Pith. sign in

REVIEW 3 major objections 6 minor 45 references

Prediction of Apophis's deformation-driven rotational evolution during its closest encounter to the Earth in 2029

T0 review · 3 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Apophis's 2029 flyby may twist its spin by degrees if the asteroid is as soft as 10 kPa.

desk verdict The paper makes a testable forward prediction—a ≤10 kPa Young's modulus could give a few-degree spin deviation within days—but the exact threshold is anchored to a borrowed, unshown spring conversion and a hand-set damping coefficient, so the numbers are provisional until a sensitivity analysis is done. read the letter →

arxiv 2507.17710 v1 pith:NBUNIPN6 submitted 2025-07-23 astro-ph.EP

Masatoshi Hirabayashi This is my paper · ORCID
classification astro-ph.EP
keywords 99942ApophisasteroidsdynamicsrotationtidessolidbodyrotationalYoung'smodulus
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

On April 13, 2029, Apophis will pass within six Earth radii, close enough for Earth's tides to change its tumbling spin. This paper argues that the spin change cannot be understood from rigid-body dynamics alone: if the asteroid deforms during the encounter, the reshaping alters its moment of inertia and thereby its angular velocity, producing a spin state that differs from the rigid-body case even when the deformation itself stays tiny. Using a dumbbell-shaped spring-damper model, it predicts that for a Young's modulus of about 1 MPa or higher the deviation stays at a few degrees over a year, whereas for about 10 kPa or less the deviation can reach a few degrees within days and possibly 90 degrees within months. The result matters because telescopes and spacecraft that will observe Apophis in 2029 could look for this signature and, if found, read off the asteroid's interior stiffness.

What carries the argument

The load-bearing object is a semi-analytic dumbbell model: Apophis is treated as two equal spherical lobes connected by a massless rod, with the momentum equation decomposed into translation, rotation, and deformation modes. Deformation is closed by a linear spring-damper, g_i(σ) = −k m_i u_i − c m_i ẋ_i, with spring coefficient k = 90E/m converted from soft-sphere discrete-element simulations and a constant damping coefficient c = 0.1 s⁻¹. This machinery converts an assumed Young's modulus E into a long-axis displacement, changes the moment of inertia I_ζ, and through angular momentum conservation changes the angular velocity; after the encounter the body settles to a new equilibrium displacement, leaving a permanent spin deviation from the rigid-body case.

What would settle it

A decisive check is to monitor Apophis's spin state continuously from before closest approach until several months after April 13, 2029, with sub-degree precision. If the observed post-encounter spin evolution matches the rigid-body prediction to within a fraction of a degree while independent radar or thermal measurements indicate a Young's modulus around 10 kPa or below, the proposed deformation-driven mechanism—or the spring–damper stiffness mapping that produces it—would be ruled out.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that Apophis's deformation-driven rotational evolution may be observable even if the deformation itself is not. The model tracks the long-axis stretching of a dumbbell-shaped two-lobe body under Earth's tidal torque, letting the changing moment of inertia feed back into the spin through angular momentum conservation. It finds a stiffness threshold: at a Young's modulus near 1 MPa or above, the deformation-driven deviation from the rigid-body spin is a few degrees over one year; at 10 kPa or below, the deviation reaches a few degrees within a few days after closest approach and can grow to about 90 degrees within months, depending on the tumbling state at encounter. Because the pre-encounter tumbling state is uncertain, the paper propagates 10,000 initial states from photometric measurements and finds that the deviation magnitude is highly sensitive to the spin state, so detailed pre-encounter characterization is needed to predict or interpret it.

Load-bearing premise

The whole prediction depends on the assumption that a simple spring-and-damper model with a spring constant set by k = 90E/m and a damping rate chosen by hand faithfully represents how Apophis actually deforms during the flyby.

