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Cited by 57Astro and Planetary ScienceStellar, planetary, and galactic studiesSpace Satellite Systems and Control

The Orbit of Planet Nine

Open access
Brown, Michael E., Batygin, Konstantin·2021·The Astronomical Journal
DOI 10.3847/1538-3881/ac2056
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Abstract

Abstract The existence of a giant planet beyond Neptune—referred to as Planet Nine (P9)—has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs). After updating calculations of observational biases, we find that the clustering remains significant at the 99.6% confidence level. We thus use these observations to determine orbital elements of P9. A suite of numerical simulations shows that the orbital distribution of the distant KBOs is strongly influenced by the mass and orbital elements of P9 and thus can be used to infer these parameters. Combining the biases with these numerical simulations, we calculate likelihood values for discrete set of P9 parameters, which we then use as input into a Gaussian-process emulator that allows a likelihood computation for arbitrary values of all parameters. We use this emulator in a Markov chain Monte Carlo analysis to estimate parameters of P9. We find a P9 mass of 6.2 − 1.3 + 2.2 Earth masses, semimajor axis of 380 − 80 + 140 au, inclination of 16 ± 5° and perihelion of 300 − 60 + 85 au. Using samples of the orbital elements and estimates of the radius and albedo of such a planet, we calculate the probability-distribution function of the on-sky position of Planet Nine and of its brightness. For many reasonable assumptions, Planet Nine is closer and brighter than initially expected, though the probability distribution includes a long tail to larger distances, and uncertainties in the radius and albedo of Planet Nine could yield fainter objects.

Integrity signals

Registry

Crossref · 10.3847/1538-3881/ac2056

Cites

33 of 33 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

14 of 15 cited sources checked · 9 supported · 1 flagged · accuracy not yet measured

  • Premisecitation

    Brown & Batygin (2016) showed that a wide range of masses and semimajor axes were acceptable with the constraints available at the time.

    “Brown & Batygin (2016) showed that a wide range of masses and semimajor axes were acceptable with the constraints available at the time”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Brown & Batygin (2016) source

      Section 2 (page not provided) says the acceptable semimajor-axis–eccentricity combinations are narrow, not wide. It reports acceptable solutions for the 10- and 20-Earth-mass simulations, but none for the 0.1-, 1-, or 30-Earth-mass simulations. (LLM, conf=0.87)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
  • Premisecitation

    All objects with q < 42 au are unstable with respect to perihelion diffusion.

    “all objects with q < 42 au are unstable with respect to perihelion diffusion”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Batygin et al. (2019) source

      Section 3 (page unavailable) says distant objects with perihelia somewhat below 40 AU are typically in a chaotic region and undergo stochastic orbital evolution. Section 2.3 (page unavailable) also describes Neptune-driven orbital diffusion among scattered-disk objects. Neither passage establishes that all objects with q < 42 AU are unstable or that the diffusion is specifically of their perihelion distances. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
  • Premisecitation

    A massive, inclined, and eccentric planet beyond approximately 250 au can cause multiple dynamical effects, notably clustering of longitude of perihelion and pole position for distant eccentric Kuiper belt objects.

    “The existence of a massive, inclined, and eccentric planet beyond ∼250 au has been shown to be able to cause multiple dynamical effects, notably including a clustering of longitude of perihelion, ϖ, and of pole position (a combination of longitude of ascending node, Ω, and inclination, i) for distant eccentric KBOs.”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites Batygin & Brown 2016 source
    • cites Batygin et al. 2019 source
  • Interpretationcitation

    The clustering of distant eccentric Kuiper belt objects is most simply explained by a giant planet on an inclined eccentric orbit with its perihelion location approximately 180° removed from those of the clustered objects.

    “Such a clustering is most simply explained by a giant planet on an inclined eccentric orbit with its perihelion location approximately 180° removed from those of the clustered KBOs.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Batygin & Brown (2016) source
  • Premisecitation

    The existence of a giant planet beyond Neptune, referred to as Planet Nine, has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects.

