Clearing the neighbourhood
"Clearing the neighbourhood" (or dynamical dominance) around a celestial body's orbit describes the body becoming gravitationally dominant such that there are no other bodies of comparable size other than its natural satellites or those otherwise under its gravitational influence.
"Clearing the neighbourhood" is one of three necessary criteria for a celestial body to be considered a planet in the Solar System, according to the definition adopted in 2006 by the International Astronomical Union (IAU).[1] In 2015, a proposal was made to extend the definition to exoplanets.[2]
In the end stages of planet formation, a planet, as so defined, will have "cleared the neighbourhood" of its own orbital zone, i.e. removed other bodies of comparable size. A large body that meets the other criteria for a planet but has not cleared its neighbourhood is classified as a dwarf planet. This includes Pluto, whose orbit intersects with Neptune's orbit and shares its orbital neighbourhood with many Kuiper belt objects. The IAU's definition does not attach specific numbers or equations to this term, but all IAU-recognised planets have cleared their neighbourhoods to a much greater extent (by orders of magnitude) than any dwarf planet or candidate for dwarf planet.[2]
The phrase stems from a paper presented to the 2000 IAU general assembly by the planetary scientists 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.[3] Steven Soter prefers to use the term dynamical dominance,[4] and Jean-Luc Margot notes that such language "seems less prone to misinterpretation".[2]
Prior to 2006, the I
Criteria
[edit]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.[3] As to the extent of orbit clearing required, Jean-Luc Margot emphasises "a planet can never completely clear its orbital zone, because gravitational and radiative forces continually perturb the orbits of asteroids and comets into planet-crossing orbits" and states that the I
Stern–Levison's Λ
[edit]In their paper, Stern and Levison sought an algorithm to determine which "planetary bodies control the region surrounding them".[3] They defined
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.[4]
If
Soter's μ
[edit]Steven Soter proposed an observationally based measure
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 with the other small Solar System bodies, so their inclusion would have little impact on the results.
Margot's Π
[edit]Astronomer Jean-Luc Margot has proposed a discriminant,
where m is the mass of the candidate body in Earth masses, a is its semi-major axis in
The formula for
To accommodate planets in orbit around brown dwarfs, an updated version of the criterion with a uniform clearing time scale of 10 billion years was published in 2024.[5] The values of
Numerical values
[edit]Below is a list of planets and dwarf planets ranked by Margot's planetary discriminant
The mass of Sedna is not known; it is very roughly estimated here as 1021 kg, on the assumption of a density of about 2 g/cm3.
Rank | Name | Margot's planetary discriminant |
Soter's planetary discriminant |
Stern–Levison parameter [b] |
Mass (kg) | Type of object | distance ( |
distance ( |
---|---|---|---|---|---|---|---|---|
1 | Jupiter | 40,115 | 6.25×105 | 1.30×109 | 1.8986×1027 | 5th planet | 64,000 | 6,220,000 |
2 | Saturn | 6,044 | 1.9×105 | 4.68×107 | 5.6846×1026 | 6th planet | 22,000 | 1,250,000 |
3 | Venus | 947 | 1.3×106 | 1.66×105 | 4.8685×1024 | 2nd planet | 320 | 2,180 |
4 | Earth | 807 | 1.7×106 | 1.53×105 | 5.9736×1024 | 3rd planet | 380 | 2,870 |
5 | Uranus | 423 | 2.9×104 | 3.84×105 | 8.6832×1025 | 7th planet | 4,100 | 102,000 |
6 | Neptune | 301 | 2.4×104 | 2.73×105 | 1.0243×1026 | 8th planet | 4,800 | 127,000 |
7 | Mercury | 129 | 9.1×104 | 1.95×103 | 3.3022×1023 | 1st planet | 29 | 60 |
8 | Mars | 54 | 5.1×103 | 9.42×102 | 6.4185×1023 | 4th planet | 53 | 146 |
9 | Ceres | 0.04 | 0.33 | 8.32×10−4 | 9.43×1020 | dwarf planet | 0.16 | 0.024 |
10 | Pluto | 0.028 | 0.08 | 2.95×10−3 | 1.29×1022 | dwarf planet | 1.70 | 0.812 |
11 | Eris | 0.020 | 0.10 | 2.15×10−3 | 1.67×1022 | dwarf planet | 2.10 | 1.130 |
12 | Haumea | 0.0078 | 0.02[6] | 2.41×10−4 | 4.0×1021 | dwarf planet | 0.58 | 0.168 |
13 | Makemake | 0.0073 | 0.02[6] | 2.22×10−4 | ~4.0×1021 | dwarf planet | 0.58 | 0.168 |
14 | Quaoar | 0.0027 | 0.007[6] | 1.4×1021 | dwarf planet | |||
15 | Gonggong | 0.0021 | 0.009[6] | 1.8×1021 | dwarf planet | |||
16 | Orcus | 0.0014 | 0.003[6] | 6.3×1020 | dwarf planet | |||
17 | Sedna | ~0.0001 | <0.07[7] | 3.64×10−7 | ? | dwarf planet |
Disagreement
[edit]Stern, the principal investigator of the New Horizons mission to Pluto, disagreed with the reclassification of Pluto on the basis of its inability to clear a neighbourhood. He argued that the IAU's wording is vague, and 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 said.[8]
The I
See also
[edit]- List of Solar System objects
- List of gravitationally rounded objects of the Solar System
- List of Solar System objects by size
- List of notable asteroids
- Sphere of influence (astrodynamics)
Notes
[edit]- ^ This expression for k can be derived by following Margot's paper as follows:
The time required for a body of mass m in orbit around a body of mass M with an orbital period P is:
With and C the number of Hill radii to be cleared.