Editorial extensions

If this is right

  • If Apophis's Young's modulus is 10 kPa or below, optical observations from Earth and spacecraft could see a spin-state deviation of a few degrees within days of closest approach, growing to about 90 degrees within months.
  • If the Young's modulus is about 1 MPa or higher, the deformation-driven deviation stays at a few degrees even a year after the encounter, making the signal hard to separate from rigid-body evolution.
  • Because the deviation is sensitive to the tumbling state, the same stiffness can produce very different observable outcomes; measuring the pre-encounter spin state to high precision is a prerequisite for interpreting post-encounter lightcurves.
  • The spin deviation appears without any irreversible resurfacing or internal failure, so a reversible elastic response alone is enough to produce a measurable rotational signature.
  • Spacecraft measurements of the moment of inertia, gravity field, or seismic and radar response before and after the encounter could separate deformation-driven spin change from rigid-body spin change and constrain bulk strength.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the spring-coefficient conversion k = 90E/m over- or under-estimates the real stiffness by, say, an order of magnitude, the quoted 10 kPa threshold would shift correspondingly, so the observable window of stiffness values is wider or narrower than the paper's numbers suggest.
  • The same deformation–spin feedback should operate in other rubble-pile asteroids that pass close to planets, offering a general way to infer bulk strength from rotational lightcurves without resolving deformation.
  • A testable extension would couple this dumbbell model to the full radar shape model, checking whether multi-axis deformation modes, which the paper argues would only increase the deviation, push the predicted angles above the few-degree level at higher stiffness.
  • If a spacecraft measures both shape elongation and spin state continuously through the encounter, inverting the observed deviation against this model could yield a direct, in-situ estimate of Apophis's Young's modulus.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper predicts that deformation of Apophis during its 2029 Earth flyby can change its spin state relative to the rigid-body case. Apophis is modeled as a dumbbell of two spherical lobes connected by a massless spring-damper element, with the deformation dynamics coupled to translation and rotation following Hirabayashi (2023). The authors propagate the observed tumbling spin state with uncertainties, run rigid-body and deformation cases from a common pre-encounter state, and report angular deviations as a function of Young's modulus via the conversion k = 90E/m. They find that for E ~ 1 MPa deviations are a few degrees over a year, while for E ~ 10 kPa deviations may reach a few degrees within days, with possible larger deviations over months. The paper includes a statistical analysis over 10,000 spin states and an analytic validation in Appendix A.

Significance. If the constitutive mapping is accepted, the paper provides a falsifiable, forward-model prediction linking Apophis's interior strength to an observable spin-state signature during the 2029 encounter. This would be valuable for the upcoming Apophis observation and mission campaigns and for constraining the bulk strength of sub-kilometer rubble-pile asteroids. The study's strengths include the forward (non-fitted) nature of the simulation, the propagation of observational spin-state uncertainties through 10,000 cases, and the explicit benchmarking of displacement magnitudes against SSDEM and FEM results. However, the quantitative headline depends almost entirely on two poorly constrained constitutive parameters introduced in Section 4.1, and the long-term deviation claims in the discussion are not supported by results shown in Section 5.

