Constraining the Formation of the Four Terrestrial Planets in the Solar System

Patryk Sofia Lykawka; Takashi Ito

REVIEW 3 major objections 5 minor 70 references

Constraining the Formation of the Four Terrestrial Planets in the Solar System

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Truncated Grand Tack-style disks cannot explain how Mercury and Mars formed.

desk verdict A careful, useful simulation survey with a system-level classification scheme; the negative result on Grand Tack disks is suggestive but the 'cannot explain' claim overreaches because the giant planets are frozen. read the letter →

arxiv 1908.04934 v2 pith:OQJFSPUI submitted 2019-08-14 astro-ph.EP

Patryk Sofia Lykawka , Takashi Ito This is my paper · ORCID

classification astro-ph.EP

keywords terrestrialplanetformationMercuryanalogMarsGrandTackmodelprotoplanetarydiskN-bodysimulationssystemsMoon-forminggiantimpact

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

This paper tries to establish that the most popular way of building the inner solar system—starting from a narrow, truncated protoplanetary disk like those produced by the Grand Tack model—systematically fails when all four terrestrial planets are required to form in the same system. Across 540 N-body simulations, the authors found only 17 systems that contained Mercury, Venus, Earth, and Mars analogs at once, and those systems misfit the real planets in the same ways: Mercury and Mars analogs were too massive, too dynamically cold, and parked too close to Venus and Earth, while Earth analogs suffered their Moon-forming giant impact too early and accreted too much mass afterward. A sympathetic reader would take this as evidence that the actual protoplanetary disk concentrated its mass in narrow core regions near 0.7–1.2 astronomical units, had a lower-mass inner region beginning at 0.3–0.4 au and an outer component near 1.0–1.2 au, stored most of its mass in embryos rather than planetesimals, and evolved with Jupiter and Saturn on eccentric orbits.

What carries the argument

The load-bearing tool is a system-level classification algorithm that, for each simulated final system, first identifies the most plausible Venus–Earth pair by mass and mass-weighted distance, then defines the Mercury and Mars regions relative to that pair and disqualifies analogs when interloping planets sit nearby. This matters because it converts a batch of planet-like objects into whole analog systems, making it possible to see correlated failures—for example, that Mercury analogs in truncated disks are all too massive and too close to Venus—that are invisible in mixed-population plots. The simulations themselves vary four disk models (fiducial, truncated, depleted, and peaked), the embryo-to-planetesimal mass ratio r, core-region size, inner and outer components, and several giant-planet orbital architectures.

What would settle it

Run the same truncated-disk initial conditions with Jupiter and Saturn allowed to migrate or undergo an instability, and include collisional fragmentation; if such runs routinely yield a Mercury analog near 0.4 au with mass below about 0.11 Earth masses, a Mars analog no more than about 1.25 Mars masses on a moderately excited orbit, and an Earth analog whose last giant impact falls at 20–140 Myr with late veneer below 2%, the paper's dismissal of truncated disks would be overturned.

Watch

Extended reading notes

Core claim

The paper's central claim is that analog systems—not individual planet look-alikes drawn from mixed populations—are the right test of terrestrial planet formation, and that by that test the standard truncated disks fail. Out of 540 runs, 194 systems produced at least three analogs, but only 17 produced all four; in the truncated-disk subset, Mercury analogs were all too massive, Mercury and Mars analogs were dynamically colder than the real planets and formed too close to the Venus/Earth pair, and the Earth analogs' last giant impacts occurred before 20 Myr with late veneer masses 2–10 times the allowed upper limit. The paper concludes that disks with mass concentrated in narrow core regions between about 0.7–0.9 and 1.0–1.2 au, an inner region starting at about 0.3–0.4 au, a less massive outer component starting at about 1.0–1.2 au, an embryo-dominated mass distribution, and eccentric Jupiter–Saturn orbits are required to reproduce the four terrestrial planets.

Load-bearing premise

Jupiter and Saturn are fixed on their starting orbits for the full 400 million years, with no gas-driven migration and no giant-planet instability; if the real giant planets stirred the inner disk, the systematic failures blamed on truncated disks might disappear.

