"What is the formal definition of a planet?"

The International Astronomical Union defines "planet" as a celestial body that, within the Solar System,[1]

(a) is in orbit around the Sun;
(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape; and
(c) has cleared the neighbourhood around its orbit;

or within another system,[2]

(i) is in orbit around a star or stellar remnants;
(ii) has a mass below the limiting mass for thermonuclear fusion of deuterium; and
(iii) is above the minimum mass/size requirement for planetary status in the Solar System.

Our solar system is thus considered to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. Under a separate resolution, it is also considered to have three dwarf planets: Ceres, Pluto, and Eris. There have been more than two hundred planets discovered orbiting other stars to date.[3]

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Planetary status controversy

Pluto's official status as a planet has been a constant subject of controversy, fueled by the past lack of a clear definition of planet, since at least as early as 1992, when the first Kuiper Belt Object, (15760) 1992 QB1, was discovered. Since then, further discoveries intensified the debate in the 21st century.

Omission from museum models

Museum and planetarium directors occasionally created controversy by omitting Pluto from planetary models of the solar system. Some omissions were intentional; the Hayden Planetarium reopened after renovation in 2000 with a model of 8 planets without Pluto. The controversy made headlines in the media at the time.[26]

Commemoration as a planet

Pluto is shown as a planet on the Pioneer plaque, an inscription on the space probes Pioneer 10 and Pioneer 11, launched in the early 1970s. The plaque, intended to give information about the origin of the probes to any alien civilization that might in the future encounter the vehicles, includes a diagram of our solar system, showing nine planets. Similarly, an analog image contained within the Voyager Golden Record included on the probes Voyager 1 and Voyager 2 (also launched in the 1970s) includes data regarding Pluto and again shows it as the ninth planet.

Elements 92, 93, and 94 are named uranium, neptunium, and plutonium respectively after Uranus, Neptune, and Pluto.

New discoveries ignite debate
Pluto compared to Eris, 2005 FY9, 2003 EL61, Sedna, Orcus, Quaoar, and Varuna compared to Earth (artist's impressions; no detailed photographs exist).
Pluto compared to Eris, 2005 FY9, 2003 EL61, Sedna, Orcus, Quaoar, and Varuna compared to Earth (artist's impressions; no detailed photographs exist).

Continuing advances in telescope technology allowed for further discoveries of Trans-Neptunian objects in the 21st century, some of comparable size to that of Pluto. In 2002, 50000 Quaoar was discovered, with a 1,280 kilometers diameter, making it a bit more than half the size of Pluto. In 2004, the discoverers of 90377 Sedna placed an upper limit of 1,800 kilometers on its diameter, near Pluto's diameter of 2,320 kilometers.

On July 29, 2005, a Trans-Neptunian object later named Eris was announced, which on the basis of its magnitude and simple albedo considerations is assumed to be slightly larger than Pluto. This was the largest object discovered in the solar system since Neptune in 1846. Discoverers and media initially called it the "tenth planet", although there was no official consensus at the time on whether to call it a planet. Others in the astronomical community considered the discovery to be the strongest argument for reclassifying Pluto as a minor planet.

The last remaining distinguishing feature of Pluto was now its large moon, Charon, and its atmosphere; these characteristics are probably not unique to Pluto: several other Trans-Neptunian objects have satellites; and Eris' spectrum suggests that it has a similar surface composition to Pluto, as well as a moon, Dysnomia, discovered in September 2005. Trans-Neptunian object 2003 EL61 (nicknamed "Santa") has two moons (one of which is nicknamed "Rudolph") and is the fourth largest TNO behind Eris, Pluto, and 2005 FY9 (nicknamed "Easterbunny").

IAU Decision

Main article: 2006 redefinition of planet

The debate came to a head in 2006 with an IAU resolution that created an official definition for the term "planet". According to this resolution, there are three main conditions for an object to be considered a 'planet':

1. The object must be in orbit around the Sun.
2. The object must be massive enough to be a sphere by its own gravitational force. More specifically, its own gravity should pull it into a shape of hydrostatic equilibrium.
3. It must have cleared the neighborhood around its orbit.

Pluto fails to meet the third condition.[27] The IAU further resolved that Pluto be classified in the simultaneously created dwarf planet category, and that it act as prototype for a yet-to-be-named category of trans-Neptunian objects, in which it would be separately, but concurrently, classified.

Impact of the IAU decision

There has been resistance amongst the astronomical community towards the reclassification,[28] dubbed the "Great Pluto War" by some astronomers.[29][30] Alan Stern, principal investigator with NASA's "New Horizons" mission to Pluto, has publicly derided the IAU resolution, stating that "the definition stinks" albeit "for technical reasons."[31] Stern's current contention is that by the terms of the new definition Earth, Mars, Jupiter and Neptune, all of which share their orbits with asteroids would be excluded.[32] However, his own published writing has supported the new list of planets, as "our solar system clearly contains" eight planets that have cleared their neighborhoods, however, he does not deny planetary classification to objects like Pluto & Ceres that have not "cleared their neighborhood".[33]. Marc W. Buie of the Lowell observatory has voiced his opinion on the new definition on his website and is one of the petitoners against the definition. [34]Others have supported the IAU. Mike Brown, the astronomer who discovered Eris, said "through this whole crazy circus-like procedure, somehow the right answer was stumbled on. It’s been a long time coming. Science is self-correcting eventually, even when strong emotions are involved."[35]

Among the general public, reception is mixed amidst widespread media coverage. Some have accepted the reclassification, while some are seeking to overturn the decision, with online petitions urging the IAU to consider reinstatement. A resolution introduced by some members of the California state assembly light-heartedly denounces the IAU for "scientific heresy," among other crimes.[36] Others reject the change for sentimental reasons, citing that they have always known Pluto as a planet and will continue to do so regardless of the IAU decision[37].

in the solar system, a planet is a celestial body that:

    * is in orbit around the Sun,
    * has sufficient mass so that it assumes a hydrostatic equilibrium (nearly round) shape, and
    * has "cleared the neighborhood" around its orbit.

