pith. sign in

arxiv: 2604.16260 · v1 · submitted 2026-04-17 · 🌌 astro-ph.EP

Challenge in Arrokoth's single merger to achieve the shape's principal axis configuration

Pith reviewed 2026-05-10 07:03 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords Arrokothcontact binaryKuiper Beltprincipal axes alignmentmerger dynamicsgravitational torquefinite element modelingorbital evolution
0
0 comments X

The pith

Arrokoth's two lobes desynchronize and misalign along their principal axes in every simulated gentle merger scenario.

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

The paper examines how the contact binary Arrokoth formed its aligned lobes through a low-velocity merger. Full two-body simulations with finite-element modeling of the irregular shapes show that the lobes' rotations quickly lose synchronization after close approach, producing substantial misalignment at contact. Mutual gravitational torques between the lobes exceed gas-driven torques by several orders of magnitude, making nebula drag ineffective at preserving alignment. Existing ideas such as gas dissipation or Lidov-Kozai cycles therefore fail to explain the observed configuration. This implies that an extra process after the initial merger, possibly a later impact, must have reoriented the body into its current state.

Core claim

Implementing the full two-body problem via finite-element modeling under the reported geophysical constraints and orbital configurations demonstrates that the rotational states of both lobes become desynchronized shortly after close approach, resulting in substantial misalignment along their principal axes at the time of soft merger; the lobes' mutual gravitational torque is several orders of magnitude higher than gas-driven torque and therefore dominates any stabilizing effect from the protosolar nebula.

What carries the argument

Full two-body finite-element simulations that numerically track mutual gravitational torques and rotational desynchronization between the irregular lobes Weeyo and Wenu.

If this is right

  • None of the existing orbital-evolution scenarios can produce the observed principal-axis alignment during a single soft merger.
  • Gas drag from the protosolar nebula plays a negligible role in stabilizing the lobes' orientations.
  • An additional post-merger process, such as the Sky-forming impact, is required to reconfigure the body into its present shape.
  • Shape irregularities drive dominant mutual torques that must be accounted for in any model of contact-binary formation.

Where Pith is reading between the lines

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

  • Similar post-merger adjustment processes may be common among other bilobate Kuiper Belt objects whose lobes are also aligned along principal axes.
  • High-resolution imaging or shape modeling of additional contact binaries could test whether misalignment is the generic outcome of gentle mergers.
  • Incorporating even modest internal dissipation or tidal effects in future simulations might alter the desynchronization timescale and should be checked against the present results.

Load-bearing premise

The reported geophysical constraints and orbital configurations accurately represent the pre-merger state, and the finite-element two-body model includes every relevant physical process without missing dissipative mechanisms.

What would settle it

A simulation or observation that keeps the lobes synchronized through contact under the same geophysical constraints and shows mutual torques comparable to or weaker than gas drag would falsify the central result.

Figures

Figures reproduced from arXiv: 2604.16260 by Ketan Kamat, Masatoshi Hirabayashi, Ryota Nakano.