    “The existence of a giant planet beyond Neptune-referred to as Planet Nine (P9)-has been inferred from the clustering of longitude of perihelion and pole position of distant eccentric Kuiper belt objects (KBOs).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Batygin & Brown (2016) source
  • May combine two claims. 27
  • Classified as probably not a substantial claim. 4

  • May combine two claims.

    Premisecitation

    The effects of Planet Nine are mainly secular, so the mean anomaly of Planet Nine does not affect the outcome.

    “As the effects of Planet Nine are now understood to be mainly secular (Beust 2016), the position of Planet Nine within its orbit (the mean anomaly, M 9 ) does not affect the outcome, so it is unused.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Beust 2016 source

      Section 2 and Appendix A show that the non-resonant secular model averages over Planet Nine’s mean anomaly, so its orbital position does not enter that model. But Section 4 says it is difficult to determine whether secular or resonant dynamics dominates, and Section 3 explains that resonant dynamics cannot be averaged over both orbits independently. The paper therefore does not support treating Planet Nine’s mean anomaly as irrelevant to the outcome generally. (LLM, conf=0.88)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The original analysis of Batygin & Brown (2016) was a simple proof of concept that an inclined eccentric massive planet could cause outer solar system clustering, so its choice of m9 = 10 Mearth, e9 = 0.7, and i9 = 30° was merely notional.

    “The original analysis of Batygin & Brown (2016) was a simple proof of concept that an inclined eccentric massive planet could cause outer solar system clustering, so the choice of m 9 = 10 M earth , e 9 = 0.7, and i 9 = 30° was merely notional.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Batygin & Brown (2016) source

      Section 5.2 (page unavailable) reports a nominal simulation in which an inclined, eccentric planet qualitatively reproduces the observed clustering, using 10 Earth masses and a 30° inclination. But its nominal eccentricity is 0.6, not 0.7. Sections 4 and 5.1 describe the parameters as representative and not unique, while also explaining that the simulations and observed clustering constrain them; the choices were not merely notional. (LLM, conf=0.90)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    Strong pole position biases exist, but none appear capable of preferentially biasing the pole in any particular direction.

    “Strong pole position biases exist, but none which appear capable of preferentially biasing the pole in any particular direction.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The maximum-likelihood Planet Nine model has M9 = 5 Mearth, a9 = 300 au, i9 = 17°, e9 = 0.15, π9 = 254°, and Ω9 = 108°, and is nearly a local peak in every dimension.

    “First, the model with the maximum likelihood, M 9 = 5 M earth , a 9 = 300 au, i 9 = 17°, e 9 = 0.15, ϖ 9 = 254°, and Ω 9 = 108°, is nearly a local peak in every dimension.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    These diffusing objects are broadly clustered around Δπ ∼ 0° instead of around Δπ ∼ 180° like the stable cluster.

    “These diffusing objects are broadly clustered around Δϖ ∼ 0° instead of around Δϖ ∼ 180° like the stable cluster.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingreasoning

    With longitudes of perihelion ranging from 7° to 118°, the 111° wide cluster is best matched by low masses, which necessitates low semimajor axes to bring the wall in as close as 200 au.

    “With longitudes of perihelion ranging from 7° to 118°, this 111° wide cluster is best matched by low masses, which necessitates low semimajor axes to bring the wall in as close as 200 au.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Semimajor axes inside of about 300 au lead to low likelihoods, but more distant Planet Nine models are viable, particularly if they are more massive, even if at reduced likelihood.

    “Semimajor axes inside of ∼300 au lead to low likelihoods, but more distant Planets Nine are viable (particularly if they are more massive), even if at reduced likelihood.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Integration of the orbit of 2013FT28 shows that it is currently metastable, with a semimajor axis that diffuses on about Gyr timescales.

    “While integration of the orbit of 2013FT28 shows that it is currently metastable, with a semimajor axis that diffuses on ∼Gyr timescales”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The likelihoods change rapidly for small values of a9, while changing more slowly at higher a9.

