pith. sign in

arxiv: 2606.23850 · v1 · pith:OE32YO4Lnew · submitted 2026-06-22 · 🌌 astro-ph.EP

Dynamical implications of the recently detected feature around Quaoar and constraints on the presence of additional satellites

Gustavo Madeira , Leandro Esteves , Bruno E. Morgado , Paulo V. S. Soares , Silvia M. Giuliatti Winter , Othon C. Winter , Bruno S. Chagas This is my paper

Pith reviewed 2026-06-26 06:50 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords QuaoarWeywotstellar occultationsatellitering confinementdynamical stabilitytriangular pointssecular perturbations
0
0 comments X

The pith

The opaque feature near Quaoar is more consistent with a small satellite than with a dense arc confined at a triangular point.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Numerical integrations of the Quaoar system show that a 15 km satellite at the reported distance acquires a small forced eccentricity and clears only a narrow resonant zone, leaving the known rings largely unaffected. In contrast, attempts to confine an arc at the triangular equilibrium point of a coorbital body fail to reproduce the observed radial extent once Weywot's secular perturbations are included, unless the confiner is as massive as Weywot itself. The paper therefore concludes that the feature is dynamically more consistent with a satellite and identifies broad stable zones where additional small moons could exist near the rings. Quaoar's triaxial shape alone is shown to drive non-resonant orbital excitation that can inhibit ring particle coagulation.

Core claim

If the reported feature is treated as an arc, azimuthal confinement around the L4 or L5 point of an unseen coorbital satellite is possible for mass ratios up to 0.001, yet Weywot's secular forcing produces radial excursions too large to match the occultation data; only confiners comparable to or exceeding Weywot's mass supply sufficient radial confinement, but such bodies would be detectable by imaging. Treating the feature instead as a satellite yields stable orbits with forced eccentricity of order 0.002 and only local clearing of kilometre-scale test particles.

What carries the argument

N-body integrations that include Quaoar's triaxial figure, Weywot, and test particles or a putative satellite, used to map stability and to track radial and azimuthal excursions under secular perturbations.

If this is right

  • Additional undetected moons can occupy broad stable regions, including near the Q1R and Q2R rings as possible shepherds.
  • Quaoar's ellipticity alone supplies enough orbital excitation to prevent ring coagulation even without resonant shepherding.
  • A satellite interpretation implies the feature clears only a narrow zone and has negligible long-term effect on the existing rings.
  • Triangular-point arcs are ruled out for this system under the observed radial width once secular perturbations are accounted for.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same secular-perturbation mechanism may limit the lifetime of narrow arcs in other trans-Neptunian systems that host known moons.
  • If small moons near the rings are confirmed, they could provide an alternative or complementary explanation for ring confinement beyond the ellipticity effect.
  • Future occultation campaigns could distinguish the two scenarios by searching for the predicted narrow cleared zone around the feature's orbit.

Load-bearing premise

That any radial confinement of an arc requires a coorbital satellite at least as massive as Weywot, which would be visible to direct imaging.

What would settle it

A non-detection of any body more massive than a few times 10^18 kg within a few hundred kilometres of the reported feature's orbit during future high-resolution imaging or occultations would falsify the arc-confiner scenario while remaining compatible with the satellite interpretation.

Figures

Figures reproduced from arXiv: 2606.23850 by Bruno E. Morgado, Bruno S. Chagas, Gustavo Madeira, Leandro Esteves, Othon C. Winter, Paulo V. S. Soares, Silvia M. Giuliatti Winter.

