How did astronomers determine Pluto wasn't a planet?
Pluto's status was change by a vote at the International Astronomical Union.
Until recently any body orbiting the Sun was called a planet. When Pluto was discovered it was naturally given planet status.
Curiously the asteroid Ceres was discovered it was initially given planet status. Ceres was discovered long before Pluto. It was however discovered that Ceres was one of many bodies orbiting between Mars and Jupiter. All of them, including Ceres, were designated asteroids.
More recently, other bodies such as Eris, have been discovered. The International Astronomical Union (IAU) voted on a more format classification system. There are three requirements for a body to be a planet.
First, the body must be orbiting the Sun. This excluded the larger moons such as Titan and Charon.
Second, the body must be in hydrostatic equilibrium. This means it must be spheroidal in shape due to its gravity.
Thirdly, the body must have cleared its orbit of other bodies, except for moons.
The IAU created a new classification called Dwarf Planet which meet the first two criteria but not the third. This lead to the demotion of Pluto to Dwarf Planet. Four other bodies, Ceres, Haumea, Makemake and Eris were promoted to Dwarf Planet status.
The decision was controversial. Many people, including myself, still regard Pluto as a planet.