Clearing the neighbourhood facet of planet
"Clearing the neighbourhood" (or dynamical dominance) around a celestial body's orbit describes the body becoming gravitationally dominant such that there are no other bodies of comparable size other than its natural satellites or those otherwise under its gravitational influence.
"Clearing the neighbourhood" is one of three necessary criteria for a celestial body to be considered a planet in the Solar System, according to the definition adopted in 2006 by the International Astronomical Union (IAU). In 2015, a proposal was made to extend the definition to exoplanets.In the end stages of planet formation, a planet, as so defined, will have "cleared the neighbourhood" of its own orbital zone, i.e. removed other bodies of comparable size. A large body that meets the other criteria for a planet but has not cleared its neighbourhood is classified as a dwarf planet. This includes Pluto, whose orbit intersects with Neptune's orbit and shares its orbital neighbourhood with many Kuiper belt objects. The IAU's definition does not attach specific numbers or equations to this term, but all IAU-recognised planets have cleared their neighbourhoods to a much greater extent (by orders of magnitude) than any dwarf planet or candidate for dwarf planet.The phrase stems from a paper presented to the 2000 IAU general assembly by the planetary scientists Alan Stern and Harold F. Levison. The authors used several similar phrases as they developed a theoretical basis for determining if an object orbiting a star is likely to "clear its neighboring region" of planetesimals based on the object's mass and its orbital period. Steven Soter prefers to use the term "dynamical dominance", and Jean-Luc Margot notes that such language "seems less prone to misinterpretation".Prior to 2006, the IAU had no specific rules for naming planets, as no new planets had been discovered for decades, whereas there were well-established rules for naming an abundance of newly discovered small bodies such as asteroids or comets. The naming process for Eris stalled after the announcement of its discovery in 2005, because its size was comparable to that of Pluto. The IAU sought to resolve the naming of Eris by seeking a taxonomical definition to distinguish planets from minor planets.where µ is a dimensionless parameter, M is the mass of the candidate planet, and m is the mass of all other bodies that share an  orbital zone, that is all bodies whose orbits cross a common radial distance from the primary, and whose non-resonant periods differ by less than an order of magnitude.The order-of-magnitude similarity in period requirement excludes comets from the calculation, but the combined mass of the comets turns out to be negligible compared to the other small Solar System bodies, so their inclusion would have little impact on the results. µ is then calculated by dividing the mass of the candidate body by the total mass of the other objects that share its orbital zone. It is a measure of the actual degree of cleanliness of the orbital zone. Soter proposed that if µ > 100, then the candidate body be regarded as a planet.Margot's Π
Astronomer Jean-Luc Margot has proposed a discriminant, Π (pi), that can categorise a body based only on its own mass, its semi-major axis, and its star's mass. Like Stern–Levison's Λ, Π is a measure of the ability of the body to clear its orbit, but unlike Λ, it is solely based on theory and does not use empirical data from the Solar System. Π is based on properties that are feasibly determinable even for exoplanetary bodies, unlike Soter's µ, which requires an accurate census of the orbital zone.
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