Figure 1
Figure 1. Figure 1: Mean particle eccentricity as a function of the steady-state velocity dispersion, physical radius, and bulk density of Q1R ring particles. In panel (a), the particle ra￾dius is varied over realistic values for a fixed bulk density of 1000 kg · m−3 , while in panel (b) the bulk density is var￾ied and the particle radius is fixed at 1 m. The colour scale represents the mean eccentricity, with the dotted line… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of eccentricity and semi-major axis of satellites (diamond markers) and test particles (black dots) around Quaoar, with each panel corresponding to a different epoch. Orange vertical dashed lines mark the locations of spin–orbit resonances with Quaoar, while green and purple dashed lines indicate first-order mean-motion resonances with the satellite (green diamond) and Weywot (purple diamond), re… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Lifetime of all simulated particles and (b) Lyapunov time of the surviving particles, both as functions of the initial semi-major axis and eccentricity. Coloured vertical lines mark the locations of mean-motion resonances, with colours corresponding to those of the associated satellites (diamond markers). Orange vertical lines indicate spin–orbit resonances with Quaoar, with the wider ones highlighting… view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of the (a) semi-major axis, (b) eccentricity, and (c) 5:7 SOR resonant angle of a test parti￾cle initially placed at the radial centre of Q2R. The blue curves correspond to the configuration without the puta￾tive satellite, while the black and red curves correspond to configurations including a putative satellite at 5676 km and 5910 km, respectively. The resonant angle is defined as ϕ Q 57 =… view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of the orbital elements and resonant angles of a test particle initially placed at the radial centre of Q1R. Blue curves correspond to the configuration with only Weywot in the system, black curves to the configuration including a putative satellite at 5676 km, and red curves to the configuration including a putative satellite at 5910 km. Panels (a) and (b) show the semi-major axis and e… view at source ↗
Figure 6
Figure 6. Figure 6: Frequency maps of test particles in the vicinity of one of the triangular equilibrium points of a satellite placed at 5676.5 km from Quaoar, with the satellite mass indicated at the top of each panel. We consider masses ranging from 10−6 to 10−3 MQ, corresponding to satellite radii of approximately 4 to 45 km. The radial origin of each map is defined by the median radial distance of the particles, r0. The … view at source ↗
Figure 7
Figure 7. Figure 7: Initial semi-major axis and physical radius of a hypothetical additional moon that survives over 104 TQ without accreting ring particles, with the colour scale indicating the maximum eccentricity induced by the moon on the ring particles. We consider the satellite associated with the feature with masses of (a) 0 (no satellite), (b) 2 × 10−5 MQ, (c) 10−4 MQ, and (d) 10−3 MQ. The hypothetical satellite (gree… view at source ↗
read the original abstract

A recently reported opaque feature in the Quaoar system, detected during the 25 June 2025 stellar occultation, has been interpreted as either a 15 km-radius satellite or a dense, sharp-edged arc orbiting at about 5600-5900 km. Here, we investigate both scenarios through numerical integrations that include Quaoar, its triaxial shape, and Weywot. If the feature is a satellite, stability maps show that it acquires a forced eccentricity of about 0.002 and has only a minor dynamical effect on the Q1R and Q2R rings. Its main effect is to clear a narrow region around its orbit, associated with the overlap of mean-motion resonances, preventing the long-term survival of kilometre-scale moons within approximately one Quaoar radius of the satellite. If instead the feature is an arc, we test confinement around the triangular equilibrium point of an unseen coorbital satellite. While azimuthal confinement is readily obtained for satellites with satellite-to-primary mass ratios up to 0.001, Weywot's secular perturbation induces large radial excursions in the arc particles, preventing reproduction of the observed radial extent. The required radial confinement is achieved only for confiners comparable to or more massive than Weywot, which would likely be detectable by direct imaging. We therefore disfavour triangular-point confinement as an explanation for a long-lived dense arc and argue that the feature is more dynamically consistent with a satellite. We identify broad stable zones where additional undetected moons could reside, including near the rings as possible shepherd moons. Furthermore, Quaoar's ellipticity alone is sufficient to induce non-resonant orbital excitation capable of preventing ring coagulation, an effect that may be enhanced by small moons near the rings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript examines the dynamical implications of a recently detected opaque feature around Quaoar (interpreted as either a ~15 km satellite or a dense arc at 5600-5900 km) via N-body integrations that incorporate Quaoar's triaxial figure and the known satellite Weywot. For the satellite case, the feature acquires a forced eccentricity of ~0.002, clears a narrow resonant region, and has only minor effects on the Q1R/Q2R rings. For the arc case, azimuthal confinement at triangular points is possible for low mass ratios, but Weywot secular perturbations drive radial excursions that exceed the observed width unless the unseen coorbital mass ratio reaches ~Weywot's value; such a body would likely be detectable by imaging. The authors therefore disfavour the arc interpretation, favor the satellite, identify broad stable zones for additional moons, and note that Quaoar's ellipticity alone can excite non-resonant orbits sufficient to inhibit ring coagulation.

