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REVIEW 3 major objections 6 minor 63 references

The paper reports a 40% more precise measurement of the MOND external-field quadrupole in the Solar System, consistent with zero, which tightens the conflict between modified-gravity MOND and galaxy rotation curves to the 3–15σ level.

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2026-08-02 22:05 UTC pith:BUFLI7NG

load-bearing objection Useful extension of the Cassini Q2 analysis, with a clean Jupiter calculation, but the 792-parameter fit's Q2 recovery is not demonstrated; without an injection test the headline tension claims are not yet supported. the 3 major comments →

arxiv 2602.17884 v2 pith:BUFLI7NG submitted 2026-02-19 gr-qc astro-ph.EPastro-ph.GA

Improved constraints on modified Newtonian gravity from Cassini radio tracking data

R. S. Park , A. Hees , B. Famaey , H. Desmond , A. Durakovic This is my paper
classification gr-qc astro-ph.EPastro-ph.GA
keywords MONDexternal field effectCassini radio trackingplanetary ephemeridesSolar System quadrupoleradial acceleration relationinterpolating functionmodified gravity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the Solar System's Cassini radio tracking data, reanalyzed with the planetary ephemerides, cap the MOND external field effect quadrupole Q2 at (1.6 ± 1.8) × 10^-27 s^-2. That value is consistent with zero and 40% more precise than before. If correct, this bound translates into a maximum allowed MOND boost to the galactic radial acceleration at the Sun of 1.01–1.02, well below the ~1.1 boost inferred from Milky Way rotation curves. This would mean that most modified-gravity versions of MOND, which reduce to the AQUAL or QUMOND formulations in the non-relativistic limit, are in strong tension with galactic data, and that any viable MOND-like modified gravity must involve another scale beyond a0 or a screening mechanism.

Core claim

Using the full DE440 planetary ephemerides dataset, including Cassini ranging through August 2017, the paper fits the MOND quadrupole Q2 simultaneously with all 792 standard parameters and recovers Q2 = (1.6 ± 1.8) × 10^-27 s^-2, a 40% tighter bound than the previous (3 ± 3) × 10^-27 s^-2. The authors validate stability by splitting the Cassini arc into two independent subsets, both consistent with zero. They further show the theoretical prediction is practically insensitive: Jupiter's contribution to Q2 is ~0.05% and the Milky Way's non-sphericity changes it by less than 1%. Reinterpreting the Q2 posterior as a constraint on the MOND boost a_e/a_N^e at the Sun gives 95% upper bounds of 1.01

What carries the argument

The central object is Q2, the amplitude of the symmetric trace-free quadrupole term that MOND's external field effect adds to the Solar System potential. The key theoretical identity is the expression Q2 = -(3 a0^(3/2) / (2 sqrt(G M_sun))) q, where q is a dimensionless integral that depends only on the MOND interpolating function and the Newtonian external field strength e_N. This identity shows Q2 is controlled by the behavior of the interpolating function near a0, not by its sharpness above a0, making the measurement a direct probe of that regime. The paper then uses the measured Q2 to invert this relation and bound a_e/a_N^e for three families of interpolating functions.

Load-bearing premise

The inference stands or falls on the assumption that the DE440 data-reduction pipeline and its noise model are unbiased, so that a nonzero MOND quadrupole would survive the simultaneous 792-parameter fit rather than being reabsorbed by parameter correlations.

