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Cited by 45Astro and Planetary ScienceStellar, planetary, and galactic studiesSpace Satellite Systems and Control

Constraints on planet nine’s orbit and sky position within a framework of mean motion resonances

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Millholland, Sarah, Laughlin, Gregory·2017·The Astronomical Journal
DOI 10.3847/1538-3881/153/3/91
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Abstract

Abstract A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of an as-yet undetected planet in the outer solar system, now referred to colloquially as “Planet Nine.” Dynamical simulations by Batygin & Brown have provided constraints on the range of the planet’s possible orbits and sky locations. We extend these investigations by exploring the suggestion of Malhotra et al. that Planet Nine is in small integer ratio mean-motion resonances (MMRs) with several of the most distant KBOs. We show that the observed KBO semimajor axes present a set of commensurabilities with an unseen planet at ∼654 au (P ∼ 16,725 years) that has a greater than 98% chance of stemming from a sequence of MMRs rather than from a random distribution. We describe and implement a Monte-Carlo optimization scheme that drives billion-year dynamical integrations of the outer solar system to pinpoint the orbital properties of perturbers that are capable of maintaining the KBOs’ apsidal alignment. This optimization exercise suggests that the unseen planet is most consistently represented with mass, m ∼ 6–12 M ⊕, semimajor axis, a ∼ 654 au, eccentricity, e ∼ 0.45, inclination, i ∼ 30°, argument of periastron, ω ∼ 150°, longitude of ascending node, Ω ∼ 50°, and mean anomaly, M ∼ 180°. A range of sky locations relative to this fiducial ephemeris are possible. We find that the region 30° ≲ R.A. ≲ 50°, −20° ≲ decl. ≲ 20° is promising.

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Crossref · 10.3847/1538-3881/153/3/91

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Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Even long-term stable KBOs do not remain bound to a single mean motion commensurability on Gyr timescales.

    “implying that even long-term stable KBOs do not remain bound to a single mean motion commensurability on Gyr timescales (which is also seen in Becker et al. 2017; Hadden et al. 2018).”

    From The planet nine hypothesis (2019) · cites this paper as Millholland and Laughlin 2017

    Section 4.2, “Resonant KBOs” (page not provided), reports that some samples lose resonance over time, but a substantial fraction maintain libration for the full billion-year integration. That directly contradicts the claim that even long-term stable KBOs do not remain bound to a single commensurability on Gyr timescales. (LLM, conf=0.88)

    Checked by a reasoning model — may be wrong.

    Experimental — accuracy not yet measured

  • Millholland and Laughlin (2017) derived a probability density function of P9 parameters that approximately maintains the KBOs in a clustered distribution while temporarily preserving commensurabilities.

    “derived a probability density function of P9 parameters that approximately maintains the KBOs in a clustered distribution, while temporarily preserving commensurabilities.”

    From The planet nine hypothesis (2019) · cites this paper as Millholland and Laughlin (2017)

    Section 2 derives a probability distribution for Planet Nine’s semimajor axis conditional on mean-motion resonances, and §4.2 examines whether configurations that better maintain KBO clustering place the bodies in period-ratio commensurabilities. But §3.2 explicitly says the broader parameter exploration does not produce a true probability density function, so the claim overstates what was derived. The cited passages do not establish that commensurabilities were temporarily preserved. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The existence of an additional, multi-Earth mass planetary member of the solar system-Planet Nine-can successfully resolve the theoretical tension posed by the anomalous structure of the distant Kuiper belt.

    “A series of recent studies (Batygin and Brown, 2016a,b; Batygin and Morbidelli, 2017; Millholland and Laughlin, 2017; Becker et al., 2017; Hadden et al., 2018; Khain et al., 2018a; C´ aceres & Gomes, 2018; Li et al., 2018) have demonstrated that the existence of an additional, multi-Earth mass planetary member of the solar system Planet Nine - can successfully resolve this theoretical tension.”

    From The planet nine hypothesis (2019) · cites this paper as Millholland and Laughlin, 2017

    The Abstract reports simulations of a 6–12 Earth-mass Planet Nine capable of maintaining the distant Kuiper Belt objects’ orbital alignment, supporting the proposed explanation. But Section 5.2 says sustained clustering matching observations is exceptionally difficult to obtain and could even count against the planet’s existence. The paper therefore does not demonstrate the unqualified success implied by the citing sentence; page numbers are unavailable in our copy. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

  • Resonant configurations generally have dynamical lifetimes considerably shorter than the age of the solar system.

