Determination of Jupiter's Primordial Physical State

Fred C. Adams; Konstantin Batygin

REVIEW 2 major objections 5 minor 86 references

Determination of Jupiter's Primordial Physical State

T0 review · 2 major / 5 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 Jupiter's primordial radius, entropy, magnetic field, and accretion rate are recovered from inner-moon resonances and spin conservation.

desk verdict A genuinely new diagnostic for Jupiter's primordial state, but the printed central equation has a typo that makes the derivation look wrong; the result survives once the present-day spin is used where the equilibrium spin is printed. read the letter →

arxiv 2505.12652 v1 pith:2MWEVGF3 submitted 2025-05-19 astro-ph.EP

Konstantin Batygin , Fred C. Adams This is my paper · ORCID

classification astro-ph.EP

keywords Jupiterformationprimordialradiuscircumplanetarydisksatelliteresonancesmagnetospherictruncationangularmomentumevolutionwarmstartentropysolarnebulalifetime

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

Jupiter's formation is usually modeled from the inside out, with outcomes depending on uncertain details of gas accretion, shock physics, and hydrogen equations of state. This paper sidesteps those uncertainties by reading Jupiter's primordial state from two conserved or recorded quantities: the planet's rotational angular momentum and the orbital resonance histories of its inner moons. It concludes that when the proto-solar nebula dissipated, roughly 3.8 million years after the first solids formed, Jupiter was 2.0 to 2.5 times its present radius, had a convective-envelope entropy of about 10.6 to 11 $k_{\rm B}$ per baryon, a surface magnetic field near 21 mT, and was accreting circumplanetary disk gas at 1.2 to 2.4 Jupiter masses per million years. These numbers are consistent with core accretion and supply a concrete snapshot of a giant planet at the end of its formation.

What carries the argument

The central identity is conservation of rotational angular momentum, $J = I M R^2 \Omega$, applied between the disk-bearing epoch and the present. The primordial spin is set by disk-locking, an equilibrium between accretion spin-up and magnetic braking that gives $\Omega^{\dagger} = \chi \sqrt{G M_{\rm J}/R_{\rm t}^3}$ with $\chi \approx 0.88$. The truncation radius is tied to Io's orbit by $R_{\rm t} = a_{\rm Io}^{\dagger}/\zeta$, with $\zeta \approx 1.13$ from numerical simulations of a three-satellite resonant chain. An integrable Hamiltonian model of second-order mean-motion resonances supplies the constraint on $a_{\rm Io}^{\dagger}$ from the inclination kicks to Amalthea and Thebe, and hydrostatic interior models supply the primordial moment-of-inertia factor as a monotonic function of radius. Equation (1) combines these pieces to solve for $R_{\rm J}^{\dagger}$.

What would settle it

High-precision astrometry of Thebe could decide whether its 1.09-degree inclination requires sequential crossings of the 6:4, 5:3, and 4:2 resonances with Io or could arise from fewer crossings. If the 4:2 crossing is ruled out, the upper bound on Io's primordial orbit disappears and the inferred radius range shifts; if all three crossings are confirmed, the radius range tightens toward its lower end.

Watch

Extended reading notes

Core claim

The central claim is that Jupiter's radius at the epoch of nebular dissipation can be inferred without invoking a specific accretion model. The paper uses the resonance-excited inclinations of the inner moons Amalthea and Thebe to fix Io's primordial semi-major axis at $a_{\rm Io}^{\dagger} = 4.02$ to $4.98\,R_{\rm J}$, then converts this to a magnetospheric truncation radius $R_{\rm t} \approx 3.6$ to $4.4\,R_{\rm J}$ using the established offset of a resonant satellite chain from the disk edge. Because magnetic coupling between Jupiter and the disk locks the primordial spin to a value determined by $R_{\rm t}$, and because Jupiter's post-nebular evolution conserves rotational angular momentum, the present-day spin and moment of inertia can be run backward to solve for the primordial radius. The result, $R_{\rm J}^{\dagger} = 2.02$ to $2.59\,R_{\rm J}$, is then used with hydrostatic interior models to infer a 'warm start' entropy of roughly $10.6$ to $11\,k_{\rm B}$ per baryon, a dynamo-scaled surface field $B_{\rm J}^{\dagger} \approx 21$ mT, and an accretion rate $\dot{M} = 1.2$ to $2.4$ Jupiter masses per million years.

Load-bearing premise

Everything rests on Io having begun its post-nebular tidal migration from a semi-major axis between 4.02 and 4.98 Jupiter radii, as inferred from the resonance excitation of Amalthea's and Thebe's orbital tilts; if that inference is wrong, the derived radius shifts by tens of percent.

Editorial extensions

If this is right

Jupiter was roughly twice to 2.5 times its present radius at about 3.8 million years after the first solids, which is a direct, datable check on core-accretion formation chronologies.
The inferred envelope entropy of about 10.6 to 11 $k_{\rm B}$ per baryon places young Jupiter in the 'warm start' regime rather than an extreme hot or cold start.
A primordial surface field near 21 mT, about 50 times today's value, combined with an accretion rate of 1.2 to 2.4 Jupiter masses per million years, constrains the dynamo and mass-feeding history of the circum-Jovian disk.
Io's orbit at disk dissipation was between 4.02 and 4.98 Jupiter radii, so the inner moons' resonance record becomes a usable chronometer for the late stages of giant-planet formation.
The method offers an observationally grounded alternative to accretion-model predictions for the terminal state of a giant planet's formation.

