Planet Formation Equation - "Clearing the neighbourhood"

Description

“Clearing the neighbourhood around its orbit” is a criterion for a celestial body to be considered a planet in the Solar System. This was one of the three criteria adopted by the International Astronomical Union (IAU) in its 2006 definition of planet.

In the end stages of planet formation, a planet will have “cleared the neighbourhood” of its own orbital zone (see below), meaning it has become gravitationally dominant, and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence. A large body which meets the other criteria for a planet but has not cleared its neighbourhood is classified as a dwarf planet. This includes Pluto, which shares its orbital neighbourhood with Kuiper belt objects such as the plutinos. The IAU’s definition does not attach specific numbers or equations to this term, but all the planets have cleared their neighbourhoods to a much greater extent than any dwarf planet, or any candidate for dwarf planet.

The phrase may be derived from a paper presented to the general assembly of the IAU in 2000 by 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.

Clearly distinguishing “planets” from “dwarf planets” and other minor planets had become necessary because the IAU had adopted different rules for naming newly discovered major and minor planets, without establishing a basis for telling them apart. The naming process for Eris stalled after the announcement of its discovery in 2005, pending clarification of this first step.

The phrase refers to an orbiting body (a planet or protoplanet) “sweeping out” its orbital region over time, by gravitationally interacting with smaller bodies nearby. Over many orbital cycles, a large body will tend to cause small bodies either to accrete with it, or to be disturbed to another orbit, or to be captured either as a satellite or into a resonant 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 to orbital resonance, such as Jupiter and its trojans, Earth and 3753 Cruithne, or Neptune and the plutinos.

In their paper, Stern and Levison sought an algorithm to determine which “planetary bodies control the region surrounding them”. They defined Λ (lambda), a measure of a body’s ability to scatter smaller masses out of its orbital region over a long period of time. Λ is a dimensionless number defined as shown here.

In the domain of the solar planetary disc, there is little variation in the average values of k for small bodies at a particular distance from the Sun.

If Λ > 1, then the body will likely clear out the small bodies in its orbital zone. Stern and Levison used this discriminant to separate the gravitionally rounded, Sun-orbiting bodies into überplanets, which are “dynamically important enough to have cleared its neighboring planetesimals”, and unterplanets. 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).

Related formulas

Variables

Λmeasure of a body's ability to scatter smaller masses out of its orbital region over a long period of time (dimensionless)
Mmass of the body (kg)
abody's semi-major axis (m)
kfunction of the orbital elements of the small body being scattered and the degree to which it must be scattered (m/kg2)