Editorial extensions

If this is right

The Grand Tack's characteristic truncated disk, and the often-used 0.7–1.0 au disk of the Empty Asteroid Belt model, are strongly disfavored as initial conditions for the inner solar system.
Mercury formation requires a mass-depleted inner region starting near 0.3–0.4 au; the only Mercury analogs that matched both orbit and mass appeared in disks with such inner components.
Earth's water budget, the Moon-forming impact timing, and the late veneer cannot be satisfied simultaneously by narrow dry disks; an outer component or water-rich planetesimals is needed, though wetting Venus and Mars too much then becomes a danger.
Models such as Early Instability and Pebble Accretion become more attractive competitors if they can deliver embryo-dominated, steeply depleted disks with eccentric giant planets.
Embryo-dominated disks (large r) produce more four-planet systems and better Mars analogs, implying that dynamical friction from planetesimals must be weak during the late stages of terrestrial accretion.

Reading between the lines

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

If the fixed-orbit restriction is relaxed, the paper's strongest conclusion—that truncated disks are ruled out—could weaken, because a late giant-planet instability might stir Mercury and Mars analogs onto the right excited orbits while keeping their masses low; the authors themselves flag giant-planet evolution as the next step.
The same system-level classification logic could be exported to exoplanetary systems, where requiring Venus–Earth–like pairs plus small outer planets in one system may be a sharper test of formation models than matching individual planet masses and orbits.
The requirement of an inner region plus giant impacts for Mercury predicts that Mercury's high core mass fraction was set by collisions rather than by gentle in-situ accretion, a prediction that can be sharpened with further geophysical data from Mercury.
A direct testable extension is to run the authors' favored disk shapes with migrating giant planets and collisional fragmentation; if Mercury and Mars analogs improve, the disk-shape constraints may be less unique than the paper suggests.

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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

Bottom line: this is a well-executed simulation survey and a useful new way of judging terrestrial-planet formation models, but it is not the last word against the Grand Tack. The paper does real work: 540 N-body runs, four disk models, and a classification algorithm that forces you to look at Mercury, Venus, Earth, and Mars in the same system rather than as a mixed population. That is genuinely new, and the attention to Mercury and to simultaneous constraints (Moon-forming timing, late veneer, water) is a step forward.

What lands: the finding that truncated-disk simulations systematically produce Mercury and Mars analogs that are too massive, too dynamically cold, and too close to Venus/Earth, with early giant impacts and heavy late veneer, is well documented internally. The consistency across independent constraints gives the result weight. The paper also gives a concrete five-point target for what a successful disk might look like, which is useful even if parts of it were already in the air.

Soft spots: the central claim "cannot explain" is stronger than the setup supports. Jupiter and Saturn are held on fixed orbits for the full 400 Myr; the authors state this and explicitly defer giant-planet evolution to future work. But the abstract does not carry that qualifier. Since the Grand Tack normally includes later migration or instability, what is actually tested is a frozen post-tack disk, not the full scenario. The paper's own Section 1.1 acknowledges that instabilities may perturb the inner system, so the caveat is not hidden, but the headline wording is not honest to it. Also, only 17 four-planet systems underlie the strongest statement, and no confidence intervals are given. I don't think the result is simple luck, but with small N and a static giant-planet approximation, the conclusion should say "disfavors" rather than "cannot explain." The classification thresholds are reasonable and the paper tests sensitivity for Mars, so that part is fair. No code or data is a transparency minus, not a correctness error.

Who gets value: the terrestrial-planet-formation community, especially people comparing Grand Tack, Empty Asteroid Belt, Early Instability, and pebble-accretion models. The proposed disk properties are a concrete target for future simulations.

Recommendation: I would send it to a serious referee. The paper deserves engagement. I would ask the authors either to soften the conclusion or to add a robustness test with evolving giant planets, even a limited one. As it stands, it is a solid contribution with an overconfident headline.