Reading between the lines

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

The same chain of reasoning could be applied to Saturn if its inner moon system preserves a similar resonance footprint, yielding an independent primordial radius and entropy for a second giant planet.
The predicted surface field of about 21 mT puts young Jupiter in a regime where cyclotron maser radio emission might be detectable from analogous young giant planets around nearby stars, offering an observational test of the scaling.
If the inferred accretion rate is representative, the circumplanetary disk must have been supplying matter vigorously right up to the end of the nebular epoch, favoring formation models in which the disk appears late and is short-lived.

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.

Desk Editor's Note

read the letter

Colleague — the headline is this: the paper has a real, publishable idea, and the printed central equation has a typo that makes the main derivation look wrong. The result survives once you replace Ω_E with the present-day spin, and the paper's own §3 iteration confirms it. But as it stands, the equation as written cancels ξ and ζ and gives ~1.4 R_J, not the quoted 2.0–2.5 R_J. That needs to be fixed before anyone cites the formula.

What's new: they chain Io's inferred primordial semi-major axis (ξ = 4.02–4.98 R_J from resonance kicks to Amalthea and Thebe) to the magnetospheric truncation radius R_t, then to the disk-locked spin, then to angular momentum conservation. That's a genuinely new diagnostic for the primordial state of a giant planet, and it gives a concrete radius, entropy (~10.6–11 k_B/baryon), field (~21 mT), and accretion rate (1.2–2.4 M_J/Myr). The MESA structure models are standard but the link to the dynamo scaling is sensible. This is a significant within-field result, not a paradigm shift.

The soft spots are real but narrow. First, Eq. (1): the text defines Ω_E as the equilibrium spin, which already contains the (ζ/ξ)^{3/2} factor; multiplying by √(ξ^3/ζ^3) kills the dependence. The quoted range only appears if Ω_E means the present-day spin. The §3 self-consistent calculation uses the correct present-day value and reproduces 2.0–2.56 R_J, so the right fix is a subscript or typo rather than a conceptual error, but it makes the central printed equation unsupported as written. In a paper whose headline is a number, that's a serious editing failure, not a nit.

Second, the ξ constraint rests on a DPS meeting abstract (Hamilton et al. 2001). The analytic resonance model in Methods 4.1 matches observations only after a ~40% correction calibrated to those simulations. The paper is upfront about that, but it means the anchor of the whole chain is weaker than it looks. Since R† scales like ξ^{3/4} (or like (ξ/ζ)^{3/2} with the corrected equation), a 10% shift in ξ changes the radius by ~7–8%, comparable to the quoted range's width. So the robustness is modest.

Bottom line: the idea is worth refereeing. Send it out, but with a firm instruction to fix Eq. (1) and either get the Hamilton et al. results into published form or present the resonance calculation with enough detail to stand alone. If those two things are handled, this becomes a citable constraint on Jupiter's formation. I'd bring it to reading group; I'd cite the corrected version.

Referee Report

2 major / 5 minor

Summary. The manuscript proposes an indirect method to determine Jupiter's radius and interior state at the time of proto-solar nebula dissipation. It combines constraints on Io's primordial semi-major axis from the resonant excitation of Amalthea and Thebe's inclinations (ξ = a†_Io/R_J = 4.02–4.98), a disk-locking equilibrium spin for Jupiter (Ω_E = χ√(GM_J/R_t^3)), and angular momentum conservation with MESA interior models that give the primordial moment-of-inertia factor I† as a function of R†. The authors derive R† = 2.02–2.59 R_J, infer a convective-envelope entropy S† ≈ 10.6–11 k_B per baryon, a surface magnetic field B† ≈ 21 mT, and an accretion rate Ṁ = 1.2–2.4 M_J/Myr, and place this state at roughly 3.8 Myr after CAI formation. A self-consistent numerical version of the calculation gives R† = 2.0–2.56 R_J, which the authors adopt as the refined range.

Significance. If the central inference survives scrutiny, the paper is significant: it offers a largely independent, observationally anchored constraint on Jupiter's primordial radius and entropy that bypasses detailed formation modeling, and it produces falsifiable predictions for the primordial field strength and accretion rate. The analytic methods are transparent, the MESA output is publicly available, and the comparison with the Stevenson et al. (2022) diffuse-core model is a useful internal consistency check. The main scientific payoff—a warm-start entropy of roughly 10.6–11 k_B per baryon and a radius of 2–2.5 R_J at disk dissipation—would help discriminate among giant-planet formation scenarios.

major comments (2)

[Section 2, Eq. (1)] The printed equation is algebraically inconsistent with the definitions given in the text. With Ω_E = χ√(GM_J/R_t³) and R_t = (ξ/ζ) R_J, one obtains Ω_E/(χ Ω_br) = (ζ/ξ)^{3/2}, which exactly cancels the printed factor √(ξ³/ζ³). Equation (1) therefore reduces to R†/R_J = √(I_J/I†) ≈ 1.4, not the quoted 2.0–2.6 R_J. The quoted range is recovered only if the ratio Ω_E/(χ Ω_br) is replaced by Ω_J/(χ Ω_br), i.e., if the present-day spin Ω_J enters the angular-momentum conservation statement. The Section 3 self-consistent calculation appears to use the present-day spin and reproduces the range, so the error is likely typographical; nevertheless, because Eq. (1) is the central quantitative claim of the paper, it must be corrected and the variable definitions made explicit and unambiguous.
[Section 2 and Methods 4.1] The constraint ξ = a†_Io/R_J = 4.02–4.98 is the linchpin of the analysis, yet it rests on a DPS meeting abstract (Hamilton et al. 2001) and on the analytic model developed here, which requires a 40% empirical reduction to match Amalthea's inclination and gives Thebe's inclination within 7% assuming a particular sequence of resonance crossings. Because R† scales as ξ^{3/4}, a 10% uncertainty in ξ shifts R† by approximately 7%, which is comparable to the width of the quoted radius range. The manuscript should present a quantitative sensitivity analysis of the final radius, entropy, and field predictions to uncertainties in ξ, and should clarify how the 40% correction is propagated through the analytic resonance model.