Figure 1
Figure 1. Figure 1: Schematic definition of the collision angle (β). The total collision angle β is calculated as the sum of the angular misalignments (β1 and β2) of each lobe’s longest principal axis (ˆx1 and ˆx2) relative to the mutual line of centers (r12). 3. IMMEDIATE APPEARANCE OF ROTATIONAL INSTABILITY We model each lobe as a tetrahedral mesh composed of 362 vertices and 1388 tetrahedrons to ensure high-fidelity gravit… view at source ↗
Figure 2
Figure 2. Figure 2: Time evolution of the relative rotational modes of Weeyo with respect to Wenu for a non-secular orbit, assuming a bulk density of 235 kg m−3 and default lobe shapes. Panel (a) shows the roll angle ϕ, panel (b) shows the pitch angle γ, and panel (c) shows the collision angle β. The precession orbits similarly result in widespread rotational instability. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Time evolution of the relative rotational modes of Weeyo with respect to Wenu for a precession orbit, assuming a bulk density of 235 kg m−3 and default lobe shapes. Panel (a) shows the roll angle ϕ, panel (b) shows the pitch angle γ, and panel (c) shows the collision angle β. Finally, the minimum-separation orbits exhibit distinct dynamical modes characterized by rapid desynchronization. This accelerated i… view at source ↗
Figure 4
Figure 4. Figure 4: Time evolution of the relative rotational modes of Weeyo with respect to Wenu for a min-separation orbit, assuming a bulk density of 235 kg m−3 and default lobe shapes. Panel (a) shows the roll angle ϕ, panel (b) shows the pitch angle γ, and panel (c) shows the collision angle β. 4. INFEASIBILITY OF A SINGLE MERGER AND PROPOSED POST-MERGER REALIGNMENT MECHANISM Our mutual dynamics simulations showed that n… view at source ↗
Figure 5
Figure 5. Figure 5: Geometry of the aerodynamic incidence angle (φ) for a given lobe. φ represents the orientation of a lobe’s long axis (ˆxi) relative to the incident velocity vector of the surrounding gas (uˆ˜). Within the protosolar nebula, the ρa value is estimated to be 3×10−11 kg m−3 and a fixed headwind velocity of 50 m s −1 (W. Lyra et al. 2021; W. B. McKinnon et al. 2020) is assumed. Under these conditions, the corre… view at source ↗
Figure 6
Figure 6. Figure 6: Ratio of gas torque to gravitational torque on Weeyo for Re = 10 in panel (a) and Re = 100 in panel (b). Apoapsis times are shown in red and periapsis times are shown in black for a non-secular orbit with the 235 kg m−3 bulk density and default lobe shapes. Based on the above analysis of all simulated orbital configurations, the gas torque is consistently found to be significantly weaker than the mutual gr… view at source ↗
Figure 7
Figure 7. Figure 7: Statistical distribution for the non-secular cases: (a) Mean collision angle, (b) Mean ratio of gas torque to gravitational torque on Weeyo for Re = 10, (c) Mean Wenu short-axis spin ratio, and (d) Mean Weeyo short-axis spin ratio. For the precession orbits, the mean collision angle exhibits a strong clustering between 85◦ and 115◦ across the entire investigated parameter space (Figure 8a). No clear correl… view at source ↗
Figure 8
Figure 8. Figure 8: Statistical distribution for the precession cases: (a) Mean collision angle, (b) Mean ratio of gas torque to gravitational torque on Weeyo for Re = 10, (c) Mean Wenu short-axis spin ratio, and (d) Mean Weeyo short-axis spin ratio. Analysis of the minimum-separation orbits reveals that the resulting collision angles show no correlation with the shapes and bulk densities of the lobes (Figure 9a). These orbit… view at source ↗
Figure 9
Figure 9. Figure 9: Statistical distribution for the min-separation cases: (a) Mean collision angle, (b) Mean ratio of gas torque to gravitational torque on Weeyo for Re = 10, (c) Deviation of mean Wenu short-axis spin ratio from unity, and (d) Deviation of mean Weeyo short-axis spin ratio from unity. The accelerated departure from relative equilibrium observed near contact results from the system’s inherent energetic instabi… view at source ↗
Figure 10
Figure 10. Figure 10: Normalized stability curvature E¯rr as a function of the normalized separation ¯r. The normalization factor rcontact is the sum of the long semi-axes for each specific lobe shape combination, ranging between 17.94 and 19.03 km. The solid curve denotes the transition from stable (blue) to unstable (orange) energetic stability (D. J. Scheeres 2009). The black dots represent the initial separations for the m… view at source ↗
Figure 11
Figure 11. Figure 11: Soft merger scenarios leading to Arrokoth’s final principal axes alignment. Panel (a) shows that gas drag from the protosolar nebula gradually shrinks the binary orbit between Weeyo and Wenu, ultimately causing a merger (W. B. McKinnon et al. 2020). However, this mechanism alone is insufficient to stabilize the proximity behavior of the lobes and align their principal axes upon merging. Panel (b) illustra… view at source ↗
read the original abstract

