlying problem is that nobody has ever defined what a planet really is.
However, in many ways Pluto does not seem to be similar to the eight bodies that are. In fact it is more like a comet: its orbit is more elliptical than ours, and is inclined to the plane of the other eight planets by 17 degrees.
Even Patrick Moore, the respected astronomer, comments in his book Mission to the Planets that: "Altogether, Pluto is a maverick, and there are grounds for doubting whether it is worthy of true satellite status." Towards the end of the book, he says: "Pluto cannot be classed as a bona fide planet."
Many astronomers think that rather than being made from material that gathered at the centre of the solar system about 6 billion years ago - as the "proper" planets did - Pluto is a comet that was captured from a far more distant group of bodies called the Kuiper Belt. That belt is thought to be the source of the comets that occasionally dive into the centre of the solar system, past the Sun.
Hence the IAU's unease. "For at least 20 years, it's been obvious that Pluto doesn't fit," says Mike A'Hearn, an astronomer at the University of Maryland, who heads the Planetary Systems Sciences Division of the IAU.
Dr A'Hearn wants to create a new class of objects for ice-balls that orbit beyond Neptune, and call them Trans-Neptunian Objects. Pluto would then be Trans-Neptunian Object No 1.
Brian Marsden, of the IAU's Minor Planet Centre, says he has a better idea. He'd like to see Pluto classified as a "minor planet," of which there are thousands, then made to take a number. The prized number 10,000 will probably come up next month. And, Professor Marsden says, it would not be a demotion for Pluto to be referred to as the 10,000th minor planet: "It's an honour," he insists.
But to Alan Hale, one of the astronomers to discover Comet Hale-Bopp, the whole debate is rather silly. "A hypothetical resident of Jupiter would probably laugh at our calling Earth a `major planet'," he points out.