minor comments (5)

[Methods 4.5, Eq. (18)] The sentence 'substituting equation (18) for the gas density' should refer to equation (17). In addition, the expression in Eq. (18) contains the ambiguous term √(2/R_t − √(4/r)), which appears dimensionally inconsistent and should be checked.
[Notation throughout] The primordial spin is denoted inconsistently: Ω_E appears in Section 2 and Eq. (1), while Ω† appears in Section 3 and Methods 4.3. Please use a single symbol for the primordial spin and define it once.
[Abstract and Section 3] The text states that B† ≈ 21 mT should be interpreted as an effective lower bound because the adopted f_ohm and γ are near the lower limits of dynamo models. The abstract and conclusion should carry this qualification, for example by saying 'at least ~21 mT', to avoid over-interpreting the quoted number.
[Section 2] The statement that any value of R† exceeding the orbital radius of Amalthea is 'unlikely to be physically meaningful' is not self-evident, because Amalthea's orbit at the epoch of disk dissipation need not equal its present-day orbit; please clarify the reasoning.
[Section 2] The simultaneity of solar-nebula and circum-Jovian-disk dispersal is justified by a one-line energy argument. A brief discussion of possible asynchrony (e.g., different photoevaporation timescales for the solar nebula and a circumplanetary disk) would strengthen the epoch assignment of 3.8 Myr after CAI formation.

Circularity Check

1 steps flagged · score 4.0 of 10

No fitted-input circularity; one printed equation is self-cancelling by definition.

self definitional [Section 2, Eq. (1), with definitions of ξ, ζ in Section 2 and Ω_E in Methods 4.3]
"R† = [(I_J/I†)(Ω_E/(χ Ω_br)) sqrt(ξ^3/ζ^3)]^{1/2} R_J (Eq. 1); “ζ = a_Io/Rt ≈ 1.13”; “Ω_E = χ sqrt(GM_J/R_t^3)”."

By the paper's definitions, Ω_E = χ(GM_J/R_t^3)^{1/2} and R_t = a_Io†/ζ = (ξ/ζ)R_J. Hence Ω_E/(χΩ_br) = (R_J/R_t)^{3/2} = (ζ/ξ)^{3/2}. Substituting into Eq. (1), the factor sqrt(ξ^3/ζ^3) = (ξ/ζ)^{3/2} cancels, leaving R† = sqrt(I_J/I†) R_J. Thus ξ, ζ, and χ drop out of the printed equation, so the quoted 2.02–2.59 R_J range does not follow from Eq. (1) as written; it follows only if Ω_E is read as the present-day spin Ω_J. This is a definitional cancellation: the equation is a tautology under the paper's own definitions. The §3 self-consistent calculation is non-circular and reproduces the range, so this is a defect of the printed derivation rather than a fit of the final answer.

full rationale

The central inference uses external constraints (Hamilton et al. 2001 for ξ; Ataiee & Kley 2021 and Masset et al. 2006 for ζ), the measured present-day angular momentum, and MESA structural models for I†. The disk-locked spin coefficient χ is derived analytically in Methods 4.3, not merely imported by self-citation; the self-citations (Batygin 2018, Batygin & Morbidelli 2020) are supporting and not load-bearing. B† and Mdot are outputs of scaling laws (Eqs. 2–3) evaluated at the inferred R†, and S† is read off the same MESA models; none of these is fitted to the target radius. The only circularity-like step is Eq. (1), which cancels by definition as detailed above; because the numerical self-consistent section reproduces the radius and the inputs are external, this is a partial/definitional defect rather than full circularity.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central radius inference rests on a chain of external constraints: the satellite resonance constraint xi (Hamilton et al. 2001, an unpublished abstract), the migration-trap ratio zeta (Ataiee and Kley 2021), and the magnetic spin equilibrium chi (Batygin 2018). The interior models supply I_dagger(R_dagger). No new physical entities are introduced. The free parameters listed affect the secondary B_dagger and Mdot estimates.

free parameters (2)

f_ohm (Ohmic dissipation fraction) = 0.5 (fiducial)
Adopted from Christensen et al. (2009) for the dynamo scaling law; the paper notes it is a lower bound and could be up to a factor of 2 higher.
gamma (interior-to-surface field ratio) = 6.5
Adopted from Christensen and Aubert (2006) for the Jovian dynamo; contributes to the B_dagger estimate.

