Pluto could be demoted to "dwarf" status when astronomers meeting in the Czech capital vote on a formal definition for the term "planet".
From hero to zero?
About 2,500 experts are in Prague for the International Astronomical Union's (IAU) general assembly.
Any decision to demote Pluto is likely to be unpopular in some quarters.
A week ago, the IAU proposed a scheme that would retain Pluto as a planet and bring three other objects into the cosmic club.
Instead, it has come up with other options that could see the ninth planet airbrushed out of school and university textbooks. The voting began at 1400 BST.
One option to be put to the vote would draw a distinction between eight "planets" - Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune - and the "dwarf planets", including Pluto. This would categorically relegate Pluto.
Another option would draw a distinction between eight "classical planets" and the "dwarf planets".
Pluto could be relegated to the category of "dwarf-planet" and become the prototype for a family of icy bodies beyond Neptune's orbit, which the resolution calls "plutonian objects".
Resolutions being considered by the group, the official arbiter of heavenly bodies, would define a planet as "a celestial body that is in orbit around the Sun, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a ... nearly round shape, and has cleared the neighborhood around its orbit."
Anything less would be either a dwarf planet, as in Pluto's case, or a small solar system body, which would cover many asteroids, comets or other natural satellites.
"There would be only eight planets, plus the dwarf planets," said Japanese astronomer Junichi Watanabe, a member of the IAU's planet definition committee.
"Some say, 'No, Pluto is a nice planet' and should remain one," he added. "It's an important object that has played an important role. But this is a natural way to draw a line."
Experts have been divided over whether Pluto - further away and considerably smaller than the eight other planets in our Solar System - deserves the title.
Since the early 1990s, astronomers have found several other objects of comparable size to Pluto in an outer region of the Solar System called the Kuiper Belt.
Some astronomers believe Pluto belongs with this population of small, icy "Trans-Neptunians", not with the objects we call planets.
Allowances were once 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 object in the Kuiper Belt.
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.