major comments (3)
  1. [Section 4.1, Eq. (8)] The central threshold E ≲ 10 kPa is controlled by the constitutive mapping k = 90E/m and the hand-set damping c = 10^-1 s^-1, but the rescaling factor behind k = 90E/m is not shown and no sensitivity analysis for c is provided. In the cited SSDEM work, the contact stiffness is particle-scale (kn ~ π R E), so translating it to a body-scale dumbbell spring requires the effective particle radius and contact network; a factor-of-10 uncertainty in that translation shifts the E threshold by a factor of 10, moving the predicted few-degree deviation across the observational detectability boundary. Please provide the derivation of the factor 90 and a sweep over both k and c.
  2. [Sections 6 and 7 vs. Abstract] The claim that at E = 10 kPa the spin deviation 'may reach 90° within two months' appears only in the Discussion and Conclusion; the Abstract states only 'a few degrees even a few days after the closest encounter,' and Section 5 presents results only over a 48-hour simulation. No figure or quantitative run supporting the 90°-in-months claim is shown. The manuscript should either present the long-term simulation used for that claim or restrict the statement to the simulated time interval.
  3. [Appendix A] The Appendix A validation checks the angular-momentum bookkeeping of Eq. (A.2) to about 20%, but it does not validate the physical mapping from Young's modulus to the spring constant or the damping model. Since the headline conclusion is a prediction of spin deviation at a given E, the lack of a direct validation of the constitutive mapping is a load-bearing gap rather than a mere technical issue.
minor comments (6)
  1. [Table 3] The system mass is listed as 6×10^6 kg in Table 3 but as 6×10^10 kg in Section 4.1; the table value is inconsistent with the stated bulk density and radius and should be corrected.
  2. [Table 3] The unit for Iζ appears as 'k m2', which is not a valid unit; it should presumably be 'kg m^2'.
  3. [Table 1] The table header contains the typo 'Unites' instead of 'Units'.
  4. [Section 4.1] The text says 'pdkgrav modeling' rather than 'pkdgrav modeling'; also, the phrase 'with pdkgrav' should be corrected.
  5. [Section 7] The conclusion states that the model uses 'two equally massive, spherical lobes,' but Section 5 explicitly parameterizes m1/m2 = 0.43, 0.67, and 1.0; this description should be revised.
  6. [Figure 6 caption] The caption says Panel c is 'identical to Panel a,' but Panel c is a maximum-angle map while Panel a is a time series; the relationship should be described more precisely.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted spin deviation is a forward-model output, not a refit of the paper's constitutive inputs.

full rationale

The paper is a forward parametric simulation. The constitutive inputs k=90E/m and c=10^-1 s^-1 are set in Section 4.1, and the deformation-driven spin deviation is computed by integrating the coupled translation-rotation-deformation equations in Section 3; it is never fitted to any observed Apophis spin quantity. The spring scale is chosen so that the model's displacement is consistent with prior SSDEM and FEM displacement levels, and displacement is a different observable from the predicted spin deviation, so the central claim does not reduce to that calibration by construction. The self-citation to Hirabayashi (2023) supplies the modeling framework, but the governing equations are re-derived in the present paper, making the citation illustrative rather than load-bearing. Appendix A provides an internal consistency check rather than a fit. The unshown rescaling factor behind k=90E/m and the hand-set damping coefficient are genuine robustness limitations, but they do not make the spin prediction equivalent to the inputs; they shift the quantitative threshold without forcing the output to equal the input. No step satisfies the bar of Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The model relies on a simplified dumbbell geometry, a linear spring-damper constitutive law, and several hand-set parameters (damping, conversion factor, density, lobe mass ratio). No new physical entities are introduced. The main free parameters are the Young's-modulus-driven spring coefficient and the damping coefficient, both varied or fixed by practical convenience rather than by direct measurement.

