Clearing The Neighbourhood - Details

Details

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 which will never collide with each other due to orbital resonance, such as Jupiter and the Trojan asteroids, 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 defined mathematically as

where M is the mass of the body, a is the length of the body's semi-major axis, and k 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 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).

Steven Soter proposed an observationally based measure µ (mu), which he called the "planetary discriminant", to separate bodies orbiting stars into planets and non-planets. Per Soter, two bodies are defined to share an orbital zone if their orbits cross a common radial distance from the primary, and their 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.

Here is a list of planets and dwarf planets ranked by Soter's planetary discriminant µ, in decreasing order. Note that for all eight planets defined by the IAU, µ is orders of magnitude greater than 100, while for all dwarf planets, µ is orders of magnitude less than 100. Also listed is the Stern–Levison parameter Λ; again, the planets are orders of magnitude greater than 1, and the dwarf planets are orders of magnitude less than 1. The scattering power relative to Earth (Λ/Λ_E) is also shown, as is the distance where Λ = 1 (where the body would change from a planet to a dwarf planet).