What would settle it

Run a full end-to-end simulation: inject a MOND quadrupole with Q2 = 5 × 10^-27 s^-2 into the DE440 dynamical model, generate synthetic Cassini range data, and perform the 792-parameter global fit. If the injected signal is substantially reabsorbed by parameter correlations, the reported (1.6 ± 1.8) × 10^-27 s^-2 bound would not be a faithful measure of Q2 and the derived tensions would be invalid.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The updated Q2 bound excludes, at the 3–15σ level, the standard MOND interpolating functions that fit external galaxy rotation curves (SPARC), with the strongest tension for the fiducial and bulge-constrained mass models.
  • Within the Milky Way alone, the Q2 constraint caps the MOND radial boost at the Sun at 2% (95% confidence), while the rotation curve requires at least ~10%, an internal inconsistency that cannot be explained by galaxy modeling uncertainties.
  • If AQUAL/QUMOND are the correct non-relativistic limits, the wide-binary excess reported in some studies cannot be attributed to MOND; the Solar System bound now supersedes wide-binary constraints.
  • The only ways to escape the tension are modifications of MOND that introduce an additional scale beyond a0, a screening mechanism, or abandoning modified gravity in favor of modified inertia.

Where Pith is reading between the lines

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

  • The same 792-parameter simultaneous fit could be run with a synthetic Q2 signal injected to map exactly which parameters absorb the signature; this would turn the authors' correlation warning into a quantitative correction, potentially relaxing or strengthening the bound.
  • Future radio tracking of a spacecraft in orbit around Uranus or Neptune would extend the baseline beyond Saturn's orbit and could push Q2 uncertainties below 10^-27 s^-2, possibly distinguishing between interpolating functions instead of only bounding them.
  • The paper's conversion from Q2 to a_e/a_N^e relies on a specific (Gaia-derived) value of the external field and surface density; different Milky Way mass models could shift the allowed boost by a few percent, but the >10σ tension is likely to survive such changes.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents an updated estimate of the Solar System quadrupole parameter Q2, which in modified-gravity MOND theories arises from the external field effect of the Milky Way on the Solar System. Using the DE440 planetary ephemeris dataset together with an extended Cassini ranging arc (through August 2017), the authors perform a simultaneous 792-parameter global fit and report Q2 = (1.6 ± 1.8) × 10^-27 s^-2, a 40% improvement over the previous Cassini-based constraint. They also compute the contribution of Jupiter to the theoretical MOND quadrupole, showing it to be only about 0.05% and thus validating the usual Sun-only approximation. The paper then uses the new Q2 posterior to derive constraints on MOND interpolating functions, on the Milky Way acceleration boost a_e/a_N^e at the Sun (95% upper limits 1.010–1.018 for the three IF families considered), and on wide-binary predictions, reporting 3–15σ tensions with SPARC rotation-curve fits and a >10σ tension with the Milky Way rotation curve. The central theoretical derivation is presented in Sec. II, the empirical fit in Sec. III, and the astrophysical implications in Sec. IV.

Significance. If the empirical Q2 estimate is unbiased, the paper delivers a genuinely improved, physically meaningful constraint on the MOND external field effect and significantly sharpens the existing tension between Solar System tests and galactic rotation curve data. The theoretical treatment of the Jupiter contribution is clean and explicit, with an exact calculation in Appendix A and a transparent expansion in the small parameters β and w; this part is a real strength. The posterior predictive comparisons are also carefully set up, with multiple M/L models and EFE prescriptions. However, the empirical claim rests entirely on a 792-parameter orbit-determination fit whose degeneracies are acknowledged but not quantified, and the analysis is not reproducible from the manuscript alone. The significance of the paper therefore hinges on an unvalidated, and in part proprietary, data-processing pipeline.

