The Inclination Distribution of the Kuiper Belt
Open accessAbstract
We develop a general method for determining the unbiased inclination distribution of the Kuiper belt using only the inclination and latitude of discovery of known Kuiper belt objects (KBOs). These two parameters are well determined for each discovered object, so we can use all 379 known KBOs (as of 2001 January 1)—without knowing the object's precise orbit, area, detection efficiency, or the latitudinal coverage of the survey that found the object—to determine the inclination distribution. We find that a natural analytic form for the inclination distribution is a sine of the inclination multiplied by a Gaussian. The inclination distribution of all KBOs is well fitted by sin i multiplied by a sum of two Gaussians with widths 2 6 and 15° ± 1°. For this inclination distribution, the Kuiper belt has an effective area of 8100 deg 2 and a FWHM of 12.5° ± 3.5° in latitude. The inclination distribution of the different dynamical classes appear different. The Plutinos are well fit by sin i mulitplied by a single Gaussian of width 10 2 , the classical KBOs cannot be fit to a single Gaussian but are well fit by sin i multiplied by the sum of two Gaussians of widths 2 2 and 17° ± 3°, and the scattered KBOs are poorly fit by sin i multiplied by a single Gaussian of width 20° ± 4°. The poor fit of the scattered objects is possibly a result of limitations of the method in dealing with large eccentricities. The effective areas of the Plutinos, classical KBOs, and scattered KBOs are 9300 ± 1800, 6100 ± 2100, and 17000 ± 3000 deg 2 , respectively. The FWHMs are 23° ± 5°, 6 8 , and 44° ± 10°, respectively. In all cases, the inclinations of the Kuiper belt objects appear larger than expected from dynamical simulations of possible perturbations.
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The broader class of classical Kuiper belt objects is divided into dynamically cold and hot sub-populations based on orbital inclinations, which show a bimodal distribution.
“The broader class of classical KBOs is often divided into dynamically 'cold' and 'hot' sub-populations, where the distinction is based on their orbital inclinations, which show a bimodal distribution (Brown, 2001).”
From The planet nine hypothesis (2019) · cites this paper as Brown, 2001
Surveys for KBOs which observe near the ecliptic are biased against high inclination objects by a factor of 1/sin(i).
“Surveys for KBOs which observe near the ecliptic are biased against high inclination objects by a factor of 1 = sin( i ) (Brown, 2001).”
From The planet nine hypothesis (2019) · cites this paper as Brown, 2001
Objects with different q and a spend different fractions of their orbital period in the vicinity of 30 au, and this geometric correction can be applied by weighting the distribution accordingly.
“To advance beyond this estimate, one important correction must be made: objects with different q and a spend different fractions of their orbital period in the vicinity of 30 au.It is, however, straightforward to apply this geometric correction and weight the distribution accordingly (Brown 2001;Morbidelli et al. 2004).”
From Generation of Low-inclination, Neptune-crossing Trans-Neptunian Objects by Planet Nine (2024) · cites this paper as Brown 2001
Section 4.4 discusses eccentric orbits and tests the inclination-distribution method with simulated scattered objects, but does not describe how much time objects with different perihelia and semimajor axes spend near 30 au. Section 3.2 applies an inclination-based correction, not the claimed weighting by time spent near 30 au. Searches for orbital-time fractions and radial weighting found no passage addressing that correction. (LLM, conf=0.76)
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“More recently, Brunini&Melita (2002) proposed that a planet on a moderate-eccentricity orbit with a 60 AU could explain the putative edge of the Kuiper belt at 50 AU (Allen et al. 2002; Trujillo & Brown 2001).”
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“Here we extend the technique developed in that paper (which is in itself an extension of the technique developed in Trujillo & Brown (2001)) to develop a method to fully include both longitude of perihelion and orbital pole position in our bias calculations.”
BackgroundMethodSelf-citationGeneration of Low-inclination, Neptune-crossing Trans-Neptunian Objects by Planet Nine
Batygin, K., Morbidelli, A., Brown, M. E., & Nesvorný, D. (2024) · The Astrophysical Journal Letters · doi:10.3847/2041-8213/ad3cd2 · Cited by 11 · see citing works
“It is, however, straightforward to apply this geometric correction, and weight the distribution accordingly (Brown 2001; Morbidelli et al. 2004).”
MethodSelf-citationNo Evidence for Orbital Clustering in the Extreme Trans-Neptunian Objects
Napier, K. J., Gerdes, D. W., Lin 林, H. W. 省., Hamilton, S. J., Bernstein, G. M., Bernardinelli, P. H., Abbott, T. M. C., Aguena, M., Annis, J., Avila, S., et al. (2021) · The Planetary Science Journal · doi:10.3847/psj/abe53e · Cited by 1 · see citing works
- Authors
- Brown, M. E.
- Affiliations
- California Institute of Technology (US)
- Corresponding author
- Brown, Michael E.
- ORCID
- Brown, Michael E.
- Venue
- The Astronomical Journal
- Publisher
- American Astronomical Society
- Published
- 2001-05
- Volume
- 121
- Issue
- 5
- Pages
- 2804-2814
- ISSN
- 0004-6256 (ISSN-L)
- OpenAlex
- W2091043849
- Cited by
- 319
- References
- 18
- Citations by year
- 2026: 9 · 2025: 6 · 2024: 5 · 2023: 16 · 2022: 9 · 2021: 16 · 2020: 12 · 2019: 18 · 2018: 8 · 2017: 12 · 2016: 8 · 2015: 6 · 2014: 12 · 2013: 7 · 2012: 12
- FWCI
- 13.86
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Astronomical Journal (publishedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Astro and Planetary Science
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Stellar, planetary, and galactic studies
- Physical Sciences › Engineering › Aerospace Engineering › Space Satellite Systems and Control
- Keywords
- Kuiper belt, orbital inclination distribution, latitude distribution, Plutinos, effective area, orbital eccentricity
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