free parameters (6)
  • Young's modulus E = 10 kPa, 100 kPa, 1 MPa (varied across simulations)
    Controls the spring stiffness k=90E/m; the central thresholds depend on this assumed range, not fitted to observation.
  • Spring coefficient k = 1.51e-5, 1.51e-4, 1.51e-3 s^-2
    Derived from E via k=90E/m; it sets the elastic response of the two-lobe model.
  • Damping coefficient c = 0.1 s^-1 (constant)
    Chosen by hand; the paper says test runs show no significant variations unless oscillatory, but no sensitivity analysis is shown.
  • Conversion factor 90 in k=90E/m = 90 (dimensionless)
    Introduced as a rescaling factor from SSDEM (DeMartini et al.); not derived in this paper, and the quantitative predictions hinge on it.
  • Bulk density = 2900 kg/m^3
    Assumed from DeMartini et al. (2019); affects mass and MOI estimates, with a stated ~35% uncertainty.
  • Lobe mass ratio m1/m2 = 0.43, 0.67, 1.0
    Varied in the study; paper finds it does not alter spin evolution because m and I_zeta are held constant.
assumptions (5)
  • domain assumption Apophis is modeled as a dumbbell of two spherical lobes connected by a massless rod
    Section 3 states this explicitly; it ignores shape details and constrains deformation modes to the long axis.
  • domain assumption The deformation follows a linear spring-damper law with constant damping coefficient
    Equations (7)-(8); the damping coefficient is set to 0.1 s^-1 without a constitutive justification.
  • domain assumption The tidal torque from Earth acts on the two point masses
    Equations (3)-(5); the model treats Earth as a point mass and lobes as point masses, which is a strong simplification.
  • ad hoc to paper The trial-case initialization (no Earth gravity) produces the same pre-encounter spin state for both rigid-body and deformation cases
    Section 4.2; this procedure is introduced to avoid initial-state mismatch but is not independently validated.
  • domain assumption Only the longest-axis deformation is considered; all other deformation modes are neglected
    Introduction and Section 3; the authors state this underestimates real displacement and gives a lower bound on rotational change.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Prediction of Apophis's deformation-driven rotational evolution during its closest encounter to the Earth in 2029." pith.science (2026). https://pith.science/paper/NBUNIPN6

@misc{pith2026250717710,
  author       = {Pith},
  title        = {Pith review of: Prediction of Apophis's deformation-driven rotational evolution during its closest encounter to the Earth in 2029},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NBUNIPN6}},
  note         = {Machine review of arXiv:2507.17710}
}
read the original abstract

In 2029, the near-Earth asteroid (99942) Apophis approaches the Earth within six Earth radii. This opportunity is one of the rarest natural experiments that we can use to better characterize a small body through telescopic observations and space missions. Earlier geological investigations consistently suggested that major geological processes might not occur on Apophis during this closest encounter, including surface processing and interior deformation. However, minor resurfacing may occur, depending on local geological conditions. A critical finding is that the rotational evolution occurs due to the tidal effect from the Earth. The present study offers an additional perspective on the rotational evolution, which may vary due to variations in interior properties. Namely, possible deformation processes may change the spin state variation from the rigid body state, even if deformation is not measurable. The effort in this work is to explore this issue using a simplified model, motivated by earlier studies by Hirabayashi (2023) and Taylor et al. (2023). The results show that the deformation-driven spin state change may be possible, depending on Young's modulus. If this asteroid's Young's modulus is ~1 MPa or higher, the spin state only deviates a few degrees from the rigid body state over one year. However, if it is ~10 kPa or less, the spin state deviation may reach a few degrees, even a few days after the closest encounter. Both telescopic observations and space missions can provide strong insights into this phenomenon.

Figures

Figures reproduced from arXiv: 2507.17710 by the authors.

Figure 1
Figure 1. Apophis’s orbital state during the closest approach. Panels a and b show the same condition in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Spin state variations at 2029 APR 13 09:00:00 TDB, given earlier photometric observations by [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Schematic of the present model. are given as m1 and m2, the forces are written as follows: f1 = − GMm1 x 3 1 x1 − Gm1m2 ∥q1 − q2∥ 3 (q1 − q2 ) (3) f2 = − GMm2 x 3 2 x2 − Gm1m2 ∥q2 − q1∥ 3 (q2 − q1 ) (4) where M is the Earth’s mass, and G is the gravitational constant. Later, subscripts 1 and 2 may be replaced with i to discuss further model formulation. Characterizing the full coupling dynamics requires accounting f… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Time evolution of displacement along the long axis, which is the [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]
Figure 5
Figure 5. Figure 5: Angular variations with time along three principal axes. The blue lines show the angular variations [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Statistical analysis using the rotational distributions from Figure 2. Panels a and b show the [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 31 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in ":" * " " * FUNCTION f...