    “Likewise, the likelihoods change rapidly for small values of a 9 , while changing more slowly at higher a 9 .”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    Clear expected correlations related to a9, m9, and e9 are present.

    “We see the clear expected correlations related to a 9 , m 9 , and e 9 .”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For the uniform prior, the marginalized perihelion and aphelion distances of Planet Nine are 300 +60 −85 au and 460 +110 −200 au, respectively.

    “For this uniform prior, the marginalized perihelion and aphelion distances of Planet Nine are -+ 300 60 85 and -+ 460 110 200 au, respectively.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The rescaled variables cause the likelihoods to appear approximately symmetric about their peak values and to peak at similar values of a' and q' for all masses.

    “These scalings cause the likelihoods to appear approximately symmetric about their peak values and to peak at similar values of ¢ a and ¢ q for all masses (Figure 6).”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    Uncertainties in the radius and albedo of Planet Nine could yield fainter objects.

    “uncertainties in the radius and albedo of Planet Nine could yield fainter objects.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    For many reasonable assumptions, Planet Nine is closer and brighter than initially expected.

    “For many reasonable assumptions, Planet Nine is closer and brighter than initially expected”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductown data

    The MCMC chains have converged; the maximum autocorrelation scale is 130 steps, 160 times smaller than the chain length.

    “We use the emcee package to calculate the autocorrelation scales of these chains and find that maximum is 130 steps, which is 160 times smaller than the length of the chain, ensuring that the chains have converged.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Both the maximum-likelihood and fully marginalized MCMC posterior distributions suggest that Planet Nine might be closer and potentially brighter than previously expected.

    “Both the maximum likelihood and the fully marginalized MCMC posterior distributions suggest that Planet Nine might be closer and potentially brighter than previously expected.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationnone given

    Despite recent discussions, statistical evidence for clustering in the outer solar system remains strong, and a massive planet on a distant inclined eccentric orbit remains the simplest hypothesis.

    “Despite recent discussions, statistical evidence for clustering in the outer solar system remains strong, and a massive planet on a distant inclined eccentric orbit remains the simplest hypothesis.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The preference for smaller values of mass and semimajor axis is robust, and the orbital angles i9, Ω9, and π9 are largely unaffected by any contamination.

    “We conclude that the preference for smaller values of mass and semimajor axis is robust, and that the orbital angles (i 9 , Ω 9 , ϖ 9 ) are largely unaffected by any contamination.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    A prior assuming formation in a cluster would put Planet Nine more distant than shown here, though it would also predict higher masses.

    “A prior assuming formation in a cluster would put Planet Nine more distant than shown here, though it would also predict higher masses.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductown data

    The Gaussian-process emulator appears to do a reasonable job of reproducing the numerical model likelihoods, interpolating between them, and smoothly extending them over the full range of interest.

    “The emulator produces a likelihood value at arbitrary values of (M 9 , a 9 , i 9 , e 9 , ϖ 9 , Ω 9 ), and appears to do a reasonable job of reproducing the likelihoods of the numerical models, interpolating between these models, and smoothly extending the models over the full range of interest.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductown data

    Although the emulator does not perfectly reproduce the simulation likelihoods, its large-scale behavior is captured with sufficient fidelity to allow interpolation between the discrete simulations.

    “While the emulator does not perfectly reproduce the simulation likelihoods, the large-scale behavior is captured with sufficient fidelity to allow us to use these results for interpolation between the discrete simulations.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    At the brightest end, Planet Nine could already have been detected in multiple surveys, while at the faintest it will require dedicated searches on 8-10 m telescopes.

    “At the brightest end, Planet Nine could already have been detected in multiple surveys, while at the faintest it will require dedicated searches on 8-10 m telescopes.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: For masses between 4 and 20 Mearth, the most likely planetary composition of Planet Nine is that of a sub-Neptune, composed of an icy-rocky core with a H-He rich envelope.
    • The authors state this as an assumption: Planet Nine's radius follows the simple mass-diameter relationship r9 = 3(m9/Mearth) Rearth.
    • The authors state this as an assumption: Planet Nine's albedo lies in the range 0.2 to 0.75.