Significance. If the numerical results hold, the work supplies concrete dynamical constraints that tilt the interpretation toward a satellite while highlighting the role of known perturbers and shape-induced excitation in small-body ring systems. The explicit inclusion of triaxial figure and Weywot in the integrations, together with the mapping of stable zones for undetected moons, strengthens the analysis relative to simpler models.

major comments (2)
  1. [Arc confinement analysis (results on radial excursions vs. mass ratio)] The central disfavouring of the arc scenario rests on the claim that radial confinement matching the observed width requires a coorbital mass comparable to or exceeding Weywot's (which would be detectable by direct imaging). No quantitative imaging sensitivity limit, magnitude calculation, or reference to existing observational constraints is supplied to support the detectability threshold; this assumption is load-bearing for rejecting the arc.
  2. [Numerical results on triangular-point confinement] The reported radial-excursion threshold is stated qualitatively in the abstract and results; explicit values (e.g., rms radial width as a function of mass ratio, or comparison to the observed radial extent) from the integrations are needed to assess how sharply the confinement boundary occurs near the Weywot mass ratio.
minor comments (1)
  1. Ensure that the naming and prior literature references for the Q1R and Q2R rings are consistent between abstract and main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive comments, which help clarify the presentation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Arc confinement analysis (results on radial excursions vs. mass ratio)] The central disfavouring of the arc scenario rests on the claim that radial confinement matching the observed width requires a coorbital mass comparable to or exceeding Weywot's (which would be detectable by direct imaging). No quantitative imaging sensitivity limit, magnitude calculation, or reference to existing observational constraints is supplied to support the detectability threshold; this assumption is load-bearing for rejecting the arc.

    Authors: We agree that the manuscript would benefit from quantitative support for the detectability statement. In the revised version we will add a brief discussion with approximate magnitude estimates for a Weywot-mass coorbital at 5600-5900 km, referencing the HST discovery observations of Weywot and published imaging limits on additional satellites in the Quaoar system. This will make the threshold more explicit while preserving the dynamical conclusion. revision: yes

  2. Referee: [Numerical results on triangular-point confinement] The reported radial-excursion threshold is stated qualitatively in the abstract and results; explicit values (e.g., rms radial width as a function of mass ratio, or comparison to the observed radial extent) from the integrations are needed to assess how sharply the confinement boundary occurs near the Weywot mass ratio.

    Authors: We concur that explicit numerical values would improve clarity. We will revise the results section to tabulate rms radial excursions versus mass ratio for the triangular-point integrations and directly compare these widths to the observed radial extent of the occultation feature. This addition will quantify the sharpness of the transition near the Weywot mass ratio. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives its main claims—that triangular-point confinement fails to reproduce the observed radial width while a satellite scenario is dynamically consistent—from independent N-body integrations that include Quaoar's triaxial figure, Weywot, and secular perturbations. These results are not obtained by fitting parameters to the target data and then relabeling them as predictions, nor do they rest on self-citations that themselves assume the conclusion. The radial-excursion threshold follows directly from the modeled dynamics rather than from any self-definitional loop or imported uniqueness theorem. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 1 invented entities

The central claim rests on standard celestial mechanics assumptions and tests of a hypothetical entity without introducing new fitted parameters or untested physics.

axioms (3)
  • standard math The gravitational interactions are governed by Newtonian mechanics in the N-body problem
    Basis for all orbital integrations described.
  • domain assumption Quaoar has a triaxial shape that contributes to its gravitational potential
    Explicitly included in the numerical model.
  • domain assumption Weywot is the only known significant perturber besides Quaoar
    Used in the simulations of both scenarios.
invented entities (1)
  • unseen coorbital satellite no independent evidence
    purpose: To provide azimuthal confinement of the arc at the triangular equilibrium point
    Hypothetical body tested for mass ratios up to 0.001 but disfavoured due to required size for radial confinement.

pith-pipeline@v0.9.1-grok · 5880 in / 1389 out tokens · 35397 ms · 2026-06-26T06:50:38.568505+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

49 extracted references · 47 canonical work pages · 1 internal anchor

  1. [1]

    1980, Meccanica, 15, 9, doi: 10.1007/BF02128236

    Benettin, G., Galgani, L., Giorgilli, A., & Strelcyn, J.-M. 1980, Meccanica, 15, 9, doi: 10.1007/BF02128236

    work page doi:10.1007/bf02128236 1980

  2. [2]

    2026, ApJL, doi: 10.3847/2041-8213/ae4751

    Braga-Ribas, F., Pereira, C., & et al. 2026, ApJL, doi: 10.3847/2041-8213/ae4751

    work page doi:10.3847/2041-8213/ae4751 2026

  3. [3]

