Astronomers are gathering in the Czech capital, Prague, hoping to define exactly what counts as a planet.
The International Astronomical Union (IAU) hopes to settle the question of Pluto, which was first spotted in 1930.
Experts are divided over whether Pluto - further away and considerably smaller than the eight other planets in our Solar System - deserves the title.
The stakes were raised when a bigger planet-type body, known as 2003 UB313, was discovered by a US astronomer.
Any decision to downgrade Pluto would send shockwaves through the scientific community, instantly outdate textbooks, and change how the basics of the Solar System are taught in schools.
There are suggestions the scientists could decide to include Pluto in a new classification system that marks it out as different to the eight larger planets.
Dr Andrew Coates of the Mullard Space Science Laboratory in Dorking said: "Pluto has always been a bit of an oddity as a planet.
"It has this orbit which is tipped with respect to the other planets and is egg-shaped, so Pluto spends some of its time a bit closer to the Sun than Neptune. But in 1930 a planet seemed to be the best way to describe it."
IAU president Ronald Ekers said astronomers had to agree on a definition for planets: "People have to be able to agree on a terminology that's used to describe things in the Universe," he told journalists in Prague.
Professor Ekers added: "We don't want an American version, a European version and a Japanese version."
Pavel Suchan, of the IAU meeting's local organisation committee, said delegates were locked in a stalemate. "One half wants Pluto to remain a planet, the other half says Pluto is not worth being called a planet."
Since 1930, astronomers have become aware of a vast population of small, icy bodies resembling Pluto that orbit the Sun beyond Neptune, in a region called the Kuiper Belt.
This led some astronomers to argue that Pluto belonged with this population of "icy dwarfs", not with the objects we call planets.
Allowances could once be made for Pluto on account of its size. At just 2,360km (1,467 miles) across, Pluto is significantly smaller than the other planets. But until recently, it was still the biggest known Kuiper Belt Object (KBO).
That changed with the discovery of 2003 UB313 by Professor Mike Brown and colleagues at the California Institute of Technology (Caltech).
After being measured with the Hubble Space Telescope, it was shown to be some 3,000km (1,864 miles) in diameter, making it larger than the ninth planet.
Now delegates to the Prague conference are being asked to agree for the first time on a formal definition of what a planet is.
"My feeling is that they would like to re-classify Pluto. One idea would be to make Pluto an "ice dwarf". This would be a new subdivision of the planet family, rather like the asteroids," said Peter Bond of the UK's Royal Astronomical Society.
One potential outcome of the meeting would be the promotion of 2003 UB313 - nicknamed Xena, after the TV warrior princess - into the exclusive club of "official" planets.
Some observers even believe the new definition of planet could cover other objects smaller than both Pluto and Xena. These include the distant objects Sedna and Quaoar.
Alternatively, Pluto's status as the ninth planet could also be in danger if the experts decide it no longer makes the grade.
"It could mean the number of planets leaps to 20 or more, or it drops to eight. But I think most people would prefer not to drop Pluto altogether," Mr Bond told the BBC News website.
About 3,000 astronomers and scientists are meeting in Prague, where the issue will be put to a vote.
The meeting opens on Monday and is due to last 12 days.