The cold-classical Kuiper Belt Object 486958 Arrokoth is a contact binary composed of two flattened lobes, Weeyo and Wenu, closely aligned along their principal axes, despite each lobe having a highly irregular shape. The object's smooth and relatively undamaged structure suggests the observed bilobate shape results from a gentle, low-velocity merger between the lobes. The existing hypotheses to explain such a merger include orbital energy dissipation from the protosolar nebula gas drag and Lidov-Kozai (LK) oscillations originating from an initially ultra-wide binary. However, what is missing is how mutual dynamics due to the lobes' shape irregularities impact their final orientations at the time of the soft merger. Here, we show that none of the proposed orbital evolution scenarios is sufficient to reproduce the contact along the lobes' longest principal axes. Implementing the full two-body problem method using finite element modeling, we numerically quantify the complex mutual interactions between Weeyo and Wenu, before the soft merger under the reported geophysical constraints and orbital configurations. All simulations demonstrate that the rotational states of both lobes become desynchronized shortly after their close approach, eventually leading to substantial misalignment along their principal axes. We also find that the lobes' mutual gravitational torque, destabilizing their aligned orientations, is several orders of magnitude higher than gas-driven torque, suggesting that gas drag plays a negligible role in stabilizing their orientations. The present study suggests the necessity of an additional process reconfiguring Arrokoth's shape after the merging process, possibly due to the Sky-forming impact.

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

3 major / 2 minor

Summary. The paper claims that finite-element simulations of the full two-body problem for Arrokoth's lobes (Weeyo and Wenu) under reported pre-merger geophysical and orbital conditions show rapid desynchronization of rotational states after close approach, producing substantial misalignment of principal axes at contact. It further asserts that mutual gravitational torques exceed gas-driven torques by several orders of magnitude, rendering gas drag insufficient to enforce alignment, and concludes that an additional post-merger reconfiguration process (possibly a Sky-forming impact) is required.

Significance. If the numerical results hold, the work demonstrates that shape irregularities in low-velocity mergers of irregular bodies generically prevent preservation of principal-axis alignment, challenging both gas-drag and Lidov-Kozai scenarios for Arrokoth's formation and implying that the observed configuration is not primordial. The finite-element F2BP implementation is a clear strength, providing a direct, shape-resolved treatment of mutual torques without reduction to point-mass or spherical approximations.

major comments (3)
  1. [Results / Discussion] The static torque-magnitude comparison used to conclude that gas drag is negligible (abstract and discussion) is performed outside the time-dependent F2BP integrations; because gas drag is omitted from the dynamical runs, the possibility that a weaker but persistently acting dissipative torque could damp relative rotation or maintain alignment over the close-approach timescale remains untested.
  2. [Methods / Results] The central claim that none of the proposed orbital-evolution scenarios reproduce principal-axis contact rests on the assumption that the adopted pre-merger orbital configurations and geophysical parameters (densities, shapes, initial spins) accurately represent the actual history; no sensitivity analysis to plausible variations in these inputs is reported, leaving open whether modest changes could permit alignment.
  3. [Methods] Numerical convergence with respect to finite-element mesh resolution, integration timestep, and material constitutive parameters is not documented; without such tests it is difficult to assess whether the reported rapid desynchronization is robust or an artifact of under-resolved contact or torque calculations.
minor comments (2)
  1. [Abstract / Conclusion] The term 'Sky-forming impact' is introduced in the abstract and conclusion without a prior definition or literature citation; a brief explanatory clause or reference would improve clarity.
  2. [Figures] Figure captions and axis labels for the torque time series should explicitly state the reference frame and normalization used, to allow direct comparison with the quoted 'several orders of magnitude' difference.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments identify areas where additional clarification and documentation will strengthen the manuscript. We respond point by point to the major comments below.

read point-by-point responses
  1. Referee: [Results / Discussion] The static torque-magnitude comparison used to conclude that gas drag is negligible (abstract and discussion) is performed outside the time-dependent F2BP integrations; because gas drag is omitted from the dynamical runs, the possibility that a weaker but persistently acting dissipative torque could damp relative rotation or maintain alignment over the close-approach timescale remains untested.

    Authors: We agree that a fully coupled simulation including gas drag would be the most direct test. However, the gravitational torques arising from the irregular shapes are several orders of magnitude larger than the estimated gas-drag torques, and the close-approach duration is only days to weeks. Under these conditions, the dissipative effect of gas drag is too weak to counteract the rapid desynchronization driven by mutual gravity. In the revised manuscript we will add an explicit comparison of the gas-drag damping timescale against the observed desynchronization timescale from the F2BP runs to quantify this point. revision: yes

  2. Referee: [Methods / Results] The central claim that none of the proposed orbital-evolution scenarios reproduce principal-axis contact rests on the assumption that the adopted pre-merger orbital configurations and geophysical parameters (densities, shapes, initial spins) accurately represent the actual history; no sensitivity analysis to plausible variations in these inputs is reported, leaving open whether modest changes could permit alignment.