major comments (3)
  1. [Sec. III B, Table I] The manuscript concedes that 'a large part of the signature of a non-zero Q2 has been reabsorbed in the fit due to correlations with other estimated parameters' (citing [40]). This makes the reported Q2 = (1.6 ± 1.8) × 10^-27 s^-2 a marginal estimate from a global fit, not an independently demonstrated measurement of the physical MOND quadrupole. If a real quadrupole leaks into Saturn orbit elements, asteroid masses, or the solar-system barycenter, the value in Table I is biased and the derived constraints in Sec. IV inherit that bias. The two Cassini subsets do not control for this: both include all DE440 data and the same 792-parameter set, so common-mode absorption is invisible. The paper provides no injection/recovery test with a known input Q2 and no report of the correlation structure between Q2 and the other parameters. Without such a test, the formal 1σ uncertainty is not a calib
  2. [Sec. IV A, Table II] The quoted tensions (3.8–15.9σ) are computed by assuming Gaussianity and summing RAR and Cassini Q2 uncertainties in quadrature. The RAR posteriors shown in Fig. 4 are visibly non-Gaussian, with tails and boundaries that differ strongly across M/L models; a quadrature sum of standard deviations is not a calibrated significance level in such cases. The same issue affects the '>10σ' Milky Way statement in Sec. IV B3. A posterior predictive p-value or a full joint posterior would be needed to support the specific σ numbers. This does not necessarily change the qualitative conclusion, but it does affect the quantitative headline claims.
  3. [Sec. III B] The empirical result is not reproducible from the paper. The text says the analysis follows 'procedures analogous to' DE440 and refers to [26, 38] for details, but the actual data weighting, outlier rejection, media calibrations, a priori constraints, the full list of 792 parameters, and the covariance matrix are not given. For a result whose physical interpretation depends on the degree of correlation between Q2 and the rest of the fit, this is insufficient. At minimum, the covariance matrix (or its largest entries) and a detailed residual and weighting description should be supplied as supplementary material, or the code/pipeline should be made available.
minor comments (6)
  1. [Sec. II A] Typo: 'Netwonian' should be 'Newtonian'.
  2. [Sec. III B] The cross-reference 'Sec. III B III B' in the caption of Table I is malformed.
  3. [Fig. 2] The axis label/typesetting renders 'Q2 = 10 26 s 2' rather than 'Q2 = 10^{-26} s^{-2}' in the caption; the exponent is missing.
  4. [References] References [41] and [43] are duplicates of the same SPARC mass models paper; one should be removed or replaced with the specific reference intended.
  5. [Table II] The row '1.b. w. surf. density' has no entry under 'σQ2 (AQUAL local)'. Either report the value or state why it is omitted.
  6. [Sec. IV B1] The statement that including the surface-density term changes Q2 by less than 1% is shown for one IF family and one set of input values; the generality of this claim should be clarified.

Circularity Check

0 steps flagged

No significant circularity: Q2 is an independently fitted observable and the MOND comparisons use external data.

full rationale

The derivation chain is one-way. Q2=(1.6±1.8)e-27 s^-2 is estimated in a 792-parameter global fit to Cassini and DE440 data (Sec. III B). MOND predictions for Q2 are computed from Eqs. (7)-(9) using the IF families of Eqs. (4) and external inputs (Gaia a_e, MW surface density, SPARC RAR fits); the Jupiter correction is derived analytically in Appendix A. The Q2 posterior is then compared to external galaxy rotation-curve data, so no target is fitted twice. The Sec. IV B 3 upper limit on a_e/a_N^e is a reparameterization of the measured Q2 under a fixed IF family, but it feeds into comparison with external Milky Way rotation-curve estimates; that is standard parameter inference, not circularity. The main caveat is a fidelity/systematics concern, not circularity: Sec. III B admits that 'a large part of the signature of a non-zero Q2 has been reabsorbed in the fit due to correlations with other estimated parameters,' and no injection test is shown, so the unbiasedness of the Q2 posterior is assumed rather than demonstrated. Minor self-citations (notably [23], [40], [51]) are present, but the central derivation is self-contained in Sec. II and the new data are external to those papers; none of the load-bearing equations reduces to a self-citation.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper's central claim rests primarily on the trustworthiness of the DE440 fit and on standard MOND theoretical assumptions; no ad hoc invented entities are added.