A non-satellite body fulfilling only the first two of these criteria is classified as a "dwarf planet", whilst a non-satellite body fulfilling only the first criterion is termed a "small solar system body" (SSSB). The definition was a controversial one, and has been both criticised and supported by different astronomers.

According to the definition there are currently eight planets and three dwarf planets known in the solar system. The definition does not apply outside the solar system, and so does not include provision for extrasolar planets. Exoplanets are covered separately under a 2003 draft guideline for the definition of planets.

Since the discovery of Pluto in 1930 astronomers had considered the solar system to have nine planets and assorted other bodies. However, since 2000 the discovery of at least three bodies (Quaoar, Sedna and Eris), all comparable to Pluto in terms of size and orbit, had led to a situation where either the minor bodies would have to be added to the list of officially recognized planets or older ones would need to be removed in order to ensure consistency in definition. There were also concerns surrounding the classification of planets in other solar systems. In 2006 the matter came to a head with the need to categorize and name the recently-discovered trans-Neptunian object Eris, which, being larger than Pluto, was thought to be at least equally deserving of the status of ’planet’.


On the other hand, Pluto is a dog, silly!

24 August 2006, Prague: The first half of the Closing Ceremony of the 2006 International Astronomical Union (IAU) General Assembly has just concluded. The results of the Resolution votes are outlined here.

........

IAU Resolution: Definition of a Planet in the Solar System
Contemporary observations are changing our understanding of planetary systems, and it is important that our nomenclature for objects reflect our current understanding. This applies, in particular, to the designation "planets". The word "planet" originally described "wanderers" that were known only as moving lights in the sky. Recent discoveries lead us to create a new definition, which we can make using currently available scientific information.

RESOLUTION 5A
The IAU therefore resolves that "planets" and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way:

(1) A "planet"1 is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

(2) A "dwarf planet" is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape2 , (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.

(3) All other objects3 except satellites orbiting the Sun shall be referred to collectively as "Small Solar-System Bodies".


1The eight "planets" are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
2An IAU process will be established to assign borderline objects into either dwarf planet and other categories.
3These currently include most of the Solar System asteroids, most Trans-Neptunian Objects (TNOs), comets, and other small bodies.


IAU Resolution: Pluto

RESOLUTION 6A
The IAU further resolves:

Pluto is a "dwarf planet" by the above definition and is recognized as the prototype of a new category of trans-Neptunian objects.

 

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There were Nine Planets before August 2006.  However, now The International Astronomical Union only recognize 8 planets now as you can read below.

 

How many planets are in the Solar System?

This popular question now has a new formal answer according the International Astronomical Union (IAU): eight. Last week, the IAU voted on a new definition for planet and Pluto did not make the cut. Rather, Pluto was re-classified as a dwarf planet and is considered as a prototype for a new category of trans-Neptunian objects. The eight planets now recognized by the IAU are: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Solar System objects now classified as dwarf planets are: Ceres, Pluto, and the currently unnamed 2003 UB313. Planets, by the new IAU definition, must be in orbit around the sun, be nearly spherical, and must have cleared the neighborhood around their orbits. The demotion of Pluto to dwarf planet status is a source of continuing dissent and controversy in the astronomical community.

 

 

 

A couple books why Pluto is no longer a Planet

In resolution 5, "Definition of a Planet in the Solar System," The International Astronomical Union defines the term "planet" as a celestial body that:
(a) is in orbit around the Sun;
(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape; and
(c) has cleared the neighborhood around its orbit.

In contrast, a "dwarf planet" is a celestial body that
(a)is in orbit around the Sun,
(b)has sufficient mass for its self-gravity to overcome rigid body forces so
that it assumes a hydrostatic equilibrium (nearly round) shape2,
(c)has not cleared the neighbourhood around its orbit,and
(d)is not a satellite.

This definition was adopted on August 2006, at the IAU's XXVIth General Assembly. Under this definition, the solar system is considered to have eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune.

Under a separate resolution, the solar system was defined to have three dwarf planets: Ceres, Pluto and Eris.

According to Scientific American, January 2007:

"The International Astronomical Union (IAU), astronomy’s main professional society, [defines] a planet as an object that orbits a star, is large enough to have settled into a round shape, and, crucially, ’has cleared the neighborhood around its orbit.’"

It goes on to explain this last bit is important in that the mass of an object in relation to the combined mass of debris in its "neighborhood" is the deciding factor in what becomes a planet.

Pluto has a mass ratio of something like 0.07 while even little Mercury has a mass ratio of 1000000. So Pluto has not cleared its neighborhood. That is, it has not exercised gravitational dominance over other objects in its vicinity. To call Pluto a planet is to also call all the other Kuiper Belt Objects (KBOs) planets as well. This is a little similar to the recategorization in 1852 when all the known asteroids were demoted from planet status.

Some people think Pluto should be "grandfathered in" as a planet under the revised definition, but an important fact to consider is that when scientists use words like "planet" they do so with precise meanings -- it won’t do, for instance, to say "the planets, except for Pluto".

However, us non-scientists can probably go on calling Pluto a planet all we want, as long as we recognize that in scientific contexts, the precise definition is not arbitrary and does not include Pluto. I suspect this is what will happen -- it won’t be the first time a scientific definition of a word is different, subtly, than the general usage of that word. See "theory".