    Authors: The adopted densities, shapes, and initial spins are taken directly from New Horizons measurements and prior geophysical modeling of Arrokoth. While a exhaustive parameter sweep would be desirable, the desynchronization is a generic consequence of the non-spherical mass distributions that generate strong, time-varying torques. We will add a short discussion in the revised text examining the effect of density variations within the observational uncertainty range and modest changes in initial spin; these tests confirm that principal-axis misalignment persists. A full Monte-Carlo exploration of all orbital histories lies beyond the scope of the present study. revision: partial

  3. Referee: [Methods] Numerical convergence with respect to finite-element mesh resolution, integration timestep, and material constitutive parameters is not documented; without such tests it is difficult to assess whether the reported rapid desynchronization is robust or an artifact of under-resolved contact or torque calculations.

    Authors: Convergence tests were performed during code development and validation. In the revised manuscript we will include a dedicated appendix that documents the dependence of the torque histories and final misalignment angles on mesh resolution (element count), integration timestep, and the adopted elastic moduli. These tests show that the reported desynchronization timescale and amplitude remain unchanged once the mesh resolves the lobe topography at the scale used in the production runs. revision: yes

Circularity Check

0 steps flagged

Direct numerical integration of F2BP produces independent dynamical outcome

full rationale

The paper's core findings—that rotational states desynchronize and principal axes misalign—emerge as outputs from time-dependent finite-element integration of the full two-body problem under externally reported geophysical constraints and orbital configurations. These inputs are taken as given from prior observations; the misalignment is not imposed by construction or by fitting any free parameter to the target alignment. The separate static comparison of gravitational versus gas-driven torque magnitudes likewise uses an independent estimate for the gas term and does not feed back into the dynamical integration. No self-definitional loop, fitted-input prediction, or load-bearing self-citation chain is present in the derivation chain. The result is therefore self-contained against the supplied external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the accuracy of prior geophysical and orbital parameters used as inputs and on the assumption that the numerical model includes all dominant torques.

axioms (1)
  • domain assumption Reported geophysical constraints and orbital configurations represent the pre-merger state of the lobes.
    Simulations are initialized with these values; if inaccurate, the desynchronization result may not apply.

pith-pipeline@v0.9.0 · 5587 in / 1170 out tokens · 57030 ms · 2026-05-10T07:03:12.791895+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

33 extracted references · 33 canonical work pages

  1. [1]

    # VC #ƄF -

    thebibliography [1] 20pt to REFERENCES 6pt =0pt \@twocolumntrue 12pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key o...

  2. [2]

    F., Gkolias, I., Tsiganis, K., et al

    Agrusa, H. F., Gkolias, I., Tsiganis, K., et al. 2021, title The excited spin state of Dimorphos resulting from the DART impact, Icarus, 370, 114624

  3. [3]

    Amarante, A., & Winter, O. C. 2020, title Surface dynamics, equilibrium points and individual lobes of the Kuiper Belt object (486958) Arrokoth, Monthly Notices of the Royal Astronomical Society, 496, 4154, 10.1093/mnras/staa1732

  4. [4]

    2019, title The HST lightcurve of (486958) 2014 MU69, Icarus, 334, 11, 10.1016/j.icarus.2019.01.023

    Benecchi, S., Porter, S., Buie, M., et al. 2019, title The HST lightcurve of (486958) 2014 MU69, Icarus, 334, 11, 10.1016/j.icarus.2019.01.023

  5. [5]

    2006, title Pole and Global Shape of 25143 Itokawa, Science, 312, 1347, 10.1126/science.1126574

    Demura, H., Kobayashi, S., Nemoto, E., et al. 2006, title Pole and Global Shape of 25143 Itokawa, Science, 312, 1347, 10.1126/science.1126574

  6. [6]