  2. [2]

    , author Oberbeck , V.R

    author Aggarwal , H.R. , author Oberbeck , V.R. , year 1974 . title Roche Limit of a Solid Body . journal The Astrophysical Journal volume 191 , pages 577--588 . :10.1086/152998

    work page doi:10.1086/152998 1974

  3. [3]

    , author Adell, P.C

    author Andrade, J.E. , author Adell, P.C. , author Amini, R.B. , author Bhaskaran, S. , author Bousquet, P. , author Chmielewski, A.B. , author Daca, A.E. , author Fesq, L.M. , author Haynes2, M. , author Herique, A. , author Raymond2, C.A. , year 2025 . title The Caltech Mission to Apophis: Status and Path Forward , in: booktitle Apophis T-4 Years: Knowl...

    work page 2025

  4. [4]

    , author Agrusa, H

    author Ballouz, R.L. , author Agrusa, H. , author Barnouin, O. , author Walsh, K. , author Zhang, Y. , author Binzel, R. , author Bray, V. , author DellaGiustina, D.N. , author Jawin, E. , author DeMartini, J. , author Marusiak, A. , author Michel, P. , author Murdoch, N. , author Richardson, D. , author Rivera-Valentín, E. , author Rivkin, A. , author Ta...

    work page 2024

  5. [5]

    , author Daly, M.G

    author Barnouin, O.S. , author Daly, M.G. , author Palmer, E.E. , author Gaskell, R.W. , author Weirich, J.R. , author Johnson, C.L. , author Al Asad, M.M. , author Roberts, J.H. , author Perry, M.E. , author Susorney, H.C.M. , author Daly, R.T. , author Bierhaus, E.B. , author Seabrook, J.A. , author Espiritu, R.C. , author Nair, A.H. , author Nguyen, L....

    work page 2019

  6. [6]

    , author Scheeres, D.J

    author Benson, C.J. , author Scheeres, D.J. , author Brozović, M. , author Chesley, S.R. , author Pravec, P. , author Scheirich, P. , year 2023 . title Spin state evolution of (99942) Apophis during its 2029 Earth encounter . journal Icarus volume 390 , pages 115324 . :10.1016/j.icarus.2022.115324

    work page arXiv 2023

  7. [7]

    , author Rivkin , A.S

    author Binzel , R.P. , author Rivkin , A.S. , author Thomas , C.A. , author Vernazza , P. , author Burbine , T.H. , author DeMeo , F.E. , author Bus , S.J. , author Tokunaga , A.T. , author Birlan , M. , year 2007 . title Spectral Properties and Composition of Potentially Hazardous Asteroid (99942) Apophis , in: booktitle AAS/Division for Planetary Scienc...

    work page 2007

  8. [8]

    , author Benner, L.A

    author Brozović, M. , author Benner, L.A. , author McMichael, J.G. , author Giorgini, J.D. , author Pravec, P. , author Scheirich, P. , author Magri, C. , author Busch, M.W. , author Jao, J.S. , author Lee, C.G. , author Snedeker, L.G. , author Silva, M.A. , author Slade, M.A. , author Semenov, B. , author Nolan, M.C. , author Taylor, P.A. , author Howell...

    work page 2018

Show all 45 references
  1. [9]

    , author Baer, J

    author Chesley, S.R. , author Baer, J. , author Monet, D.G. , year 2010 . title Treatment of star catalog biases in asteroid astrometric observations . journal Icarus volume 210 , pages 158--181 . :10.1016/j.icarus.2010.06.003

    2010 doi

  2. [10]

    , author Milani , A

    author Chesley, S.R. , author Milani , A. , author Tholen , D. , author Bernardi , F. , author Chodas , P. , author Micheli , M. , year 2009 . title An Updated Assessment Of The Impact Threat From 99942 Apophis , in: booktitle AAS/Division for Planetary Sciences Meeting Abstra...

    2009

  3. [11]

    , author Hirabayashi, M

    author Daca, A. , author Hirabayashi, M. , author Kim, Y. , author DeMartini, J. , author Raymond, C. , author Herique, A. , author Haynes, M. , author Plettemeier, D. , author Davidsson, B. , author Andrade, J. , author the Caltech Mission Team , year 2025 . title The Caltech...