assumptions (7)

domain assumption Magnetospheric disk truncation formula (Ghosh and Lamb 1978) with dipole field coupling alpha=1.96 (Mohanty and Shu 2008) applies to the circum-Jovian disk.
Used in equations (3) and (13) to relate R_t, B_dagger, and Mdot.
domain assumption Dynamo scaling law (Christensen et al. 2009): surface field strength is determined by convective energy flux, B proportional to (F q)^(1/3) rho^(1/6).
Used in equation (2) to infer B_dagger.
domain assumption Planetary spin is in the equilibrium state Omega_E = chi sqrt(GM/R_t^3) with chi=0.88 (Batygin 2018) at the time of disk dissipation.
Self-cited prior result; load-bearing for the spin used in angular momentum conservation.
domain assumption The inner edge of the satellite resonant chain is locked at zeta = a_dagger_Io / R_t approximately 1.13 (Ataiee and Kley 2021).
External simulation calibration; sets R_t from the inferred a_dagger_Io.
domain assumption Hydrostatic interior models with a 25 Earth-mass core at density 10 g/cc and solar-composition envelope computed with MESA reliably give I_dagger(R_dagger).
Used to convert angular momentum conservation into R_dagger; checked against Stevenson et al. (2022).
standard math After nebula dissipation, Jupiter's spin angular momentum is conserved (no significant external torques).
Standard physics; the paper notes tidal satellite migration extracts negligible spin.
domain assumption The circumplanetary disk dissipates simultaneously with the solar nebula at approximately 3.8 Myr after CAI (Wang et al. 2017).
Sets the epoch for the inferred radius.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Determination of Jupiter's Primordial Physical State." pith.science (2026). https://pith.science/paper/2MWEVGF3

@misc{pith2026250512652,
  author       = {Pith},
  title        = {Pith review of: Determination of Jupiter's Primordial Physical State},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2MWEVGF3}},
  note         = {Machine review of arXiv:2505.12652}
}

abstract

The formation and early evolution of Jupiter played a pivotal role in sculpting the large-scale architecture of the solar system, intertwining the narrative of Jovian early years with the broader story of the solar system's origins. The details and chronology of Jupiter's formation, however, remain elusive, primarily due to the inherent uncertainties of accretionary models, highlighting the need for independent constraints. Here we show that by analyzing the dynamics of Jupiter's satellites concurrently with its angular momentum budget, we can infer Jupiter's radius and interior state at the time of proto-solar nebula's dissipation. In particular, our calculations reveal that Jupiter was $2$ to $2.5$ times as large as it is today, 3.8 million years after the formation of the first solids in the solar system. Our model further indicates that young Jupiter possessed a magnetic field of approximately $B_{\rm{J}}^{\dagger} \approx 21$ mT (a factor of $\sim50$ higher than its present-day value) and was accreting material through a circum-Jovian disk at a rate of $\dot{M} = 1.2-2.4$ Jupiter masses per million years. Our findings are fully consistent with the core-accretion theory of giant planet formation and provide an evolutionary snapshot that pins down properties of the Jovian system at the end of the protosolar nebula's lifetime.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

86 extracted references · 9 canonical work pages

[1]

Les m´ ethodes nouvelles de la m´ ecanique c´ eleste

Poincar´ e, H. Les m´ ethodes nouvelles de la m´ ecanique c´ eleste. (Paris, Gauthier- Villars et fils, 1892)
[2]

Arnol’d, V. I. Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics. Russian Mathematical Surveys 18, 85–191. doi:10.1070/RM1963v018n06ABEH001143 (1963)

doi:10.1070/rm1963v018n06abeh001143 1963
[3]

& Chierchia, L

Celletti, A. & Chierchia, L. On the Stability of Realistic Three-Body Problems. Comm. Math. Phys. 186, 413–449. doi:10.1007/s002200050115 (1997). 20

work page doi:10.1007/s002200050115 1997
[4]

J., Morbidelli, A., Raymond, S

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., & Mandell, A. M. A low mass for Mars from Jupiter’s early gas-driven migration. Nature 475, 206–209. doi:10.1038/nature10201 (2011)

doi:10.1038/nature10201 2011
[5]

& Laughlin, G

Batygin, K. & Laughlin, G. Jupiter’s decisive role in the inner Solar System’s early evolution. Proc. Nat. Acad. Sci. 112, 4214–4217. doi:10.1073/pnas.1423252112 (2015)

doi:10.1073/pnas.1423252112 2015
[6]

S., Burkhardt, C., Budde, G

Kruijer, T. S., Burkhardt, C., Budde, G. & Kleine, T. Age of Jupiter inferred from the distinct genetics and formation times of meteorites. Proc. Nat. Acad. Sci. 114, 6712–6716. doi:10.1073/pnas.1704461114 (2017)

doi:10.1073/pnas.1704461114 2017
[8]

N., Helled, R., Ikoma, M., Line, M

Guillot, T., Fletcher, L. N., Helled, R., Ikoma, M., Line, M. R. & Paramentier, V. Giant Planets from the Inside-Out. Protostars and Planets VII 534, 947 (2023)

2023
[9]

Miguel, Y. et al. Jupiter’s inhomogeneous envelope. Astron. Astrophys. 662. doi:10.1051/0004-6361/202243207 (2022)

doi:10.1051/0004-6361/202243207 2022

Show all 86 references

[10]

Howard, S. et al. Exploring the hypothesis of an inverted Z gradient inside Jupiter. Astron. Astrophys. 680. doi:10.1051/0004-6361/202348129 (2023)

2023 doi
[11]

& Hubbard, W

Militzer, B. & Hubbard, W. B. Study of Jupiter’s interior: Comparison of 2, 3, 4, 5, and 6 layer models. Icarus 411. doi:10.1016/j.icarus.2024.115955 (2024)

