solar system - Planets and Pluto? Neptune?

I answered this same question at physics.SE. I specifically joined this part of the SE network to address this duplicate question at this site.

The astronomy community faced two crises with regard to what constitutes a "planet", first in the mid 19th century, and more recently at the start of the 21st century. The first crisis involved the asteroids. The second involved trans-Neptunian objects. Both crises challenged astronomers to question what a "planet" was.

1 Ceres, 2 Pallas, 3 Juno, and 4 Vesta were discovered in quick succession during the first decade of the 19th century. There was no international astronomical organization at the time of these discoveries; the International Astronomical Union wouldn't be formed for another century. Instead, the designation of what constituted a "planet" fell on the major astronomical almanacs such as the Berliner Astronomisches Jahrbuch (BAJ). Those discoveries at the start of the 19th century were treated as newly discovered "planets". This situation remained static for about 40 years.

That changed in 1845 with the discovery of 5 Astraea. During the 1850s, the list of objects orbiting the Sun grew to 50, and during the 1860s, the list grew to over 100. The response of the BAJ and others was to demote Ceres, Pallas, Juno, and Vesta from planethood status to some lesser status, either minor planet or asteroid. Astronomers didn't have a clear-cut concept of what constituted a planet other than that they should somehow be large. Ceres, the largest of the bunch, is not very large. The end result of all of these discoveries starting in 1845 was that the first four discovered asteroids were demoted from planethood status.

The second crisis started in 1992 with the discovery of (15760) 1992 QB₁. By 2006, the number of trans-Neptunian objects had grown significantly. Were these things "planets", or something else? Some astronomers, notably Alan Stern, wanted the term "planet" to be extremely inclusive. Most astronomers balked at this idea.

Paradoxically, it was Alan Stern himself, along with Harold Levison, who provided the key criterion of "clearing the neighborhood" that lies at the heart of what the IAU deems to constitute a "planet." Their paper, Stern and Levison, "Regarding the criteria for planethood and proposed planetary classification schemes," Highlights of Astronomy 12 (2002): 205-213 suggested splitting "planet" into two categories, "überplanet" (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune) and "unterplanet" (Pluto+Charon, Eris, Ceres, Sedna, and a host of others).

Stern is being quite hypocritical when he rants that there is no clear-cut boundary between "planets" and "dwarf planets." The boundary is huge, and Stern knows this. The ratio of the square of an object's mass to its orbital radius about the Sun is key in determining whether an object can clear most of the junk from the vicinity of the object's orbit. There is a five order of magnitude difference between the smallest of the planets and the largest of the dwarf planets in terms of this ratio. This five order of magnitude difference figures predominantly in that paper by Stern and Levison.

The only difference between the proposal by Stern and Levison versus the voted-upon IAU resolution is that while Stern and Levison wanted to designate hundreds (and perhaps thousands) of objects into subcategories of "planet" ("überplanet" and "interplant"). On the other hand, the IAU chose to designate those objects as the mutually exclusive terms "planets" and "dwarf planets". This is consistent with how astronomers dealt with that first crisis. Planets should be "large." Stern and Levison provided the necessary ammunition to distinguish large from not so large.