# Clearing the Neighbourhood: Definition of 'Orbital Region'?

I am trying to determine how wide a 'neighbourhood' a planet is expected to clear.

However, the Wikipedia article on the matter provides no clarity, simply stating that a planet is expected to clear it's 'orbital region' with no definition provided.

I suspect that the correct answer is that a planet is expected to clear a region around it's orbit equal to the radius of its Hill Sphere, but I am not certain of it.

Furthermore, for a planet of Earth mass, the Hill Sphere radius is a measly 0.01AU, which doesn't seem like much of a neighbourhood!

Is there a formal way to define the 'neighbourhood'?

• Interesting question. Soter's original paper doesn't define 'within an order of magnitude'. Intuitively, one would expect order of magnitude to mean the inner and outer limits are within ~ 10x of each other, making that to be between $\frac{\sqrt10} {10}$ =0.316 and $\sqrt10$ =3.16 that of the orbital radius. However, for Earth, this intersects the orbits of Mercury, Venus and Mars! Clearly there is some other measurement used. Aug 21 '19 at 23:51
• @Ingolifs For Jupiter, it seems like that measure would include the entire asteroid belt, which definitely hasn't been cleared. Aug 22 '19 at 0:12

The IAU gives no definition, it leaves the term somewhat vague.

Various calculations of the "planetariness" of solar system bodies use slightly different notions of the "neighbourhood"

Soter's $$\mu$$ considers bodies to be in the neighbourhood if they share a common radial distance (ie the orbits cross each other) and the orbital periods differ by less than an order of magnitude

Margot's $$\Pi$$ uses $$2\sqrt 3$$ times the Hill radius.

Stern and Levinson's $$\Lambda$$ in the original paper consider the neighbourhood to be bodies that cross the orbit of the planet, while not in an orbital resonance, to be in its neighbourhood, in a somewhat complex way that requires knowledge of the relative inclinations and and orbital velocities of bodies that cross orbits.

Changing the details of these values doesn't change the conclusion of the calculations: There is a clear and measurable difference between bodies like Mars and Neptune that are (to use Stern and Levinson's term) uberplanets and Ceres and Pluto that are unterplanets (or dwarf planets as termed by the IAU).

• Interesting. Thank you for your answer. Margot's method, when considering the Earth, still only results in a neighbourhood of ~0.035AU. I'm curious as to why the gap between the 'neighbourhoods' of Earth and Venus, for instance, isn't therefore full of other bodies? Aug 21 '19 at 20:36
• There wasn't much there to begin with, and over billions of years such bodies had their orbits perturbed until they crossed the orbit of a planet and either collided or were ejected (ie cleared) Aug 22 '19 at 7:27
• That makes sense. Is Jupiter, and to lesser extent Saturn, likely to be responsible for this perturbation? Aug 22 '19 at 20:20

No, it is a vague term that isn't defined anyhow by the IAU. If you consider the object's hill sphere as what is meant, then Pluto and Eris "cleared their neighbourhood" too. If you consider it the way that Pluto's orbit overlaps with Neptune for instance, then no planet cleared their orbits. There are Mercury-crossing asteroids, Near-Earth asteroids, Trojans crossing Jupiter's orbit et cetera. If we consider it as being meant that the bodies must be the most massive ones in their area (which again is vague) then Eris and Ceres should be planets and perhaps Pluto too (if you look three-dimensionally on the ecliptic). If you set an arbitrary border, either Ceres would be a planet or there wouldn't be planets at all.

So the 2006 planet definition is pure nonsense and shouldn't be considered valid and it isn't by many.

• That you are posting these incorrect statements fourteen years after the fact is a sign of willful ignorance. Is that truly how you want to be perceived? Instead of posting falsehoods / nonsense I suggest that you read the underlying papers. Feb 16 '20 at 23:06
• For example, If you consider it the way that Pluto's orbit overlaps with Neptune for instance, then no planet cleared their orbits is flat out wrong. Neptune has forced Pluto's orbit to be in resonance with Neptune's orbit such that Neptune is far removed from Pluto every time that Pluto crosses Neptune's orbit. The same is true for a number of other Kuiper belt objects. Forcing this resonance is one way of "clearing the neighborhood." Feb 16 '20 at 23:18
• Furthermore, even if one did consider those plutinos as being in the way, Neptune still qualifies as having "cleared its neighborhood", by all three of the contending metrics. Clearing the neighborhood is not an all or nothing proposition. Instead there are numerical assessments for the degree to which a planet has / will clear its neighborhood by the time the Sun dies. See the answer by @JamesK for a description of the three contending metrics. The nice thing about all of these metrics is that each exhibits a multiple order of magnitude gap between planets and non-planets. Feb 16 '20 at 23:23
• That the resolution itself was vague is rather common for resolutions in scientific societies. The presentations for and against describe some of the underlying reasoning. The scientific papers on which those presentations are based describe even more. The voting members in a scientific society are expected to be well-read with regard to the relevant scientific literature. The IAU did not want to say exactly which of the three contending metrics is the one to use, especially since all three said more or less the same thing: There are eight planets in the solar system, period. Feb 16 '20 at 23:35
• I am speechless. Feb 17 '20 at 9:00