    L., et al

    Braga-Ribas, F., Sicardy, B., Ortiz, J. L., et al. 2014, Nature, 508, 72, doi: 10.1038/nature13155

    work page doi:10.1038/nature13155 2014

  4. [4]

    G., Hatzes, A., & Lin, D

    Bridges, F. G., Hatzes, A., & Lin, D. N. C. 1984, Nature, 309, 333, doi: 10.1038/309333a0

    work page doi:10.1038/309333a0 1984

  5. [5]

    C., et al

    Charnoz, S., Crida, A., Castillo-Rogez, J. C., et al. 2011, Icarus, 216, 535, doi: 10.1016/j.icarus.2011.09.017

    work page doi:10.1016/j.icarus.2011.09.017 2011

  6. [6]

    C., & Brown, M

    Fraser, W. C., & Brown, M. E. 2010, ApJ, 714, 1547, doi: 10.1088/0004-637X/714/2/1547

    work page doi:10.1088/0004-637x/714/2/1547 2010

  7. [7]

    G., Elliot, J

    French, R. G., Elliot, J. L., & Levine, S. E. 1986, Icarus, 67, 134, doi: 10.1016/0019-1035(86)90181-8 Giuliatti Winter, S. M., Madeira, G., Ribeiro, T., et al. 2023, A&A, 679, A62, doi: 10.1051/0004-6361/202345864

    work page doi:10.1016/0019-1035(86)90181-8 1986

  8. [8]

    , keywords =

    Goldreich, P., & Tremaine, S. 1982, ARA&A, 20, 249, doi: 10.1146/annurev.aa.20.090182.001341

    work page doi:10.1146/annurev.aa.20.090182.001341 1982

  9. [9]

    Goldreich, P., & Tremaine, S. D. 1978, Icarus, 34, 227, doi: 10.1016/0019-1035(78)90164-1

    work page doi:10.1016/0019-1035(78)90164-1 1978

  10. [10]

    P., Bridges, F

    Hatzes, A. P., Bridges, F. G., & Lin, D. N. C. 1988, MNRAS, 231, 1091, doi: 10.1093/mnras/231.4.1091

    work page doi:10.1093/mnras/231.4.1091 1988

  11. [11]

    M., Murray, C

    Hedman, M. M., Murray, C. D., Cooper, N. J., et al. 2009, Icarus, 199, 378, doi: 10.1016/j.icarus.2008.11.001

    work page doi:10.1016/j.icarus.2008.11.001 2009

  12. [12]

    2015, ApJ, 799, 40, doi: 10.1088/0004-637X/799/1/40

    Hyodo, R., Ohtsuki, K., & Takeda, T. 2015, ApJ, 799, 40, doi: 10.1088/0004-637X/799/1/40

    work page doi:10.1088/0004-637x/799/1/40 2015

  13. [13]

    G., Marton, G., et al

    Kiss, C., M¨ uller, T. G., Marton, G., et al. 2024, A&A, 684, A50, doi: 10.1051/0004-6361/202348054

    work page doi:10.1051/0004-6361/202348054 2024

  14. [14]

    L., & Shevchenko, I

    Lages, J., Shepelyansky, D. L., & Shevchenko, I. I. 2017, AJ, 153, 272, doi: 10.3847/1538-3881/aa7203

    work page doi:10.3847/1538-3881/aa7203 2017

  15. [15]

    Lissauer, J. J. 1985, Nature, 318, 544, doi: 10.1038/318544a0

    work page doi:10.1038/318544a0 1985

  16. [16]

    Madeira, G., Esteves, L., & Pinheiro, T. F. L. L. 2025a, European Physical Journal Special Topics, doi: 10.1140/epjs/s11734-025-01985-2

    work page doi:10.1140/epjs/s11734-025-01985-2

  17. [17]

    Madeira, G., Esteves, L., Pinheiro, T. F. L. L., et al. 2025b, Planet. Space Sci., 266, 106168, doi: 10.1016/j.pss.2025.106168

    work page doi:10.1016/j.pss.2025.106168 2025

  18. [18]

    Madeira, G., & Giuliatti Winter, S. M. 2020, European Physical Journal Special Topics, 229, 1527, doi: 10.1140/epjst/e2020-900129-5

    work page doi:10.1140/epjst/e2020-900129-5 2020

  19. [19]