  • May combine two claims.

    Study design and conductnone given

    The diameter and albedo of Planet Nine are not directly constrained.

    “To estimate the magnitude of Planet Nine we need not just the mass, but also the diameter and the albedo, neither of which we directly constrain.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The two posterior distributions agree within 1σ, but their differences are sufficiently large that predictions of expected magnitude could be affected.

    “While the two posterior distributions agree within 1σ, the differences are sufficiently large that predictions of expected magnitude, for example, could be affected.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationreasoning

    Combining the effects of the cluster-formation prior, the magnitude distribution would shift fainter by about a magnitude near aphelion but would change little close to perihelion.

    “Combining those effects we find that the magnitude distribution seen in Figure 8 would shift fainter by about a magnitude near aphelion but would change little close to perihelion.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Planet Nine's albedo lies in the range 0.2 to 0.75.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationown data

    The posterior distributions for m9 and a9 have large tails toward larger values, so the possibility of a closer, brighter Planet Nine needs to be seriously considered.

    “While the posterior distributions for m 9 and a 9 have large tails toward larger values, the possibility of a closer brighter Planet Nine needs to be seriously considered.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The median expected Planet Nine semimajor axis is significantly closer than previously understood, though the range of potential distances remains large.

    “We find that the median expected Planet Nine semimajor axis is significantly closer than previously understood, though the range of potential distances remains large.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning

    At its brightest predicted magnitude, Planet Nine could well be in range of the large number of sky surveys being performed with modest telescopes, so the current lack of detection suggests it is not at the brightest end of the distribution, though few detailed analyses of these surveys have yet been published.

    “At its brightest predicted magnitude, Planet Nine could well be in range of the large number of sky surveys being performed with modest telescope, so we expect that the current lack of detection suggests that it is not as the brightest end of the distribution, though few detailed analysis of these surveys has yet been published.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: The LSST survey of the Vera Rubin telescope has a single-image detection limit of r ∼ 24.3.
    • Rests on an assumption: The current LSST survey plan does not extend as far north as the full predicted path of Planet Nine.

  • May combine two claims.

    Interpretationnone given

    The caveats affect the distance, mass, and brightness of Planet Nine, but have no effect on the sky-plane position shown in Figure 8.

    “While all of these caveats affect the distance, mass, and brightness of Planet Nine, they have no affect on the sky-plane position shown in Figure 8.”
    Quote in the paperSubstantial claim
29 of 29

  • The paper relies on this without support.

    The observed distant Kuiper belt objects are statistically independent, so the full likelihood is the product of the individual object likelihoods.

    “The full likelihood,  P9 is the product of the individual object likelihoods.”

  • The paper relies on this without support.

    The two angular parameters ϖ9 and Ω9 yield rotationally symmetric results, so they need not be individually simulated.

    “The two angular parameters, ϖ 9 and Ω 9 , yield results that are rotationally symmetric so we need not individually simulate these results but rather rotate our reference frame to vary these parameters later.”

  • The authors state this as an assumption.

    For masses between 4 and 20 Mearth, the most likely planetary composition of Planet Nine is that of a sub-Neptune, composed of an icy-rocky core with a H-He rich envelope.

    “For masses between 4 and 20 M earth we assume that the most likely planetary composition is that of a sub-Neptune, composed of an icy-rocky core with a H-He rich envelope (we discuss alternatives below).”

  • The authors state this as an assumption.

    Planet Nine's radius follows the simple mass-diameter relationship r9 = 3(m9/Mearth) Rearth.

    “We assume a simple massdiameter relationship of r 9 = 3(m 9 /M earth ) R earth based on fits to (admittedly much warmer) planets in this radius and mass range by Wu & Lithwick (2013).”

  • The authors state this as an assumption.

    Planet Nine's albedo lies in the range 0.2 to 0.75.

    “We conservatively assume a full range of albedos from 0.2-half that of Neptune-to 0.75.”