    2025

  4. [12]

    , author Nolan, M.C

    author DellaGiustina, D.N. , author Nolan, M.C. , author Polit, A.T. , author Moreau, M.C. , author Golish, D.R. , author Simon, A.A. , author Adam, C.D. , author Antreasian, P.G. , author Ballouz, R.L. , author Barnouin, O.S. , author Becker, K.J. , author Bennett, C.A. , aut...

    2023

  5. [13]

    , author Murdoch , N

    author DeMartini , J. , author Murdoch , N. , author Garcia , R. , author Richardson , D. , year 2024 . title SSDEM Discrete Seismology Models with Applications to the Apophis 2029 Close Earth Encounter , in: booktitle European Planetary Science Congress . :10.5194/epsc2024-737

    2024 doi

  6. [14]

    , author Richardson, D.C

    author DeMartini, J.V. , author Richardson, D.C. , author Barnouin, O.S. , author Schmerr, N.C. , author Plescia, J.B. , author Scheirich, P. , author Pravec, P. , year 2019 . title Using a discrete element method to investigate seismic response and spin change of 99942 apophi...

    2019

  7. [15]

    , author Brozovic, M

    author Dotson, J.L. , author Brozovic, M. , author Chesley, S. , author Jarmak, S. , author Moskovitz, N. , author Rivkin, A. , author Sanchez, P. , author Souami, D. , author Titus, T.N. , year 2022 . title Apophis specific action team report . type Technical Report

    2022

  8. [16]

    , author Chesley, S

    author Farnocchia, D. , author Chesley, S. , author Vokrouhlický, D. , author Milani, A. , author Spoto, F. , author Bottke, W. , year 2013 . title Near Earth Asteroids with measurable Yarkovsky effect . journal Icarus volume 224 , pages 1--13 . :10.1016/j.icarus.2013.02.004

    2013 doi

  9. [17]

    , author Kawaguchi, J

    author Fujiwara, A. , author Kawaguchi, J. , author Yeomans, D.K. , author Abe, M. , author Mukai, T. , author Okada, T. , author Saito, J. , author Yano, H. , author Yoshikawa, M. , author Scheeres, D.J. , author Barnouin-Jha, O. , author Cheng, A.F. , author Demura, H. , aut...

    2006

  10. [18]

    , author Yeomans, D

    author Giorgini, J. , author Yeomans, D. , author Chamberlin, A. , author Chodas, P. , author Jacobson, R. , author Keesey, M. , author Lieske, J. , author Ostro, S. , author Standish, E. , author Wimberly, R. , year 1996 . title PL’s On-Line Solar System Data Service , in: bo...

    1996

  11. [19]

    , author Benner, L.A

    author Giorgini, J.D. , author Benner, L.A. , author Ostro, S.J. , author Nolan, M.C. , author Busch, M.W. , year 2008 . title Predicting the Earth encounters of (99942) Apophis . journal Icarus volume 193 , pages 1--19 . :10.1016/j.icarus.2007.09.012

    2008 doi

  12. [20]

    , author Minton, D.A

    author Hesselbrock, A.J. , author Minton, D.A. , year 2017 . title An ongoing satellite--ring cycle of Mars and the origins of Phobos and Deimos . journal Nature Geoscience volume 10 , pages 266--269 . :10.1038/ngeo2916

    2017 doi

  13. [21]

    , year 2023

    author Hirabayashi, M. , year 2023 . title Dynamics of a deforming planetary body . journal Icarus volume 389 , pages 115258 . :10.1016/j.icarus.2022.115258

    2023

  14. [22]

    , author Mimasu, Y

    author Hirabayashi, M. , author Mimasu, Y. , author Sakatani, N. , author Watanabe, S. , author Tsuda, Y. , author Saiki, T. , author Kikuchi, S. , author Kouyama, T. , author Yoshikawa, M. , author Tanaka, S. , author Nakazawa, S. , author Takei, Y. , author Terui, F. , autho...