    Madeira, G., & Giuliatti Winter, S. M. 2022, MNRAS, 513, 297, doi: 10.1093/mnras/stac944

    work page doi:10.1093/mnras/stac944 2022

  20. [20]

    Winter, O. C. 2022, MNRAS, 510, 1450, doi: 10.1093/mnras/stab3552

    work page doi:10.1093/mnras/stab3552 2022

  21. [21]

    E., Pereira, C

    Madeira, G., Morgado, B. E., Pereira, C. L., et al. 2025c, ApJ, 994, 268, doi: 10.3847/1538-4357/ae169e

    work page doi:10.3847/1538-4357/ae169e

  22. [22]

    2024, Master’s thesis, Universidade Tecnol´ ogica Federal do Paran´ a

    Margoti, G., et al. 2024, Master’s thesis, Universidade Tecnol´ ogica Federal do Paran´ a

    2024

  23. [23]

    E., Sicardy, B., Braga-Ribas, F., et al

    Morgado, B. E., Sicardy, B., Braga-Ribas, F., et al. 2021, A&A, 652, A141, doi: 10.1051/0004-6361/202141543

    work page doi:10.1051/0004-6361/202141543 2021

  24. [24]

    , year = 2023, month = feb, volume =

    Morgado, B. E., Sicardy, B., Braga-Ribas, F., et al. 2023, Nature, 614, 239, doi: 10.1038/s41586-022-05629-6

    work page doi:10.1038/s41586-022-05629-6 2023

  25. [25]

    D., Persson, S

    Nicholson, P. D., Persson, S. E., Matthews, K., Goldreich, P., & Neugebauer, G. 1978, AJ, 83, 1240, doi: 10.1086/112318

    work page doi:10.1086/112318 1978

  26. [26]

    M., Nesvorn´ y, D., & Thirouin, A

    Noll, K., Grundy, W. M., Nesvorn´ y, D., & Thirouin, A. 2020, in The Trans-Neptunian Solar System, ed. D. Prialnik, M. A. Barucci, & L. Young, 201–224, doi: 10.1016/B978-0-12-816490-7.00009-6

    work page doi:10.1016/b978-0-12-816490-7.00009-6 2020

  27. [27]

    V., Proudfoot, B

    Nolthenius, R., Bender, K., Cotton, D. V., Proudfoot, B. C. N., & Irwin, J. 2025, Research Notes of the American Astronomical Society, 9, 226, doi: 10.3847/2515-5172/adfeda

    work page doi:10.3847/2515-5172/adfeda 2025

  28. [28]

    , keywords =

    Ortiz, J. L., Santos-Sanz, P., Sicardy, B., et al. 2017, Nature, 550, 219, doi: 10.1038/nature24051

    work page doi:10.1038/nature24051 2017

  29. [29]

    L., Sicardy, B., Morgado, B

    Pereira, C. L., Sicardy, B., Morgado, B. E., et al. 2023, A&A, 673, L4, doi: 10.1051/0004-6361/202346365

    work page doi:10.1051/0004-6361/202346365 2023

  30. [30]

    L., Braga-Ribas, F., Sicardy, B., et al

    Pereira, C. L., Braga-Ribas, F., Sicardy, B., et al. 2025, arXiv e-prints, arXiv:2510.12388. https://arxiv.org/abs/2510.12388

    arXiv 2025

  31. [31]

    2025a, PSJ, 6, 285, doi: 10.3847/PSJ/ae18da

    Proudfoot, B., Grundy, W., Ragozzine, D., & Fern´ andez-Valenzuela, E. 2025a, PSJ, 6, 285, doi: 10.3847/PSJ/ae18da

    work page doi:10.3847/psj/ae18da

  32. [32]

    J., Arimatsu, K., et al

    Proudfoot, B., Holler, B. J., Arimatsu, K., et al. 2025b, PSJ, 6, 146, doi: 10.3847/PSJ/addd02

    work page doi:10.3847/psj/addd02

  33. [33]

    J., et al

    Proudfoot, B., Nolthenius, R., Holler, B. J., et al. 2025c, ApJL, 993, L38, doi: 10.3847/2041-8213/ae1585

    work page doi:10.3847/2041-8213/ae1585 2041

  34. [34]