Referee Report

3 major / 5 minor

Summary. The manuscript reports 540 N-body simulations of terrestrial planet formation with four disk models (fiducial, truncated, depleted, peaked), several static giant-planet orbital architectures, and a classification algorithm that identifies Mercury, Venus, Earth, and Mars analogs within each simulated system. The authors find 194 systems with at least three analogs and 17 systems with four analogs. They conclude that truncated disks representative of typical Grand Tack outcomes cannot explain the formation of the terrestrial planets: Mercury and Mars analogs are too dynamically cold, too close to the Venus/Earth analogs, and too massive; Earth analogs experience Moon-forming giant impacts too early and accrete too much late veneer; and Earth analogs are too dry. They propose that forming the terrestrial planets requires disks with mass concentrated in narrow core regions, an inner component starting near 0.3-0.4 au, a low-mass outer component, embryo-dominated mass, and eccentric Jupiter-Saturn orbits.

Significance. If the negative claim held, this would be an important constraint on the Grand Tack and Empty Asteroid Belt models of terrestrial planet formation. The study is strong in scale and documentation: 540 runs, a transparent system-level classification algorithm, small time steps for the Mercury region, and simultaneous application of orbital, mass, timing, late-veneer, and water constraints. The analog-system framework is a useful contribution to the field. However, the headline conclusion is broader than the simulations support, primarily because the giant planets are held on fixed orbits and because the decisive four-planet sample consists of only 17 systems without confidence intervals.

major comments (3)

[Section 2 and Section 1.1] The central claim that truncated disks 'cannot explain' the terrestrial planets rests on simulations in which Jupiter and Saturn are held on fixed orbits for the full 400 Myr (Section 2: 'the giant planets do not migrate'), with only four static giant-planet architectures. Several of the systematic failures that drive the conclusion—dynamically too-cold Mercury and Mars analogs, overly early Moon-forming impacts, excessive late veneer, and too-compact systems—are precisely the quantities most sensitive to the degree of dynamical excitation imposed by the giant planets. The paper itself finds that more eccentric giant-planet configurations improve Mars analogs (Section 3.2.2) and acknowledges in Section 1.1 that planetesimal-driven migration and giant-planet instabilities 'may strongly perturb the planets and other bodies in the inner solar system.' A concrete test would be to rerun the truncated-disk scenarios with an early giant-planet instability or planetesimal-driven migration and check whether Mercury/Mars excitation, the Moon-forming impact timing, and the late veneer move into the observed ranges. As written, the simulations exclude static-giant-planet truncated disks, not all plausible Grand Tack realizations; the negative conclusion should be scoped accordingly or supported by additional simulations.
[Section 3.4 and Table 3] The impossibility claim is based on only 17 four-planet analog systems, 11 of which come from truncated disks, with no confidence intervals or cross-tabulation of simultaneous constraint satisfaction. Table 3 shows several non-negligible success rates for truncated disks: C5 (Moon-forming impact timing) is satisfied by 21% of analog systems and C6 (late veneer) by 10%, while C7 (water) is never satisfied. With these small numbers, the absence of a single system satisfying all constraints simultaneously could be a small-sample effect rather than a physical exclusion. The text should report binomial confidence intervals for the key success rates and state the negative conclusion as 'no system in our sample satisfied all constraints' rather than as a general impossibility.
[Section 1.1 (constraint G) and Section 4 (item G)] The water-delivery failure is not robust enough to support the global 'cannot explain' conclusion because the water mass fractions are assigned through an assumed radial profile whose parameters are explicitly uncertain. The paper notes that if outer-disk objects carried 10% water by weight (O'Brien et al. 2014), Earth analogs in truncated disks would reach WMF ~2E-3, within the observed range, while Venus and Mars analogs would become too wet. This is a model-dependent trade-off, not a robust exclusion. The water constraint should be presented as a conditional result of the adopted water model rather than as an independent disproof of truncated disks.

minor comments (5)

[Section 2.1] The classification algorithm is described entirely in prose; a pseudocode block or structured list would substantially improve reproducibility and make the disqualification rules easier to audit.
[Section 1.1, constraint F] There is a typo in 'Mars’ss formation timescale'; it should read 'Mars’s formation timescale.'
[Section 5 and Abstract] The abstract and summary state the negative conclusion in absolute terms, whereas Sections 1.1 and 2 carry important caveats about giant-planet migration and instabilities. The wording should be harmonized so that the abstract reflects the scope of the simulations actually performed.
[Table 3] The symbol Mpf is defined in the notes, but the name 'Mars analog production factor' is somewhat opaque; consider renaming it to something like 'Mars analogs per Mars-bearing system' for clarity.
[Section 2] The initial conditions for all 540 simulations are summarized only in aggregate tables; depositing the full initial-condition files and final outputs in a public repository would aid reproducibility and follow-up studies.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the simulation outcomes are judged against externally given solar system constraints, and the central conclusions do not reduce to the initial conditions or to self-citations.

