Systematic and Statistical Uncertainties in the Non-Gravitational Acceleration of 3I/ATLAS

Abstract: We present a detailed analysis of the trajectory of the interstellar comet 3I/ATLAS, focusing on its non-gravitational acceleration (NGA) parameters and their uncertainties. Orbital solutions are computed with models that implement symmetric, time-offset, and asymmetric radial dependence of the outgassing law relative to perihelion. We assess solution robustness through multiple data-selection strategies and comparison with independent determinations. The radial and normal NGA components (A_1 and A_3) are broadly consistent across all configurations, whereas the transverse component (A_2) is more sensitive to data selection, parameter correlations, and orbital phase coverage. Models with asymmetric radial decay slopes marginally improve the fit, but they also introduce additional degeneracies, contributing to systematic uncertainties. The magnitude of the NGA scaled to 1 au constrains the nucleus size of 3I. While our total acceleration estimates agree well with that of JPL's Small-Body Database solution, inclusion of systematic modeling effects implies a significantly larger uncertainty in the inferred radius of 3I.

• The paper quantifies systematic and statistical uncertainties in 3I/ATLAS's non-gravitational acceleration using various NGA modeling approaches.
• It employs rigorous methods including weighted least squares, MCMC posterior sampling, and jackknife resampling to assess outgassing effects and orbital dynamics.
• The findings highlight significant parameter degeneracies that affect nucleus size estimation and volatile composition inference.

Systematic and Statistical Uncertainties in the Non-Gravitational Acceleration of 3I/ATLAS

Introduction

The interstellar comet 3I/ATLAS, the third detected object of its kind traversing the solar system on a hyperbolic trajectory, provides a test-bed for constraining non-gravitational acceleration (NGA) mechanisms in cometary dynamics. Its detection affords a unique opportunity to analyze the physical and dynamical properties of extrasolar small bodies, with particular emphasis on the role of volatile-driven outgassing effects that perturb the orbit beyond gravitational forces. This work systematically quantifies the NGAs acting on 3I, explores the sensitivity of their estimates to astrometric data selection and model parameterizations, and evaluates the associated uncertainties. Accurate NGA characterization is critical both for reliable orbit reconstruction and for inferring intrinsic nucleus properties, including size and volatile composition.

Astrometric Dataset and Orbital Geometry

3I was monitored over 7788 epochs spanning May 2025 to February 2026 using a global network of ground- and space-based facilities, with Solar System reference orbits derived in the heliocentric ecliptic frame. The data traverse a broad arc from 6.31 au pre-perihelion to 4.05 au post-perihelion, covering perihelion at 1.356 au. Conservative astrometric error characterization was adopted, notably accommodating the high uncertainty ($\sim$20 arcseconds) of TESS archival detections.

Figure 1: Orbit of 3I in the heliocentric ecliptic plane, with observation endpoints and perihelion highlighted; gray region denotes negative $Z_\epsilon$.

The hyperbolic character, with $e \approx 6.1$ and $v_\infty \approx 58$ km s$^{-1}$, makes 3I the fastest recorded interstellar object in the solar system, with dynamical sensitivity especially pronounced near perihelion.

Dynamical Modeling and Orbit Determination

The nucleus trajectory was modeled as a sum of gravitational and NGA contributions, integrating the equations of motion in the J2000 equatorial frame via the heyoka Taylor Adaptive integrator. Planetary and lunar perturbations were computed using the analytical VSOP2013 and ELP2000 theories, and relativistic corrections were applied in the post-Newtonian approximation. NGA was parameterized using the Marsden formalism as:

$${\bf a}_\mathrm{NG} = g(r) \left[A_1 {\bf e}_R + A_2 {\bf e}_T + A_3 {\bf e}_N\right]$$

with $g(r)$ set to a canonical $1/r^2$ scaling, appropriate for highly-volatile driven outgassing.

A suite of orbital solution classes were analyzed:

• gr0: Gravity-only;
• ng1: NGA symmetric about perihelion;
• ng2: NGA with peak offset in time from perihelion (asymmetry via free parameter $DT$);
• ng3: NGA with distinct pre-/post-perihelion radial decay slopes (parameter $\delta_m$).