    Rein, H., & Liu, S. F. 2012, A&A, 537, A128, doi: 10.1051/0004-6361/201118085

    work page internal anchor Pith review doi:10.1051/0004-6361/201118085 2012

  35. [35]

    Rein, H., & Spiegel, D. S. 2015, MNRAS, 446, 1424, doi: 10.1093/mnras/stu2164

    work page doi:10.1093/mnras/stu2164 2015

  36. [36]

    2004, Celestial Mechanics and Dynamical Astronomy, 88, 397, doi: 10.1023/B:CELE.0000023420.80881.67 17

    Renner, S., & Sicardy, B. 2004, Celestial Mechanics and Dynamical Astronomy, 88, 397, doi: 10.1023/B:CELE.0000023420.80881.67 17

    work page doi:10.1023/b:cele.0000023420.80881.67 2004

  37. [37]

    2014, A&A, 563, A133, doi: 10.1051/0004-6361/201321910

    Renner, S., Sicardy, B., Souami, D., Carry, B., & Dumas, C. 2014, A&A, 563, A133, doi: 10.1051/0004-6361/201321910

    work page doi:10.1051/0004-6361/201321910 2014

  38. [38]

    Winter, S. M. 2023, MNRAS, 525, 44, doi: 10.1093/mnras/stad2362

    work page doi:10.1093/mnras/stad2362 2023

  39. [39]

    C., Mour˜ ao, D., Boldrin, L

    Ribeiro, T., Winter, O. C., Mour˜ ao, D., Boldrin, L. A. G., & Carvalho, J. P. S. 2021, MNRAS, 506, 3068, doi: 10.1093/mnras/stab1880 Rodr´ ıguez, A., Morgado, B. E., & Callegari, Jr., N. 2023, MNRAS, 525, 3376, doi: 10.1093/mnras/stad2413

    work page doi:10.1093/mnras/stab1880 2021

  40. [40]

    2010, Icarus, 209, 771, doi: 10.1016/j.icarus.2010.05.030

    Salmon, J., Charnoz, S., Crida, A., & Brahic, A. 2010, Icarus, 209, 771, doi: 10.1016/j.icarus.2010.05.030

    work page doi:10.1016/j.icarus.2010.05.030 2010

  41. [41]

    2026, arXiv e-prints, arXiv:2601.06975, doi: 10.48550/arXiv.2601.06975

    Salo, H., & Sicardy, B. 2026, arXiv e-prints, arXiv:2601.06975, doi: 10.48550/arXiv.2601.06975

    work page doi:10.48550/arxiv.2601.06975 2026

  42. [42]

    Scheeres, D. J. 1994, Icarus, 110, 225, doi: 10.1006/icar.1994.1118

    work page doi:10.1006/icar.1994.1118 1994

  43. [43]

    H., & Stewart, G

    Shu, F. H., & Stewart, G. R. 1985, Icarus, 62, 360, doi: 10.1016/0019-1035(85)90181-2

    work page doi:10.1016/0019-1035(85)90181-2 1985

  44. [44]

    2025, A&A, 704, A23, doi: 10.1051/0004-6361/202556950

    Souami, D. 2025, A&A, 704, A23, doi: 10.1051/0004-6361/202556950

    work page doi:10.1051/0004-6361/202556950 2025

  45. [45]

    A., & Lewis, M

    Sickafoose, A. A., & Lewis, M. C. 2024, PSJ, 5, 32, doi: 10.3847/PSJ/ad151c

    work page doi:10.3847/psj/ad151c 2024

  46. [46]

    1964, Astrophys

    Toomre, A. 1964, ApJ, 139, 1217, doi: 10.1086/147861

    work page doi:10.1086/147861 1964

  47. [47]

    C., Borderes-Motta, G., & Ribeiro, T

    Winter, O. C., Borderes-Motta, G., & Ribeiro, T. 2019, MNRAS, 484, 3765, doi: 10.1093/mnras/stz246

    work page doi:10.1093/mnras/stz246 2019

  48. [48]

    1980, AJ, 85, 1122, doi: 10.1086/112778

    Wisdom, J. 1980, AJ, 85, 1122, doi: 10.1086/112778

    work page doi:10.1086/112778 1980

  49. [49]

    B., Swinney, H

    Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. 1985, Physica D Nonlinear Phenomena, 16, 285, doi: 10.1016/0167-2789(85)90011-9

    work page doi:10.1016/0167-2789(85)90011-9 1985