  • The paper relies on this without support.

    The LSST survey of the Vera Rubin telescope has a single-image detection limit of r ∼ 24.3.

    “Much of the predicted magnitude range of Planet Nine is within the single-image detection limit of the LSST survey of the Vera Rubin telescope, r ∼ 24.3”

  • The paper relies on this without support.

    The current LSST survey plan does not extend as far north as the full predicted path of Planet Nine.

    “though the current survey plan does not extend as far north as the full predicted path of Planet Nine.”
7 of 7

Claims other papers make about this one

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

  • The Planet Nine hypothesis envisages a body of about 4.9-8.4 Earth masses, semimajor axis 300-520 au, inclination 11-21 degrees, perihelion 240-385 au, and eccentricities 0.2-0.538.

    “The Planet Nine hypothesis encompasses a body of about 5-8 Earth's masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240-385 astronomical units.”

    From Has Kronos Devoured Planet Nine and Its Epigones? (2026) · cites this paper as [18]

  • Within the expected declination interval by Brown and Batygin, the lighter version of Planet Nine can exist at not less than about 560 au for just a narrow range of values of its RA, and at not less than about 600 au for most of the values of its RA.

    “It can be noted that, within the expected interval for its declination by Brown and Batygin [18], the lighter version of P9 can exist at not less than about 560 au for just a narrow range of values of its RA, and at not less than about 600 au for most of the values of its RA.”

    From Has Kronos Devoured Planet Nine and Its Epigones? (2026) · cites this paper as [18]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Two different simulations are identified as the maximum-likelihood model

    Major

    The table note places the maximum at a semimajor axis of 310 au, inclination of 15°, and eccentricity of 0.10. Section 4.3 instead identifies a maximum at 300 au, 17°, and 0.15; the listed table row for the latter also has the highest displayed log-likelihood.

  • Figure 1 gives a different inclination for the maximum-likelihood model

    Minor

    The Figure 1 description calls a model with inclination 16° the maximum-likelihood model, whereas Section 4.3 gives 17° for that model.

  • Simulation particle counts fall outside the stated range

    Minor

    The methods state that each simulation began with 16,800-64,900 test particles, but Table 2 lists simulations with 120,500 particles and with 13,600 particles.

  • The stated parameter-space dimension differs from the parameter list

    Minor

    The paper calls the likelihood's parameter space seven-dimensional, but its explicit list of model parameters contains six: mass and five orbital elements.

  • The object designated for retention is absent from the sample

    Minor

    The exclusion procedure says 2013FT29 is always retained, but Table 1 lists 2013FT28 and contains no 2013FT29.

  • Figure 8 is cited for magnitudes but depicts orbital-parameter distributions

    Minor

    The text directs readers to Figure 8 for predicted magnitudes, while its caption describes parameter histograms and covariances. The magnitude distributions are described in the Figure 9 caption.

6 of 6

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Pedregosa, 2011, J. Mach. Learn. Res., 12, 2825

Cited by

Sorted by citations

Related

Authors
Brown, M. E., & Batygin, K.
Affiliations
California Institute of Technology (US)
Corresponding author
Brown, Michael E.
ORCID
Venue
The Astronomical Journal
Publisher
American Astronomical Society
Published
2021-10-28
Volume
162
Issue
5
Pages
219
ISSN
  • 0004-6256 (ISSN-L)
  • 1538-3881
DOI
10.3847/1538-3881/ac2056
OpenAlex
W3047658502
Cited by
57
References
33
Citations by year
2026: 7 · 2025: 19 · 2024: 8 · 2023: 12 · 2022: 10 · 2021: 1
FWCI
4.16
Type
journal article
Language
en
Open access
Licence
Locations
  • The Astronomical Journal (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
  • arXiv (Cornell University) (cc-by)
  • EPSC-DPS Joint Meeting 2019
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, orbital elements, Kuiper belt objects, observational bias, orbital dynamics, Gaussian process emulation, Markov chain Monte Carlo, planetary mass, orbital inclination

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