    2021

  15. [23]

    , author Morimoto, M.Y

    author Hirabayashi, M. , author Morimoto, M.Y. , author Yano, H. , author Kawaguchi, J. , author Bellerose, J. , year 2010 . title Linear stability of collinear equilibrium points around an asteroid as a two-connected-mass: Application to fast rotating Asteroid 2000EB14 . jour...

    2010 doi

  16. [24]

    , year 2003

    author Hughes, T.J. , year 2003 . title The finite element method: linear static and dynamic finite element analysis . publisher Courier Corporation

    2003

  17. [25]

    , author Hirabayashi, M

    author Kim, Y. , author Hirabayashi, M. , author Binzel, R.P. , author Brozovi \'c , M. , author Scheeres, D.J. , author Richardson, D.C. , year 2021 . title The surface sensitivity of rubble-pile asteroids during a distant planetary encounter: Influence of asteroid shape elon...

    2021

  18. [26]

    , author Martino , P

    author K \"u ppers , M. , author Martino , P. , author Carnelli , I. , author Michel , P. , year 2024 . title Status of ESA's Rapid Apophis Mission for Space Safety (RAMSES) Concept , in: booktitle European Planetary Science Congress , pp. pages EPSC2024--199 . :10.5194/epsc2024-199

    2024 doi

  19. [27]

    , author Whitman, R.V

    author Lambe, T.W. , author Whitman, R.V. , year 2008 . title Soil mechanics SI version . publisher John Wiley & Sons

    2008

  20. [28]

    , author Kim, M.J

    author Lee, H.J. , author Kim, M.J. , author Marciniak, A. , author Kim, D.H. , author Moon, H.K. , author Choi, Y.J. , author Zoła, S. , author Chatelain, J. , author Lister, T.A. , author Gomez, E. , author Greenstreet, S. , author Pál, A. , author Szakáts, R. , author Erasm...

    2022

  21. [29]

    , author Marchi, S

    author Levison, H.F. , author Marchi, S. , author Noll, K.S. , author Spencer, J.R. , author Statler, T.S. , author Bell, J.F. , author Bierhaus, E.B. , author Binzel, R. , author Bottke, W.F. , author Britt, D. , author Brown, M.E. , author Buie, M.W. , author Christensen, P....

    2024

  22. [30]

    , author Melnikov, A.V

    author Lobanova, K.S. , author Melnikov, A.V. , year 2024 . title Disturbances in the Rotational Dynamics of Asteroid (99942) Apophis at its Approach to the Earth in 2029 . journal Solar System Research volume 58 , pages 208--219 . :10.1134/S0038094623700107

    2024 doi

  23. [31]

    , author Mannocchi, A

    author Morelli, A.C. , author Mannocchi, A. , author Giordano, C. , author Ferrari, F. , author Topputo, F. , year 2024 . title Initial Trajectory Assessment of a low-thrust option for the RAMSES Mission to (99942) Apophis . journal Advances in Space Research volume 73 , pages...

    2024 doi

  24. [32]

    , author Dermott, S.F

    author Murray, C.D. , author Dermott, S.F. , year 2000 . title Solar System Dynamics . publisher Cambridge University Press

    2000

  25. [33]

    , author Kiss, C

    author Müller, T.G. , author Kiss, C. , author Scheirich, P. , author Pravec, P. , author O’Rourke, L. , author Vilenius, E. , author Altieri, B. , year 2014 . title Thermal infrared observations of asteroid (99942) Apophis with Herschel . journal Astronomy & Astrophysics volu...

    2014 doi

  26. [34]

    , author Scheirich, P

    author Pravec, P. , author Scheirich, P. , author Ďurech, J. , author Pollock, J. , author Kušnirák, P. , author Hornoch, K. , author Galád, A. , author Vokrouhlický, D. , author Harris, A. , author Jehin, E. , author Manfroid, J. , author Opitom, C. , author Gillon, M. , auth...