full rationale

The paper's derivation chain is self-contained in the relevant sense: 540 N-body simulations with varied protoplanetary disk initial conditions are compared against externally given constraints on the inner solar system (orbits, masses, Moon-forming impact timing, late veneer, water content, asteroid belt structure). The disk initial conditions are not fitted to those constraints; in fact, most runs fail the constraints, and truncated disks are rejected because they systematically violate them. The classification algorithm in Section 2.1 defines Mercury, Venus, Earth, and Mars analogs using thresholds based on the real planets (e.g., mass ranges 0.03–0.17, 0.4–2.0, and 0.05–0.32 Earth masses), which determines what counts as an analog without forcing success. The negative claim about Grand Tack-style truncated disks follows from direct comparison of simulation outputs with these externally fixed criteria, not from any equation that equates input disk profiles with output analogs. The favorable disk properties listed in Section 5 are inferred by identifying which explored initial conditions produced the most analog systems satisfying the constraints; this is standard parameter inference from a simulation survey rather than a prediction equivalent to the inputs by construction. There is minor reliance on the authors' own prior work, notably Lykawka & Ito (2017), for the linear inner-region surface-density profile and for supporting Mercury water/volatile findings, but this is not load-bearing: the central result that truncated disks cannot explain the terrestrial planets is generated by the new simulation suite and does not reduce to those citations. The static giant-planet assumption (Section 2: 'the giant planets do not migrate') is a genuine modeling limitation that could affect external validity, but it is an assumption about the model setup, not a circular step in the derivation. No step was found in which a predicted quantity is identical by construction to a fitted input or in which a self-citation is invoked as the sole justification for a forbidden alternative.

Assumptions & free parameters 6 free parameters · 5 assumptions · 1 invented entities

The central claim rests on a suite of hand-chosen initial conditions and constraint thresholds. None of these are fitted to the target result, but several directly shape the conclusion: the core mass, the embryo-to-planetesimal ratio, the giant planet eccentricities, the success thresholds for the Moon-forming impact and late veneer, the water profile, and the I-belt construct.

free parameters (6)

Core region mass and boundaries = 2.0-2.1 M_Earth in 0.7-1.0 or 0.7-1.2 au
Chosen to match Hansen (2009) and Grand Tack expectations; not fitted to the four-planet outcome, but the central conclusion depends on this choice.
Inner and outer region disk components = Inner 0.3-0.9 au with 0.5-1.3 M_Earth; outer 1.0-4.3 au with 0.2-0.7 M_Earth
Hand-selected to explore mass-depleted inner and outer regions; the recommendations for an inner component and a less massive outer component are derived from these choices.
Embryo-to-planetesimal mass ratio r = 1, 4, 8 for truncated/depleted; about 6 and 19 for peaked
Chosen to test the effect of dynamical friction; results showing better outcomes for r = 4 or 8 drive the recommendation that embryos carry most of the disk mass.
Giant planet orbital architectures = JS23, JS23me, JS12he, NC
Taken from resonant migration literature; eccentric configurations produce better Mars analogs, so the recommendation of eccentric Jupiter and Saturn depends on these chosen inputs.
Success constraint thresholds = Moon-forming impact timing 20-140 Myr; late veneer 0.1-2%; water mass fraction 2.5e-4 to 1e-2
Adopted from literature with hand-set uncertainty ranges; these thresholds define the failures of truncated disks and are therefore load-bearing for the central claim.
Water mass fraction radial profile = 0.001% inward of 1.5 au; 0.01% at 1.5-2 au; 0.1% at 2-2.5 au; 5% at 2.5-3 au; 10% beyond 3 au
A simplified adopted model from prior work; the conclusion that Earth analogs are too dry depends on this profile, and the authors acknowledge the profile is not unique.

