Clearing the neighbourhood

"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. Steven Soter prefers to use the term "dynamical dominance".

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.

Criteria

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.

Stern-Levison's Λ

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 period of time equal to the age of the Universe (Hubble time). Λ is a dimensionless number defined as

$\Lambda = \frac{M^2}{a^\frac{3}{2}}\,k$

where M is the mass of the body, a is 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).

Soter's µ

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.

Margot's Π

Astronomer Jean-Luc Margot has proposed a discriminant, Π (Pi), which can categorise a planet-candidate body based upon its mass, its semi-major axis, and its star's mass. Like the Stern-Levison Λ, Π is a measure of the ability of the body to clear its orbit, but, unlike Λ, it is solely based upon theory and does not use empirical data from the Solar system. Π is based upon properties that are feasibly determinable even for extrasolar planet-candidates, unlike Soter's µ which requires an accurate census of the orbital zone.

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

where m is the mass of the candidate body, a is its semi-major axis, M is the mass of the parent star, and k is a constant dependent upon the units of measure used. The denominator is the minimum mass necessary to clear the given orbit. If Π > 1, then the body is a planet.

The formulation of Π can be parameterised by the extent of clearing desired and the time required to do so. Margot selected an extent of $2\sqrt{3}$ times the Hill radius, and a time limit of the parent star's lifetime on the main sequence (which is a function of the mass of the star). Using Solar masses for the unit of mass for the star, Earth masses for the unit of mass for the planet-candidate, and AU for the unit of distance for the semi-major axis, k = 833.

Π is based upon 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 unlike Λ, which uses an average of the clearing times required for a sample of main belt asteroids, and is thus biased to a region of the Solar system. Π's use of the main sequence lifetime means that the body will eventually clear an orbit of the star; Λ's use of a Hubble time means that the star might disrupt its planetary system (e.g. by going nova) before the candidate-planet is actually able to clear its orbit.

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

Numerical values

Here is a list of planets and dwarf planets ranked by Margot's planetary discriminant Π, in decreasing order. Note that 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's Λ and Soter's µ; again, the planets are orders of magnitude greater than 1 for Λ and 100 for µ, and the dwarf planets are orders of magnitude less than 1 for Λ and 100 for µ. Also shown are the distances where Π = 1 and Λ = 1 (where the body would change from a planet to a dwarf planet).

Rank	Name	Margot's planetary discriminant Π	Soter's planetary discriminant µ	Stern–Levison parameter Λ	Mass (kg)	Type of object	Π = 1 distance (AU)	Λ = 1 distance (AU)
1	Jupiter	4.0 × 104	6.25 × 105	1.30 × 109	1.8986 × 1027	5th planet	65,000	6,220,000
2	Saturn	6.1 × 103	1.9 × 105	4.68 × 107	5.6846 × 1026	6th planet	22,000	1,250,000
3	Venus	9.5 × 102	1.35 × 106	1.66 × 105	4.8685 × 1024	2nd planet	320	2,180
4	Earth	8.1 × 102	1.7 × 106	1.53 × 105	5.9736 × 1024	3rd planet	390	2,870
5	Uranus	4.2 × 102	2.9 × 104	3.84 × 105	8.6832 × 1025	7th planet	4,200	102,000
6	Neptune	3.0 × 102	2.4 × 104	2.73 × 105	1.0243 × 1026	8th planet	4,800	127,000
7	Mercury	1.3 × 102	9.1 × 104	1.95 × 103	3.3022 × 1023	1st planet	30	60
8	Mars	5.4 × 101	1.8 × 105	9.42 × 102	6.4185 × 1023	4th planet	53	146
9	Ceres	4.0 × 10−2	0.33	8.32 × 10−4	9.43 × 1020	dwarf planet	0.16	0.0245
10	Pluto	2.8 × 10−2	0.077	2.95 × 10−3	1.29 × 1022	dwarf planet	1.7	0.812
11	Eris	2.0 × 10−2	0.10	2.15 × 10−3	1.67 × 1022	dwarf planet	2.1	1.13
12	Haumea	7.9 × 10−3	0.02	2.68 × 10−4	4.2 ± 0.1 × 1021	dwarf planet	0.59	0.179
13	Makemake	7.4 × 10−3	0.02	2.22 × 10−4	~4 × 1021	dwarf planet	0.58	0.168
Note: 1 light-year ≈ 63,241 AU

Disagreement

Orbits of celestial bodies in the Kuiper belt with approximate distances and inclination. Objects marked with red are in orbital resonances with Neptune, with Pluto (the largest red circle) located in the "spike" of plutinos at the 2:3 resonance

Stern, currently leading the NASA New Horizons mission to Pluto, disagrees with the reclassification of Pluto on the basis that—like Pluto—Earth, Mars, Jupiter and Neptune have not cleared their orbital neighbourhoods either. Earth co-orbits with 10,000 near-Earth asteroids (NEAs), and Jupiter has 100,000 trojans in its orbital path. "If Neptune had cleared its zone, Pluto wouldn't be there", he now says.

This is a shift from Stern's statement in 2000: "we define an überplanet 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. Stern and Levison's paper shows that it is possible to estimate whether an object is likely to dominate its neighborhood given only the object's mass and orbital period, known values even for extrasolar planets. In any case, the recent IAU definition specifically limits itself only to objects orbiting the Sun.

See also

• List of Solar System objects
• List of Solar System objects in hydrostatic equilibrium
• List of Solar System objects by size
• List of notable asteroids
• Mesoplanet

External links

• Ottawa Citizen: The case against Pluto (P. Surdas Mohit) Thursday, August 24, 2006