    Nature , author =

    Grishin, E., Malamud, U., Perets, H. B., Wandel, O., & Schäfer, C. M. 2020, title The wide-binary origin of (2014) MU69-like Kuiper belt contact binaries, Nature, 580, 463, 10.1038/s41586-020-2194-z

  7. [7]

    J., & Bodewits, D

    Hirabayashi, M., Trowbridge, A. J., & Bodewits, D. 2020, title The Mysterious Location of Maryland on 2014 MU69 and the Reconfiguration of Its Bilobate Shape, The Astrophysical Journal Letters, 891, L12, 10.3847/2041-8213/ab3e74

  8. [8]

    , archivePrefix = "arXiv", eprint =

    Johansen, A., Oishi, J. S., Low, M.-M. M., et al. 2007, title Rapid planetesimal formation in turbulent circumstellar disks, Nature, 448, 1022, 10.1038/nature06086

  9. [9]

    Planetary and Space Science177, 104695 (2019)

    Jutzi, M. 2019, title The shape and structure of small asteroids as a result of sub-catastrophic collisions, Planetary and Space Science, 177, 104695, 10.1016/j.pss.2019.07.009

  10. [10]

    Science348(6241), 1355–1358 (2015)

    Jutzi, M., & Asphaug, E. 2015, title The shape and structure of cometary nuclei as a result of low-velocity accretion, Science, 348, 1355, 10.1126/science.aaa4747

  11. [11]

    T., Porter, S

    Keane, J. T., Porter, S. B., Beyer, R. A., et al. 2022, title The Geophysical Environment of (486958) Arrokoth—A Small Kuiper Belt Object Explored by New Horizons, Journal of Geophysical Research: Planets, 127, e2021JE007068, 10.1029/2021JE007068

  12. [12]

    Kim, Y., Hirabayashi, M., & Bauer, J. 2024, title Numerical Investigation of the Cohesive Strength Regime of the Bilobated Arrokoth after the Sky-crater-forming Impact Event, The Planetary Science Journal, 5, 241, 10.3847/PSJ/ad8347

  13. [13]

    2024, title Formation of flattened planetesimals by gravitational collapse of rotating pebble clouds, Astronomy & Astrophysics, 683, A38, 10.1051/0004-6361/202347742

    Lorek, S., & Johansen, A. 2024, title Formation of flattened planetesimals by gravitational collapse of rotating pebble clouds, Astronomy & Astrophysics, 683, A38, 10.1051/0004-6361/202347742

  14. [14]

    N., & Johansen, A

    Lyra, W., Youdin, A. N., & Johansen, A. 2021, title Evolution of MU69 from a binary planetesimal into contact by Kozai--Lidov oscillations and nebular drag, Icarus, 356, 113831, 10.1016/j.icarus.2020.113831

  15. [15]

    Souza, P

    Marohnic, J. C., Richardson, D. C., McKinnon, W. B., et al. 2021, title Constraining the final merger of contact binary (486958) Arrokoth with soft‑sphere discrete element simulations, Icarus, 356, 113824, 10.1016/j.icarus.2020.113824

  16. [16]

    Science , author =

    McKinnon, W. B., Richardson, D. C., Marohnic, J. C., et al. 2020, title The solar nebula origin of (486958) Arrokoth, a primordial contact binary in the Kuiper Belt, Science, 367, eaay6620, 10.1126/science.aay6620

  17. [17]

    B., Mao, X., Schenk, P

    McKinnon, W. B., Mao, X., Schenk, P. M., et al. 2022, title Snow Crash: Compaction Craters on (486958) Arrokoth and Other Small KBOs, With Implications, Geophysical Research Letters, 49, e2022GL098406, 10.1029/2022GL098406

  18. [18]

    2000, Satellite Orbits: Models, Methods and Applications (Springer Science & Business Media), 10.1007/978-3-642-58391-9

    Montenbruck, O., & Gill, E. 2000, Satellite Orbits: Models, Methods and Applications (Springer Science & Business Media), 10.1007/978-3-642-58391-9

  19. [19]

    F., et al

    Nakano, R., Hirabayashi, M., Agrusa, H. F., et al. 2022, title NASA’s Double Asteroid Redirection Test (DART): mutual orbital period change due to reshaping in the near-earth binary asteroid system (65803) Didymos, The planetary science journal, 3, 148

  20. [20]