assumptions (5)

domain assumption The modified MERCURY N-body integrator with timesteps 2.43-4.57 days resolves orbital evolution down to Mercury's orbit reliably.
Standard integrator in the field, but the modified code is not independently verified or released (Section 2).
domain assumption Gas disk mass is negligible after 5-10 Myr, so gas dynamics can be ignored.
Standard assumption for late-stage accretion and supported by references to Haisch et al. (2001) and Gorti et al. (2016), as stated in Section 2.
ad hoc to paper Jupiter and Saturn do not migrate during the 400 Myr simulations.
The authors explicitly set migration aside and defer it to future work (Section 2, footnote 5). The central negative claim about truncated disks would be weakened if giant planet evolution perturbed the inner disk.
domain assumption Collisional fragmentation is not crucial for the conclusions.
Based on prior studies (Kokubo & Genda 2010; Chambers 2013; Walsh & Levison 2016); the authors note fragments enhance dynamical friction but argue that thousands of planetesimals can mimic this effect (Section 2).
domain assumption The truncated disk setup with 0.7-1.0 or 0.7-1.2 au core and S/C planetesimal split represents typical Grand Tack outcomes.
The authors construct this setup from Walsh et al. (2011) and related work; if the real Grand Tack disk was structurally different, the conclusion that truncated disks cannot explain the terrestrial planets would not transfer (Section 2).

invented entities (1)

Ice belts (I-belts)
purpose: Massive icy planetesimal belts at 3.4-4.3 au used to test the effect of icy bodies on Mars formation and water delivery.
A model construct inferred from the possible ice-line location, not an observed structure; the authors conclude that I-belts probably did not exist at the time of terrestrial planet formation (Section 2, Table 2, Section 4.3).

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Cite this review

Pith. "Pith review of Constraining the Formation of the Four Terrestrial Planets in the Solar System." pith.science (2026). https://pith.science/paper/OQJFSPUI

@misc{pith2026190804934,
  author       = {Pith},
  title        = {Pith review of: Constraining the Formation of the Four Terrestrial Planets in the Solar System},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OQJFSPUI}},
  note         = {Machine review of arXiv:1908.04934}
}

read the original abstract

To reproduce the orbits and masses of the terrestrial planets (analogs) of the solar system, most studies scrutinize simulations for success as a batch. However, there is insufficient discussion in the literature on the likelihood of forming planet analogs simultaneously in the same system (analog system). To address this issue, we performed 540 N-body simulations of protoplanetary disks representative of typical models in the literature. We identified a total of 194 analog systems containing at least three analogs, but only 17 systems simultaneously contained analogs of the four terrestrial planets. From an analysis of our analog systems, we found that, compared to the real planets, truncated disks based on typical outcomes of the Grand Tack model produced analogs of Mercury and Mars that were too dynamically cold and located too close to the Venus and Earth analogs. Additionally, all the Mercury analogs were too massive, while most of the Mars analogs were more massive than Mars. Furthermore, the timing of the Moon-forming impact was too early in these systems, and the amount of additional mass accreted after the event was too great. Therefore, such truncated disks cannot explain the formation of the terrestrial planets. Our results suggest that forming the four terrestrial planets requires disks with the following properties: 1) Mass concentrated in narrow core regions between ~0.7-0.9 and ~1.0-1.2 au; 2) an inner region component starting at ~0.3-0.4 au; 3) a less massive component beginning at ~1.0-1.2 au; 4) embryos rather than planetesimals carrying most of the disk mass; and 5) Jupiter and Saturn placed on eccentric orbits.

Figures

Figures reproduced from arXiv: 1908.04934 by the authors.

**Figure 4.** Comparison of individual 4-P analog systems (#1–17) obtained after 400 Myr of dynamical evolution with the solar system planets and Ceres (shown as “system #0” at the top). The data are combined according to fiducial (none), truncated (#1–11), depleted-only (#12–14), depleted-IB (#15–16), and peaked (#17) protoplanetary disks. The inclination of the system objects is represented by the angle between the vector and t… view at source ↗

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