2024
[12]

Formation of the Giant Planets

Mizuno, H. Formation of the Giant Planets. Prog. Theor. Phys. 64, 544–557. doi:10.1143/PTP.64.544 (1980)

1980 doi
[13]

Stevenson, D. J. Formation of the giant planets. Plan. Space Sci. 30, 755–764. doi:10.1016/0032-0633(82)90108-8 (1982)

1982 doi
[14]

& Pollack, J

Bodenheimer, P. & Pollack, J. B. Calculations of the accretion and evolution of giant planets: The effects of solid cores. Icarus 67, 391–408. doi:10.1016/0019- 1035(86)90122-3 (1986)

1986 doi
[15]

B., Hubickyj, O., Bodenheimer, P., Lissauer, J

Pollack, J. B., Hubickyj, O., Bodenheimer, P., Lissauer, J. J., Podolak, M. & Greenzweig, Y. Formation of the Giant Planets by Concurrent Accretion of Solids and Gas. Icarus 124, 62–85. doi:10.1006/icar.1996.0190 (1996)

1996
[16]

& Lissauer, J

Hubickyj, O., Bodenheimer, P. & Lissauer, J. J. Accretion of the gaseous envelope of Jupiter around a 5 10 Earth-mass core. Icarus 179, 415–431. doi:10.1016/j.icarus.2005.06.021 (2005)

2005 doi
[18]

J., Lissauer, J

D’Angelo, G., Weidenschilling, S. J., Lissauer, J. J. & Bodenheimer, P. Growth of Jupiter: Formation in disks of gas and solids and evolution to the present epoch. Icarus 355. doi:10.1016/j.icarus.2020.114087 (2021)

2021
[19]

The mass of gas giant planets: Is Saturn a failed gas giant?

Helled, R. The mass of gas giant planets: Is Saturn a failed gas giant?. Astron. Astrophys. 675. doi:10.1051/0004-6361/202346850 (2023)

2023 doi
[20]

J., Bodenheimer, P., Lissauer, J

Stevenson, D. J., Bodenheimer, P., Lissauer, J. J. & D’Angelo, G. Mixing of Condensable Constituents with H-He during the Formation and Evolution of Jupiter. Plan. Sci. J. 3. doi:10.3847/PSJ/ac5c44 (2022)

2022 doi
[21]

& Venturini, J

Cumming, A., Helled, R. & Venturini, J. The primordial entropy of Jupiter. Mon. Not. R. Astron. Soc. 477, 4817–4823. doi:10.1093/mnras/sty1000 (2018)

2018 doi
[22]

& Chabrier, G

Leconte, J. & Chabrier, G. A new vision of giant planet interiors: Impact of double diffusive convection. Astron. Astrophys. 540. doi:10.1051/0004-6361/201117595 (2012)

2012 doi
[23]

Burns, J. A. et al. Jupiter’s Ring-Moon System. Jupiter 241 (2007)

2007
[24]

& Morbidelli, A

Batygin, K. & Morbidelli, A. Formation of Giant Planet Satellites. Astrophys. J
[25]

J., Terada, H., Pyo, T.-S

Takato, N., Bus, S. J., Terada, H., Pyo, T.-S. & Kobayashi, N. Detection of a Deep 3-µm Absorption Feature in the Spectrum of Amalthea (JV). Science 306, 2224–2227. doi:10.1126/science.1105427 (2004)

2004 doi
[26]

P., Proctor, A

Hamilton, D. P., Proctor, A. L. & Rauch, K. P. An Explanation for the High Incli- nations of Thebe and Amalthea. AAS/Division for Planetary Sciences Meeting Abstracts #33 (2001)

2001
[27]

Canup, R. M. & Ward, W. R. Formation of the Galilean Satellites: Conditions of Accretion. Astron. J. 124, 3404–3423. doi:10.1086/344684 (2002)

2002 doi
[28]

& Johansen, A

Ronnet, T. & Johansen, A. Formation of moon systems around giant planets. Cap- ture and ablation of planetesimals as foundation for a pebble accretion scenario. Astron. Astrophys. 633. doi:10.1051/0004-6361/201936804 (2020)

2020 doi
[29]

S., Morbidelli, A., Crida, A

Masset, F. S., Morbidelli, A., Crida, A. & Ferreira, J. Disk Surface Density Tran- sitions as Protoplanet Traps. Astrophys. J. 642, 478–487. doi:10.1086/500967 (2006)

2006 doi
[30]

& Kley, W

Paardekooper, S.-J., Baruteau, C. & Kley, W. A torque formula for non- isothermal Type I planetary migration - II. Effects of diffusion. Mon. Not. R. Astron. Soc. 410, 293–303. doi:10.1111/j.1365-2966.2010.17442 (2011)

2011
[31]

& Kley, W

Ataiee, S. & Kley, W. Pushing planets into an inner cavity by a resonant chain. Astron. Astrophys. 648. doi:10.1051/0004-6361/202038772 (2021). 22

2021 doi
[32]

On the Terminal Rotation Rates of Giant Planets

Batygin, K. On the Terminal Rotation Rates of Giant Planets. Astron. J. 155. doi:10.3847/1538-3881/aab54e (2018)

2018 doi
[33]