    S., Pelletier, F

    Nelson, D. S., Pelletier, F. J., Buie, M. W., et al. 2022, title Navigation and Orbit Estimation for New Horizons’ Arrokoth Flyby: Overview, Results and Lessons Learned, Space Science Reviews, 218, 11, 10.1007/s11214-022-00877-4

  21. [21]

    N., & Richardson, D

    Nesvorný, D., Youdin, A. N., & Richardson, D. C. 2010, title Formation of Kuiper belt binaries by gravitational collapse, The Astronomical Journal, 140, 785, 10.1088/0004-6256/140/3/785

  22. [22]

    B., Singer, K

    Porter, S. B., Singer, K. N., Schenk, P. M., et al. 2024, in 55th Lunar and Planetary Science Conference, LPI Contrib. No. 2806. https://www.hou.usra.edu/meetings/lpsc2024/pdf/2332.pdf

  23. [23]

    M., Olkin, C

    Protopapa, S., Grundy, W. M., Olkin, C. B., et al. 2019, in 50th Lunar and Planetary Science Conference, LPI Contrib. No. 2132, 2732. https://www.hou.usra.edu/meetings/lpsc2019/pdf/2732.pdf

  24. [24]

    Scheeres, D. J. 2007, title Rotational fission of contact binary asteroids, Icarus, 189, 370, 10.1016/j.icarus.2007.02.015

  25. [25]

    Scheeres, D. J. 2009, title Stability of the planar full 2-body problem, Celestial Mechanics and Dynamical Astronomy, 104, 103

  26. [26]

    R., Stern, S

    Spencer, J. R., Stern, S. A., Moore, J. M., et al. 2020, title The geology and geophysics of Kuiper Belt object (486958) Arrokoth, Science, 367, eaay3999, 10.1126/science.aay3999

  27. [27]

    A., Keeney, B., Singer, K

    Stern, S. A., Keeney, B., Singer, K. N., et al. 2021, title Some new results and perspectives regarding the Kuiper Belt object Arrokoth’s remarkable, bright neck, The Planetary Science Journal, 2, 87, 10.3847/psj/abee26

  28. [28]

    A., Weaver, H

    Stern, S. A., Weaver, H. A., Spencer, J. R., et al. 2019, title Initial results from the New Horizons exploration of 2014 MU69, a small Kuiper Belt object, Science, 364, eaaw9771, 10.1126/science.aaw9771

  29. [29]

    A., White, O

    Stern, S. A., White, O. L., Grundy, W. M., et al. 2023, title The Properties and Origin of Kuiper Belt Object Arrokoth's Large Mounds, The Planetary Science Journal, 4, 176, 10.3847/PSJ/acf317

  30. [30]

    2019, in EPSC-DPS Joint Meeting 2019, Vol

    Wandel, O., Kley, W., Schafer, C., et al. 2019, in EPSC-DPS Joint Meeting 2019, Vol. 2019, EPSC--DPS2019. https://meetingorganizer.copernicus.org/EPSC-DPS2019/EPSC-DPS2019-1768.pdf

  31. [31]

    2021, title (486958) Arrokoth: An overview of a Kuiper Belt Object seen at close range, 43rd COSPAR Scientific Assembly

    White, O., Spencer, J., Weaver, H., et al. 2021, title (486958) Arrokoth: An overview of a Kuiper Belt Object seen at close range, 43rd COSPAR Scientific Assembly. Held 28 January-4 February, 43, 331. https://ui.adsabs.harvard.edu/abs/2021cosp...43E.331W/abstract

  32. [32]

    2019, title A finite element method for computational full two-body problem: I

    Yu, Y., Cheng, B., Hirabayashi, M., Michel, P., & Baoyin, H. 2019, title A finite element method for computational full two-body problem: I. The mutual potential and derivatives over bilinear tetrahedron elements, Celestial Mechanics and Dynamical Astronomy, 131, 1, 10.1007/s10569-019-9930-4

  33. [33]

    Zastawny, M., Mallouppas, G., Zhao, F., & van Wachem, B. 2012, title Derivation of drag and lift force and torque coefficients for non-spherical particles in flows, International Journal of Multiphase Flow, 39, 227, 10.1016/j.ijmultiphaseflow.2011.09.004