This gives
requiring that the clearing time to be less than a characteristic timescale gives:
this means that a body with a mass m can clear its orbit within the designated timescale if it satisfies
This can be rewritten as follows
so that the variables can be changed to use solar masses, Earth masses, and distances in
AU by and Then, equating to be the main-sequence lifetime of the star , the above expression can be rewritten using with the main-sequence lifetime of the Sun, and making a similar change in variables to time in years This then gives Then, the orbital-clearing parameter is the mass of the body divided by the minimum mass required to clear its orbit (which is the right-hand side of the above expression) and leaving out the bars for simplicity gives the expression forΠ as given in this article: which means that Earth's orbital period can then be used to remove and from the expression: which gives so that this becomes Plugging in the numbers gives k = 807. - ^ These values are based on a value of k estimated for Ceres and the asteroid belt: k equals 1.53×105
AU 1.5/ME2, whereAU is the astronomical unit and ME is the mass of Earth. Accordingly,Λ is dimensionless.
References
[edit]- ^ "IAU 2006 General Assembly: Result of the I
AU Resolution votes". IAU. 24 August 2006. Retrieved 2009-10-23. - ^ a b c d e f Margot, Jean-Luc (2015-10-15). "A Quantitative Criterion for Defining Planets". The Astronomical Journal. 150 (6): 185–191. arXiv:1507.06300. Bibcode:2015AJ....150..185M. doi:10.1088/0004-6256/150/6/185.
- ^ a b c d Stern, S. Alan; Levison, Harold F. (2002). "Regarding the criteria for planethood and proposed planetary classification schemes" (PDF). Highlights of Astronomy. 12: 205–213, as presented at the XXIVth General Assembly of the IAU–2000 [Manchester, UK, 7–18 August 2000]. Bibcode:2002HiA....12..205S. doi:10.1017/S1539299600013289.
- ^ a b c d e Soter, Steven (2006-08-16). "What Is a Planet?". The Astronomical Journal. 132 (6): 2513–2519. arXiv:astro-ph/0608359. Bibcode:2006AJ....132.2513S. doi:10.1086/508861. S2CID 14676169.
- ^ Margot, Jean-Luc; Gladman, Brett; Yang, Tony (1 July 2024). "Quantitative Criteria for Defining Planets". The Planetary Science Journal. 5 (7): 159. arXiv:2407.07590. Bibcode:2024PSJ.....5..159M. doi:10.3847/PSJ/ad55f3.
- ^ a b c d e Calculated using the estimate for the mass of the Kuiper belt found in Iorio, 2007 of 0.033 Earth masses
- ^ Calculated using the estimate of a minimum of 15 Sedna mass objects in the region. Estimate found in Schwamb, Megan E; Brown, Michael E; Rabinowitz, David L (2009). "A Search for Distant Solar System Bodies in the Region of Sedna". The Astrophysical Journal. 694 (1): L45–8. arXiv:0901.4173. Bibcode:2009ApJ...694L..45S. doi:10.1088/0004-637X/694/1/L45. S2CID 15072103.
- ^ Rincon, Paul (25 August 2006). "Pluto vote 'hijacked' in revolt". BBC News. Retrieved 2006-09-03.
- ^ "Pluto's Planet Title Defender: Q & A With Planetary Scientist Alan Stern". Space.com. 24 August 2011. Retrieved 2016-03-08.