The size of 3I/ATLAS from non-gravitational acceleration

The third macroscopic interstellar object detected in the solar system recently passed through perihelion, with the best-fitting models of its trajectory now featuring non-gravitational accelerations. We assess how much mass loss is required to produce plausible non-gravitational acceleration solutions and compare with estimates of the mass loss. We find that they are consistent when the nucleus of 3I/ATLAS is around 1 km in diameter. For a recent solution with a time lag in the acceleration from Eubanks et al, we find diameters between 820 meters and 1050 meters, assuming an outgassing asymmetry factor $ζ=0.5$ and a density of the comet nucleus $ρ=0.5$ g cm$^{-3}$. The limits on the diameter scale as $(ζ/ρ)^{1/3}$. Substantial extrapolation is required in general to compare non-gravitational accelerations to mass loss rates, so reliable estimates of the mass loss rate at other stages of the comet’s trajectory will substantially reduce the systematic uncertainty in this estimate.

💡 Research Summary

The manuscript presents a quantitative assessment of the nucleus size of the interstellar object 3I/ATLAS by linking its observed non‑gravitational accelerations (NGAs) to the comet’s mass‑loss rate. The authors begin by reviewing the physical basis for NGAs: asymmetric outgassing of volatile ices (primarily CO₂ in this case) imparts a recoil force on the nucleus, which can be inferred from deviations in the object’s orbital trajectory. They note that NGAs are derived from cumulative astrometric residuals, whereas mass‑loss rates are measured at discrete epochs, requiring a careful conversion between the two quantities.

To perform this conversion, the authors adopt a momentum‑conservation framework expressed as M |a| ≈ ζ Ṁ v_th, where M is the nucleus mass, a is the measured acceleration, ζ is an outgassing asymmetry factor (0 ≤ ζ ≤ 1), Ṁ is the total mass‑loss rate, and v_th is a characteristic thermal outflow speed. The thermal speed is modeled as v_th = 0.8 km s⁻¹ (r/1 au)⁻⁰·⁵, following recent cometary studies, and ζ is set to a canonical value of 0.5, reflecting moderate asymmetry. The nucleus bulk density ρ is assumed to be 0.5 g cm⁻³, a typical value for cometary nuclei.

Two families of NGA solutions are examined. The first consists of several JPL Small‑Body Database solutions that originally employed the classic Marsden water‑sublimation law and later were updated to a CO₂‑appropriate r⁻² dependence. The second is the time‑lagged acceleration model presented by Eubanks et al. (2025), which incorporates a delay between solar heating and outgassing response. For each solution, the authors compute a family of Ṁ curves as a function of assumed nucleus diameter, retaining explicit dependence on ζ and ρ.

These theoretical Ṁ curves are then compared with observational constraints on CO₂ production obtained from JWST, SPHEREx, ALMA, TRAPPIST‑North, and Swift. JWST provides both an upper and a lower bound on CO₂ output on 6 August 2025, while SPHEREx offers contemporaneous measurements. Ground‑based facilities contribute lower limits where CO₂ lines are inaccessible. Dust‑loss rates are excluded from the analysis because dust velocities are typically much lower than gas velocities, making their contribution to recoil negligible for the purposes of this study.

The comparison reveals that the Eubanks time‑lagged model can simultaneously satisfy the JWST upper bound and the TRAPPIST‑North lower bound when ζ = 0.5 and ρ = 0.5 g cm⁻³. Under these assumptions the nucleus diameter is constrained to 820 m × (ζ/ρ)¹ᐟ³ ≤ D ≤ 1050 m × (ζ/ρ)¹ᐟ³. In contrast, the JPL solutions cannot meet both constraints at the same time, suggesting that the simplifying assumptions of constant ζ, constant mass loss, or a single dominant volatile may be insufficient. The authors discuss possible resolutions, including variable ζ (e.g., strong jets could raise ζ toward unity) or multi‑species outgassing, and note that relaxing the assumption of a single dominant gas could alleviate the tension.

A key result is the scaling relation D ∝ (ζ/ρ)¹ᐟ³, which quantifies how uncertainties in outgassing asymmetry and bulk density propagate into the size estimate. The authors emphasize that the current systematic uncertainty is dominated by the lack of time‑resolved mass‑loss measurements; improved monitoring of gas production throughout the comet’s trajectory would dramatically tighten the size constraints.

In conclusion, the paper argues that 3I/ATLAS likely has a nucleus diameter of order one kilometre, with the most robust estimate (820–1050 m) derived from the Eubanks time‑lagged acceleration model under standard assumptions. The methodology demonstrates how NGAs, when combined with contemporaneous gas‑production data, can serve as a powerful tool for estimating the physical properties of interstellar comets, especially when direct imaging is unavailable. The authors call for coordinated multi‑wavelength campaigns to obtain dense temporal coverage of outgassing, which will reduce the dominant systematic uncertainties and enable more precise characterizations of future interstellar visitors.