D., Schubert, G

Helled, R., Anderson, J. D., Schubert, G. & Stevenson, D. J. Jupiter’s moment of inertia: A possible determination by Juno. Icarus 216, 440–448. doi:10.1016/j.icarus.2011.09.016 (2011)

2011 doi
[34]

Wahl, S. M. et al. Comparing Jupiter interior structure models to Juno grav- ity measurements and the role of a dilute core. Geophys. Research Lett. 44, 4649–4659. doi:10.1002/2017GL073160 (2017)

2017 doi
[37]

& Guillot, T

Vazan, A., Helled, R. & Guillot, T. 2018. Jupiter’s evolution with primordial composition gradients. Astron. Astrophys. 610. doi:10.1051/0004-6361/201732522

2018 doi
[38]

& Helled, R

Valletta, C. & Helled, R. The Deposition of Heavy Elements in Giant Proto- planetary Atmospheres: The Importance of Planetesimal-Envelope Interactions. Astrophys. J. 871. doi:10.3847/1538-4357/aaf427 (2019)

2019 doi
[39]

Helled, R. et al. Revelations on Jupiter’s formation, evolution and interior: Challenges from Juno results. Icarus 378. doi:10.1016/j.icarus.2022.114937 (2022)

2022
[40]

Spiegel, D. S. & Burrows, A. Spectral and Photometric Diagnostics of Giant Planet Formation Scenarios. Astrophys. J. 745. doi:10.1088/0004- 637X/745/2/174 (2012)

2012 doi
[41]

& Cumming, A

Berardo, D. & Cumming, A. Hot-start Giant Planets Form with Radiative Interiors. Astrophys. J. 846. doi:10.3847/2041-8213/aa81c0 (2017)

2017 doi
[42]

S., Fortney, J

Marley, M. S., Fortney, J. J., Hubickyj, O., Bodenheimer, P. & Lissauer, J. J. On the Luminosity of Young Jupiters. Astrophys. J. 655, 541–549. doi:10.1086/509759 (2007)

2007 doi
[43]

Luminosity of young Jupiters revisited

Mordasini, C. Luminosity of young Jupiters revisited. Massive cores make hot planets. Astron. Astrophys. 558. doi:10.1051/0004-6361/201321617 (2013)

2013 doi
[44]

& Molli` ere, P

Mordasini, C., Marleau, G.-D. & Molli` ere, P. Characterization of exoplanets from their formation. III. The statistics of planetary luminosities. Astron. Astrophys
[45]

The Evolution of Gas Giant Entropy During Formation by Runaway Accretion

Berardo, D., Cumming, A., & Marleau, G.-D. The Evolution of Gas Giant Entropy During Formation by Runaway Accretion. Astrophys. J. 834. doi:10.3847/1538-4357/834/2/149 (2017)

2017 doi
[46]

& Kuiper, R

Marleau, G.-D., Mordasini, C. & Kuiper, R. The Planetary Accretion Shock. II. Grid of Postshock Entropies and Radiative Shock Efficiencies for Nonequilibrium Radiation Transport. Astrophys. J. 881. doi:10.3847/1538-4357/ab245b (2019)

2019 doi
[47]

Wang, H. et al. Lifetime of the solar nebula constrained by meteorite paleomag- netism. Science 355, 623–627. doi:10.1126/science.aaf5043 (2017)

2017 doi
[48]

& Lamb, F

Ghosh, P. & Lamb, F. K. Disk accretion by magnetic neutron stars. Astrophys. J. 223, L83–L87. doi:10.1086/182734 (1978)

1978 doi
[49]

& Seebeck, J

Carvalho, A., Hillenbrand, L. & Seebeck, J. Disk Cooling and Wind Lines as Seen in the Spectral Line Evolution of V960 Mon. Astrophys. J. 958. doi:10.3847/1538- 4357/acff59 (2023)

2023 doi
[50]

Zhu, Z., Stone, J. M. & Calvet, N. A global 3D simulation of magnetospheric accretion - I. Magnetically disrupted discs and surface accretion. Mon. Not. R. Astron. Soc. 528, 2883–2911. doi:10.1093/mnras/stad3712 (2024)

2024 doi
[51]

R., Holzwarth, V

Christensen, U. R., Holzwarth, V. & Reiners, A. Energy flux determines magnetic field strength of planets and stars. Nature 457, 167–169. doi:10.1038/nature07626 (2009)

2009 doi
[52]

Christensen, U. R. & Aubert, J. Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Int. 166, 97–114. doi:10.1111/j.1365-246X.2006.03009.x (2006)

2006 arXiv
[53]

& Shu, F

Mohanty, S. & Shu, F. H. Magnetocentrifugally Driven Flows from Young Stars and Disks. VI. Accretion with a Multipole Stellar Field. Astrophys. J. 687, 1323–1338. doi:10.1086/591924 (2008)

2008 doi
[54]

Murray, C. D. & Dermott, S. F. Solar System Dynamics (Cambridge, UK: Cambridge University Press, ISBN 0521575974, doi:10.1017/CBO9781139174817, 1999)

1999 doi
[55]

Modern celestial mechanics: Aspects of solar system dynamics

Morbidelli, A. Modern celestial mechanics: Aspects of solar system dynamics. (London: Taylor & Francis, ISBN 0415279399, 2002)

2002
[56]

Classical mechanics

Goldstein, H. Classical mechanics. (Reading, Mass.: Addison-Wesley, 1950)

1950
[57]