    2014

  27. [35]

    , author Kelley, M.S

    author Reddy, V. , author Kelley, M.S. , author Dotson, J. , author Farnocchia, D. , author Erasmus, N. , author Polishook, D. , author Masiero, J. , author Benner, L.A.M. , author Bauer, J. , author Alarcon, M.R. , author Balam, D. , author Bamberger, D. , author Bell, D. , a...

    2022

  28. [36]

    , author Junkins, J.L

    author Schaub, H. , author Junkins, J.L. , year 2003 . title Analytical mechanics of space systems . publisher AIAA

    2003

  29. [37]

    , author Benner, L

    author Scheeres, D. , author Benner, L. , author Ostro, S. , author Rossi, A. , author Marzari, F. , author Washabaugh, P. , year 2005 . title Abrupt alteration of Asteroid 2004 MN4's spin state during its 2029 Earth flyby . journal Icarus volume 178 , pages 281--283 . :10.101...

    2005 doi

  30. [38]

    , author French, A.S

    author Scheeres, D.J. , author French, A.S. , author Tricarico, P. , author Chesley, S.R. , author Takahashi, Y. , author Farnocchia, D. , author McMahon, J.W. , author Brack, D.N. , author Davis, A.B. , author Ballouz, R.L. , author Jawin, E.R. , author Rozitis, B. , author E...

    2020

  31. [39]

    , author Wang, H.S

    author Scheeres, D.J. , author Wang, H.S. , author Sánchez, P. , year 2025 . title Modeling Apophis as a Bi-Lobate Rubble Pile Body using Contact Dynamics , in: booktitle 9th IAA Planetary Defense Conference 2025

    2025

  32. [40]

    , author Lhotka, C

    author Souchay, J. , author Lhotka, C. , author Heron, G. , author Hervé, Y. , author Puente, V. , author Folgueira Lopez, M. , year 2018 . title Changes of spin axis and rate of the asteroid (99942) Apophis during the 2029 close encounter with Earth: A constrained model . jou...

    2018 doi

  33. [41]

    , author Seligman, D.Z

    author Taylor, A.G. , author Seligman, D.Z. , author MacAyeal, D.R. , author Hainaut, O.R. , author Meech, K.J. , year 2023 . title Numerical Simulations of Tidal Deformation and Resulting Light Curves of Small Bodies: Material Constraints of 99942 Apophis and 1I/‘Oumuamua . j...

    2023 doi

  34. [42]

    title Near-Earth Objects Workshops to Assess Reconnaissance for Planetary Defense: Working Groups Final Report

    author The NEO WARP Working Group , year 2025 . title Near-Earth Objects Workshops to Assess Reconnaissance for Planetary Defense: Working Groups Final Report . type Technical Report . Goddard Space Flight Center . https://ntrs.nasa.gov/citations/20250005751

    2025

  35. [43]

    , author Winter, O.C

    author Valvano, G. , author Winter, O.C. , author Sfair, R. , author Machado Oliveira , R. , author Borderes-Motta , G. , author Moura, T.S. , year 2021 . title APOPHIS – effects of the 2029 Earth’s encounter on the surface and nearby dynamics . journal Monthly Notices of the ...

    2021 doi

  36. [44]

    , author Hirabayashi, M

    author Watanabe, S. , author Hirabayashi, M. , author Hirata, N. , author Hirata, N. , author Noguchi, R. , author Shimaki, Y. , author Ikeda, H. , author Tatsumi, E. , author Yoshikawa, M. , author Kikuchi, S. , author Yabuta, H. , author Nakamura, T. , author Tachibana, S. ,...

    2019

  37. [45]

    , author Richardson, D.C

    author Yu, Y. , author Richardson, D.C. , author Michel, P. , author Schwartz, S.R. , author Ballouz, R.L. , year 2014 . title Numerical predictions of surface effects during the 2029 close approach of Asteroid 99942 Apophis . journal Icarus volume 242 , pages 82--96 . :10.101...

    2014 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.