Incelestial mechanics, "clearing the neighbourhood" (ordynamical dominance) around acelestial body's orbit describes the body becoming gravitationally dominant such that there are no other bodies of comparable size other than itsnatural satellites or those otherwise under its gravitational influence.

"Clearing the neighbourhood" is one of three necessary criteria for a celestial body to be considered aplanet in theSolar System, according tothe definition adopted in 2006 by theInternational Astronomical Union (IAU).^[1] In 2015, a proposal was made to extend the definition toexoplanets.^[2]

In the end stages ofplanet formation, aplanet, 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 adwarf planet. This includesPluto, whose orbit is partly insideNeptune's and shares its orbital neighbourhood with manyKuiper 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 (byorders of magnitude) than any dwarf planet or candidate for dwarf planet.^[2]

The phrase stems from a paper presented to the 2000 IAU general assembly by theplanetary scientistsAlan Stern andHarold F. Levison. The authors used several similar phrases as they developed a theoretical basis for determining if an object orbiting astar is likely to "clear its neighboring region" ofplanetesimals based on the object'smass and itsorbital period.^[3]Steven Soter prefers to use the termdynamical dominance,^[4] andJean-Luc Margot notes that such language "seems less prone to misinterpretation".^[2]

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 forEris 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 fromminor planets.

The phrase refers to an orbiting body (a planet orprotoplanet) "sweeping out" itsorbital region over time, bygravitationally interacting with smallerbodies nearby. Over many orbital cycles, a large body will tend to cause small bodies either toaccrete with it, or to be disturbed to another orbit, or to be captured either as asatellite or into aresonant orbit. As a consequence it does not then share its orbital region with other bodies of significant size, except for its own satellites, or other bodies governed by its own gravitational influence. This latter restriction excludes objects whose orbits may cross but that will never collide with each other due toorbital resonance, such asJupiter andits trojans,Earth and3753 Cruithne, orNeptune and theplutinos.^[3] As to the extent of orbit clearing required,Jean-Luc Margot emphasises "a planet can never completely clear its orbital zone, because gravitational and radiative forces continually perturb the orbits of asteroids and comets into planet-crossing orbits" and states that the IAU did not intend the impossible standard of impeccable orbit clearing.^[2]

In their paper,Stern andLevison sought an algorithm to determine which "planetary bodies control the region surrounding them".^[3] They definedΛ (lambda), a measure of a body's ability to scatter smaller masses out of its orbital region over a period of time equal to the age of the Universe (Hubble time).Λ is a dimensionless number defined as

$${\displaystyle \mathrm{\Lambda }=\frac{m^2}{a^{3/2}}k}$$

wherem is the mass of the body,a is the body's semi-major axis, andk is a function of the orbital elements of the small body being scattered and the degree to which it must be scattered. In the domain of the solar planetary disc, there is little variation in the average values ofk for small bodies at a particular distance from the Sun.^[4]

IfΛ > 1, then the body will likely clear out the small bodies in its orbital zone. Stern and Levison used this discriminant to separate thegravitationally rounded, Sun-orbiting bodies intoüberplanets, which are "dynamically important enough to have cleared [their] neighboring planetesimals", andunterplanets. The überplanets are the eight most massive solar orbiters (i.e. the IAU planets), and the unterplanets are the rest (i.e. the IAU dwarf planets).

Steven Soter proposed an observationally based measureμ (mu), which he called the "planetary discriminant", to separate bodies orbiting stars into planets and non-planets.^[4] He definesμ as$${\displaystyle \mu =\frac{M}{m}}$$whereμ is a dimensionless parameter,M is the mass of the candidate planet, andm is the mass of all other bodies that share anorbital 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.^[4]

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 with 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 ifμ > 100, then the candidate body be regarded as a planet.^[4]

AstronomerJean-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.^[2] Like Stern–Levison'sΛ,Π is a measure of the ability of the body to clear its orbit, but unlikeΛ, 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'sμ, which requires an accurate census of the orbital zone.

$${\displaystyle \mathrm{\Pi }=\frac{m}{M^{5/2}{a}^{9/8}}k}$$

wherem is the mass of the candidate body inEarth masses,a is its semi-major axis inAU,M is the mass of the parent star insolar masses, andk is a constant chosen so thatΠ > 1 for a body that can clear its orbital zone.k depends on the extent of clearing desired and the time required to do so. Margot selected an extent of${\displaystyle 2\sqrt{3}}$ times theHill radius and a time limit of the parent star's lifetime on themain sequence (which is a function of the mass of the star). Then, in the mentioned units and a main-sequence lifetime of 10 billion years,k = 807.^[a] The body is a planet ifΠ > 1. The minimum mass necessary to clear the given orbit is given whenΠ = 1.

Π is based on a calculation of the number of orbits required for the candidate body to impart enough energy to a small body in a nearby orbit such that the smaller body is cleared out of the desired orbital extent. This is unlikeΛ, which uses an average of the clearing times required for a sample of asteroids in theasteroid belt, and is thus biased to that region of the Solar System.Π's use of the main-sequence lifetime means that the body will eventually clear an orbit around the star;Λ's use of aHubble time means that the star might disrupt its planetary system (e.g. by going nova) before the object is actually able to clear its orbit.

The formula forΠ assumes a circular orbit. Its adaptation to elliptical orbits is left for future work, but Margot expects it to be the same as that of a circular orbit to within an order of magnitude.

To accommodate planets in orbit around brown dwarfs, an updated version of the criterion with a uniform clearing time scale of 10 billion years was published in 2024.^[5] The values ofΠ for Solar System bodies remain unchanged.

Below is a list of planets and dwarf planets ranked by Margot's planetary discriminantΠ, in decreasing order.^[2] For all eight planets defined by the IAU,Π is orders of magnitude greater than 1, whereas for all dwarf planets,Π is orders of magnitude less than 1. Also listed are Stern–Levison'sΛ and Soter'sμ; again, the planets are orders of magnitude greater than 1 forΛ and 100 forμ, and the dwarf planets are orders of magnitude less than 1 forΛ and 100 forμ. Also shown are the distances whereΠ = 1 andΛ = 1 (where the body would change from being a planet to being a dwarf planet).

The mass of Sedna is not known; it is very roughly estimated here as10²¹ kg, on the assumption of a density of about2 g/cm³.

Stern, theprincipal investigator of theNew Horizons mission to Pluto, disagreed with the reclassification of Pluto on the basis of its inability to clear a neighbourhood. He argued that the IAU's wording is vague, and that — like Pluto —Earth,Mars, Jupiter and Neptune have not cleared their orbital neighbourhoods either. Earth co-orbits with 10,000near-Earth asteroids (NEAs), and Jupiter has 100,000trojans in its orbital path. "If Neptune had cleared its zone, Pluto wouldn't be there", he said.^[8]

The IAU category of 'planets' is nearly identical to Stern's own proposed category of 'überplanets'. In the paper proposingStern and Levison'sΛ discriminant, they stated, "we define anüberplanet as a planetary body in orbit about a star that is dynamically important enough to have cleared its neighboring planetesimals ..." and a few paragraphs later, "From a dynamical standpoint, our solar system clearly contains 8 überplanets" — including Earth, Mars, Jupiter, and Neptune.^[3] Although Stern proposed this to define dynamical subcategories of planets, he rejected it for defining what a planet is, advocating the use of intrinsic attributes over dynamical relationships.^[9]

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