& Goldreich, P

Borderies, N. & Goldreich, P. A Simple Derivation of Capture Probabilities for the J+1:J and J+2:J Orbit-Orbit Resonance Problems. Celest. Mech. 32, 127–136. doi:10.1007/BF01231120 (1984). 24

1984 doi
[58]

Canonical Perturbation Theories - Degenerate Systems and Res- onance

Ferraz-Mello, S. Canonical Perturbation Theories - Degenerate Systems and Res- onance. Universidade de S˜ ao Paulo, Brazil. Series: Astrophysics and Space Science Library, Vol. 345. Springer US. doi:10.1007/978-0-387-38905-9 (2007)

2007 doi
[59]

& Lemaitre, A

Henrard, J. & Lemaitre, A. A Second Fundamental Model for Resonance. Celest. Mech. 30, 197–218. doi:10.1007/BF01234306 (1983)

1983 doi
[60]

& Batygin, Y

Batygin, K. & Batygin, Y. K. Chaotic dynamics driven by particle-core interac- tions. Phys. Plasmas 28. doi:10.1063/5.0056306 (2021)

2021 doi
[61]

& Tremaine, S

Goldreich, P. & Tremaine, S. Disk-satellite interactions.. Astrophys. J. 241, 425–441. doi:10.1086/158356 (1980)

1980 doi
[62]

& Masset, F

Crida, A., Morbidelli, A. & Masset, F. On the width and shape of gaps in protoplanetary disks. Icarus 181, 587–604. doi:10.1016/j.icarus.2005.10.007 (2006)

2006 doi
[63]

C., Laughlin, G

Adams, F. C., Laughlin, G. & Bloch, A. M. Turbulence Implies that Mean Motion Resonances are Rare. Astrophys. J. 683, 1117–1128. doi:10.1086/589986 (2008)

2008 doi
[64]

& Adams, F

Batygin, K. & Adams, F. C. An Analytic Criterion for Turbulent Disruption of Planetary Resonances. Astron. J. 153. doi:10.3847/1538-3881/153/3/120 (2017)

2017 doi
[65]

& Lin, D

Wu, Y., Chen, Y.-X. & Lin, D. N. C. Chaotic Type I migration in turbulent discs. Mon. Not. R. Astron. Soc. 528, L127–L132. doi:10.1093/mnrasl/slad183 (2024)

2024 doi
[66]

& Pringle, J

Livio, M. & Pringle, J. E. Dwarf nova outbursts - the ultraviolet delay and the effect of a weakly magnetized white dwarf.. Mon. Not. R. Astron. Soc. 259, 23P. doi:10.1093/mnras/259.1.23P (1992)

1992 doi
[67]

A., K¨ onigl, A

Uzdensky, D. A., K¨ onigl, A. & Litwin, C. Magnetically Linked Star-Disk Systems. II. Effects of Plasma Inertia and Reconnection in the Magnetosphere. Astrophys. J. 565, 1205–1215. doi:10.1086/324724 (2002)

2002 doi
[68]

& Pudritz, R

Matt, S. & Pudritz, R. E. The spin of accreting stars: dependence on magnetic coupling to the disc. Mon. Not. R. Astron. Soc. 356, 167–182. doi:10.1111/j.1365- 2966.2004.08431.x (2005)

2005
[69]

Armitage, P. J. & Clarke, C. J. Magnetic braking of T Tauri stars. Mon. Not. R. Astron. Soc. 280, 458–468. doi:10.1093/mnras/280.2.458 (1996)

1996 doi
[70]

The Change in Jupiter’s Moment of Inertia Due to Core Erosion and Planetary Contraction

Helled, R. The Change in Jupiter’s Moment of Inertia Due to Core Erosion and Planetary Contraction. Astrophys. J. 748. doi:10.1088/2041-8205/748/1/L16 (2012)

2012 doi
[71]

Paxton, B. et al. Modules for Experiments in Stellar Astrophysics (MESA): Planets, Oscillations, Rotation, and Massive Stars. Astrophys. J. Suppl. 208. doi:10.1088/0067-0049/208/1/4 (2013). 25

2013 doi
[72]

& van Horn, H

Saumon, D., Chabrier, G. & van Horn, H. M. An Equation of State for Low-Mass Stars and Giant Planets. Astrophys. J. Suppl. 99, 713. doi:10.1086/192204 (1995)

1995 doi
[73]

& Sauval, A

Grevesse, N. & Sauval, A. J. Standard Solar Composition. Space Sci. Rev. 85, 161–174. doi:10.1023/A:1005161325181 (1998)

1998 doi
[74]

S., Marley, M

Freedman, R. S., Marley, M. S. & Lodders, K. Line and Mean Opacities for Ultracool Dwarfs and Extrasolar Planets. Astrophys. J. Supplement Series 174, 504–513. doi:10.1086/521793 (2008)

2008 doi
[75]

& Soubiran, F

Chabrier, G., Mazevet, S. & Soubiran, F. A New Equation of State for Dense Hydrogen-Helium Mixtures. Astrophys. J. 872. doi:10.3847/1538-4357/aaf99f (2019)

2019 doi
[76]

& Guillot, T

Saumon, D. & Guillot, T. Shock Compression of Deuterium and the Interiors of Jupiter and Saturn. Astrophys. J. 609, 1170–1180. doi:10.1086/421257 (2004)

2004 doi
[77]