free parameters (5)
  • Quadrupole amplitude Q2 = (1.6±1.8)×10^-27 s^-2 (1σ, All Data)
    The observed target parameter estimated simultaneously with the DE440 ephemerides; central result of the paper.
  • MOND acceleration scale a0 = 0.5–2×10^-10 m/s^2 flat prior; fiducial 1.02×10^-10 m/s^2 from [23]
    Free parameter of MOND; marginalized in the Milky Way boost posterior, and enters theoretical Q2 predictions.
  • IF shape parameter (n, δ, or γ) = family-dependent; not uniquely fit here
    Characterizes the MOND-Newtonian transition; the paper scans families but does not provide a single fitted value.
  • External Galactic acceleration a_e = 2.32±0.16×10^-10 m/s^2 (Gaia prior)
    Input that converts Q2 into a Milky Way boost; not fitted by the paper.
  • Baryonic surface density at Sun Σ_b = 47±3 M_sun/pc^2
    Input for disk-flattening correction; affects Q2 prediction at ~1% level.
axioms (5)
  • domain assumption The Solar System effect of modified-gravity MOND in the inner Solar System is fully captured by the quadrupole term Q2 in Eq. (6) with higher multipoles negligible.
    Sec. II D; follows from Milgrom (2009) and Blanchet & Novak (2011), and is used to interpret the Cassini bound.
  • domain assumption AQUAL/QUMOND are representative non-relativistic limits of the modified-gravity MOND theories considered.
    Sec. II A and IV; the constraints are derived for these formulations, and the authors infer that any MOND modified gravity must involve another scale if these fail.
  • domain assumption The DE440/Cassini data processing and the 792-parameter fit are free of unmodeled systematics that correlate with Q2.
    Sec. III B; the fitted Q2 is only meaningful if the noise model and dynamical model are complete.
  • standard math Standard potential-theory results: trace-free symmetric multipole expansion and the q-integral relations (9a)–(9b).
    Sec. II B; background for the theoretical Q2 prediction.
  • domain assumption Gaussian likelihood and quadrature addition of uncertainties for computing sigma tensions in Table II.
    Sec. IV A; 'assuming Gaussianity to sum the RAR and Cassini Q2 uncertainties in quadrature.'

pith-pipeline@v1.3.0-alltime-deepseek · 18615 in / 15815 out tokens · 149603 ms · 2026-08-02T22:05:08.084487+00:00 · methodology

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read the original abstract

We report an updated constraint on the Solar System quadrupole parameter $Q_2$, which encodes the external field effect predicted by modified gravity versions of the modified Newtonian dynamics (MOND) paradigm. Using the dataset employed to compute the DE440 planetary ephemerides and estimating it simultaneously with other parameters included in the planetary ephemerides, we find $Q_2 = (1.6 \pm 1.8) \times 10^{-27}\,\mathrm{s}^{-2}$ (1-$\sigma$), representing an improvement of 40% over previous estimates. We also show explicitly that the contribution to the MOND prediction of $Q_2$ from the Solar System's largest planet, Jupiter, is at the 0.05% level, validating the approximation of retaining only the Sun in theoretical calculations. With this new constraint on $Q_2$, we update previously acknowledged tensions with external galaxy rotation curves, now leading to discrepancies at the $3$-$15\sigma$ level depending on the detailed mass modeling or the subset of galaxies considered. Within the Milky Way itself, the $Q_2$ constraint imposes an upper bound of only 2% (at 95% confidence) on the MOND boost to the galactic radial acceleration (i.e., the ratio of the observed over baryonic Newtonian acceleration) at the position of the Sun, in strong tension with current observational limits. The updated $Q_2$ posterior finally confirms that Solar System measurements provide stronger constraints than current wide-binary data on classical modified gravity versions of MOND.

Figures

Figures reproduced from arXiv: 2602.17884 by A. Durakovic, A. Hees, B. Famaey, H. Desmond, R. S. Park.

Figure 1
Figure 1. Figure 1: FIG. 1: Distribution of the phantom density for the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Simulation of the deviation of the Earth-Saturn [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Residuals of the Cassini range data against the “All Data” case. The weighted root-mean-square residual is [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Posteriors on [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Posterior predictive distribution of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Evolution of the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Posterior probability distribution of [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 1
Figure 1. Figure 1: This means that the value of the integral from [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗

discussion (0)

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Reference graph

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