    “resonant configurations generally have dynamical lifetimes that are considerably shorter than the age of the solar system”

    From The planet nine hypothesis (2019) · cites this paper as Millholland and Laughlin (2017)

    Section 4.2 (page unavailable) reports that the fraction of sampled Sedna and 2012 VP113 configurations remaining in resonance declines over a billion-year integration. It also says a substantial fraction remain resonant for the full integration, so it does not establish that resonant configurations generally have lifetimes considerably shorter than the age of the solar system. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • Mean-motion resonances with Planet Nine are relevant to the dynamical evolution of the distant Kuiper belt.

    “Are mean-motion resonances (MMRs) with Planet Nine relevant to the dynamical evolution of the distant Kuiper belt? Strictly speaking, the answer is yes (Millholland and Laughlin, 2017; Becker et al., 2017; Hadden et al., 2018; Bailey et al., 2018)”

    From The planet nine hypothesis (2019) · cites this paper as Millholland and Laughlin, 2017

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Cites

Flagged first, then by citations

Research works printed but not linked: 19

  1. Bailey, E., Batygin, K., & Brown, M. E. 2016, AJ, 152, 126 · DOI · Paper page
  2. Batygin, K., & Brown, M. E. 2016b, ApJL, 833, L3 · DOI
  3. Beust, H. 2016, A&A, 590, L2 · DOI · Paper page
  4. Bromley, B. C., & Kenyon, S. J. 2016, ApJ, 826, 64 · DOI
  5. Chen, Y.-T., Lin, H. W., Holman, M. J., et al. 2016, ApJL, 827, L24 · DOI · Paper page
  6. de la Fuente Marcos, C., & de la Fuente Marcos, R. 2014, MNRAS, 443, L59 · DOI · Paper page
  7. de la Fuente Marcos, C., de la Fuente Marcos, R., & Aarseth, S. J. 2016, MNRAS, 460, L123 · DOI
  8. Fienga, A., Laskar, J., Manche, H., & Gastineau, M. 2016, A&A, 587, L8 · DOI · Paper page
  9. Gomes, R., Deienno, R., & Morbidelli, A. 2017, AJ, 153, 27 · DOI · Paper page
  10. Holman, M. J., & Payne, M. J. 2016b, AJ, 152, 94 · DOI · Paper page
  11. Hoyt, W. G. 1980, Planets X and Pluto (Tucson, AZ: Univ. Arizona Press)
  12. Kenyon, S. J., & Bromley, B. C. 2016, ApJ, 825, 33 · DOI · Paper page
  13. Lai, D. 2016, AJ, 152, 215 · DOI · Paper page
  14. Linder, E. F., & Mordasini, C. 2016, A&A, 589, A134 · DOI · Paper page
  15. Malhotra, R., Volk, K., & Wang, X. 2016, ApJL, 824, L22 · DOI · Paper page
  16. Mustill, A. J., Raymond, S. N., & Davies, M. B. 2016, MNRAS, 460, L109 · DOI · Paper page
  17. Shankman, C., Kavelaars, J., Lawler, S. M., Gladman, B. J., & Bannister, M. T. 2016, arXiv:1610.04251 · arXiv
  18. Ter Braak, C. J. F. 2006, Stat. Comput., 16, 239 · DOI
  19. Toth, I. 2016, A&A, 592, A86 · DOI

Cited by

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Authors
Millholland, S., & Laughlin, G.
Affiliations
Yale University (US)
Corresponding author
Millholland, Sarah
ORCID
Venue
The Astronomical Journal
Publisher
American Astronomical Society
Published
2017-02-02
Volume
153
Issue
3
Pages
91
ISSN
  • 0004-6256 (ISSN-L)
  • 1538-3881
DOI
10.3847/1538-3881/153/3/91
OpenAlex
W2578820441
Cited by
45
References
10
Citations by year
2025: 2 · 2024: 2 · 2023: 3 · 2022: 1 · 2021: 4 · 2020: 5 · 2019: 7 · 2018: 13 · 2017: 8
FWCI
4.94
Type
journal article
Language
en
Open access
Licence
Locations
  • The Astronomical Journal (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
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
Planet Nine, mean motion resonance, Kuiper belt objects, orbital alignment, apsidal alignment, outer solar system dynamics, Monte Carlo optimization, orbital constraints, undiscovered planet, orbital commensurability

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