& Fayon, L

Miguel, Y., Guillot, T. & Fayon, L. Jupiter internal structure: the effect of differ- ent equations of state. Astron. Astrophys. 596. doi:10.1051/0004-6361/201629732 (2016)

2016 doi
[78]

& Soubiran, F

Mazevet, S., Licari, A. & Soubiran, F. Benchmarking the ab initio hydrogen equation of state for the interior structure of Jupiter. Astron. Astrophys. 664. doi:10.1051/0004-6361/201935764 (2022)

2022 doi
[79]

Howard, S., Guillot, T. 2023. Accounting for non-ideal mixing effects in the hydrogen-helium equation of state. Astron. Astrophys. 672. doi:10.1051/0004- 6361/202244851

2023 doi
[80]

et al, Jupiter’s interior from Juno: Equation-of-state uncertainties and dilute core extent

Howard, S. et al, Jupiter’s interior from Juno: Equation-of-state uncertainties and dilute core extent. Astron. Astrophys. 672. doi:10.1051/0004-6361/202245625 (2023)

2023 doi
[81]

& Helled, R

Knierim, H. & Helled, R. Convective mixing in giant planets and the connection to atmospheric measurements. Preprint at arXiv.2407.09341 (2024)

2024 arXiv
[82]

H., Najita, J., Ruden, S

Shu, F. H., Najita, J., Ruden, S. P. & Lizano, S. Magnetocentrifugally Driven Flows from Young Stars and Disks. II. Formulation of the Dynamical Problem. Astrophys. J. 429, 797. doi:10.1086/174364 (1994)

1994 doi
[83]

& Nakazawa, K

Adachi, I., Hayashi, C. & Nakazawa, K. The gas drag effect on the elliptical motion of a solid body in the primordial solar nebula.. Prog. Theor. Phys. 56, 1756–1771. doi:10.1143/PTP.56.1756 (1976)

1976 doi
[84]

& Guillot, T

Szul´ agyi, J., Masset, F., Lega, E., Crida, A., Morbidelli, A. & Guillot, T. Cir- cumplanetary disc or circumplanetary envelope?. Mon. Not. R. Astron. Soc. 460, 2853–2861. doi:10.1093/mnras/stw1160 (2016). 26

2016 doi
[85]

P., Crida, A

Lambrechts, M., Lega, E., Nelson, R. P., Crida, A. & Morbidelli, A. Quasi-static contraction during runaway gas accretion onto giant planets. Astron. Astrophys
[86]

M., Youdin, A

Krapp, L., Kratter, K. M., Youdin, A. N., Ben´ ıtez-Llambay, P., Masset, F. & Armitage, P. J. A thermodynamic criterion for the formation of Circumplanetary Disks. Preprint at arXiv.2402.14638 (2024)

2024 arXiv
[87]

Adams, F. C. & Batygin, K. Analytic Approach to the Late Stages of Giant Planet Formation. Astrophys. J. 934. doi:10.3847/1538-4357/ac7a3e (2022). 27

2022 doi
[608]

doi:10.1051/0004-6361/201630077 (2017). 23

2017 doi
[630]

doi:10.1051/0004-6361/201834413 (2019)

2019 doi
[894]

doi:10.3847/1538-4357/ab8937 (2020)

2020 doi

Pith tools

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

[1] [1]

Les m´ ethodes nouvelles de la m´ ecanique c´ eleste

Poincar´ e, H. Les m´ ethodes nouvelles de la m´ ecanique c´ eleste. (Paris, Gauthier- Villars et fils, 1892)

[2] [2]

Arnol’d, V. I. Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics. Russian Mathematical Surveys 18, 85–191. doi:10.1070/RM1963v018n06ABEH001143 (1963)

doi:10.1070/rm1963v018n06abeh001143 1963

[3] [3]

& Chierchia, L

Celletti, A. & Chierchia, L. On the Stability of Realistic Three-Body Problems. Comm. Math. Phys. 186, 413–449. doi:10.1007/s002200050115 (1997). 20

work page doi:10.1007/s002200050115 1997

[4] [4]

J., Morbidelli, A., Raymond, S

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., & Mandell, A. M. A low mass for Mars from Jupiter’s early gas-driven migration. Nature 475, 206–209. doi:10.1038/nature10201 (2011)

doi:10.1038/nature10201 2011

[5] [5]

& Laughlin, G

Batygin, K. & Laughlin, G. Jupiter’s decisive role in the inner Solar System’s early evolution. Proc. Nat. Acad. Sci. 112, 4214–4217. doi:10.1073/pnas.1423252112 (2015)

doi:10.1073/pnas.1423252112 2015

[6] [6]

S., Burkhardt, C., Budde, G

Kruijer, T. S., Burkhardt, C., Budde, G. & Kleine, T. Age of Jupiter inferred from the distinct genetics and formation times of meteorites. Proc. Nat. Acad. Sci. 114, 6712–6716. doi:10.1073/pnas.1704461114 (2017)

doi:10.1073/pnas.1704461114 2017

[7] [8]

N., Helled, R., Ikoma, M., Line, M

Guillot, T., Fletcher, L. N., Helled, R., Ikoma, M., Line, M. R. & Paramentier, V. Giant Planets from the Inside-Out. Protostars and Planets VII 534, 947 (2023)

2023

[8] [9]

Miguel, Y. et al. Jupiter’s inhomogeneous envelope. Astron. Astrophys. 662. doi:10.1051/0004-6361/202243207 (2022)

doi:10.1051/0004-6361/202243207 2022