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'?

  • $\begingroup$ 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. $\endgroup$ – Ingolifs Aug 21 '19 at 23:51
  • $\begingroup$ @Ingolifs For Jupiter, it seems like that measure would include the entire asteroid belt, which definitely hasn't been cleared. $\endgroup$ – Arkenstein XII 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).

  • $\begingroup$ 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? $\endgroup$ – Arkenstein XII Aug 21 '19 at 20:36
  • $\begingroup$ 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) $\endgroup$ – James K Aug 22 '19 at 7:27
  • $\begingroup$ That makes sense. Is Jupiter, and to lesser extent Saturn, likely to be responsible for this perturbation? $\endgroup$ – Arkenstein XII Aug 22 '19 at 20:20

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