Weighted least-squares orbit determination was performed, implementing outlier rejection and systematic bias corrections. Both full-arc and time-restricted solutions (pre- or post-perihelion) were assessed for sensitivity to data selection.

Residual Analysis and NGA Model Comparison

Residual analysis for the gravity-only model showed clear systematic trends in both coordinates, supporting the need for outgassing-driven perturbations.

Figure 2: Normalized post-fit residuals for gravity-only model (gr0), showing systematic structure about perihelion.

Inclusion of symmetric NGA terms (ng1) markedly improved fit quality, reducing RMS residuals and eliminating long-term trends.

Figure 3: Residuals with symmetric NGA (ng1), indicating elimination of systematic orbital phase trends.

Allowing for asymmetric NGA (ng2: peak shifted from perihelion, ng3: different decay rates before/after perihelion), marginally improved fit statistics, but at the cost of introducing significant degeneracy among parameters—particularly between the overall NGA amplitude and decay exponents.

Statistical and Systematic Uncertainty Quantification

Uncertainties were rigorously estimated using linearized covariance analysis, MCMC posterior sampling, and jackknife resampling with both time-window and observing-station exclusion strategies.

Figure 4: Sampled posterior distributions for NGA and state parameters (ng1 model), overlaid with 1- and 2-$\sigma$ contours.

NGA vector components at 1 au are robustly centered about $A_1=3.78 \times 10^{-8}$ au d$^{-2}$, $A_2=3.86 \times 10^{-8}$ au d$^{-2}$, $A_3=-0.65 \times 10^{-8}$ au d$^{-2}$ (ng1), with tight relative statistical uncertainties ($\sim5\%$). Jackknife analyses revealed that, while $A_3$ remains stable, $A_2$ is acutely sensitive to orbital arc coverage and data from critical observing stations (notably Psyche and TGO), underscoring the importance of spacecraft-based astrometry for interstellar trajectory constraints.

Figure 5: Illustration of jackknife data-removal strategies, indicating sensitivity of the NGA estimates to orbital arc and station.

Model Degeneracies and Physical Interpretation

Models incorporating radial decay asymmetry (ng3) or time-shifted NGA maxima (ng2) show that changes in decay slope or outgassing peak timing can yield nearly indistinguishable integrated dynamical effects across a moderately sampled heliocentric range. Parameter degeneracy is pronounced; for $m$ (average radial decay exponent) spanning 2–5, NGA amplitude at 1 au can vary by over a factor of three, with only weak statistical preference among models.

Figure 6: NGA amplitude versus time for different model prescriptions, showing comparable integrated forcing across perihelion despite model differences.

In all plausible parameterizations, the dominant sources of uncertainty propagate primarily into the NGA amplitude and hence into inferred estimates of the nucleus radius. Even under highly-volatile-driven activity, radius uncertainties of 50% are unavoidable due to these model systematics.

Implications and Contextualization

Comparison with JPL SBDB and other published NGA determinations for 3I reveals general consistency in the total amplitude but significant discrepancies in component ratios—particularly $A_2/A_1$, which in the present work is near unity while being significantly smaller in JPL’s solution. High-resolution imaging confirms the presence of anisotropic, high-latitude jets and a likely pole orientation near the sunward direction, supporting the plausibility of a substantial transverse component to the NGAs.

The robustness of normal and radial NGA terms contrasts with large variance in the transverse component, compounded by weak orbital coupling on hyperbolic trajectories. The ability to map orbital perturbations back to nucleus size and activity thus critically relies on model selection and availability of diversified, phase-resolved astrometry.

Model Propagation and Validation

The computational framework, leveraging heyoka and analytical planetary/lunar ephemerides, was benchmarked against numerical ephemerides and alternative propagators (ASSIST), confirming negligible (<1%) effect on NGA parameter inference across the fitting interval and validation of integration approaches at sub-kilometer accuracy.

Figure 7: Ephemeris comparison between VSOP2013/ELP2000 and DE440 implementations.

Figure 8: Time evolution of position and velocity differences between heyoka and ASSIST propagators, demonstrating convergence through pre- and post-Jupiter encounter.

Conclusion

The analysis establishes that while symmetric and simple time-offset NGA models are broadly successful, systematic uncertainties arising from degeneracies in outgassing prescription limit inferences about both physical parameters (e.g., nucleus size) and the decomposition of activity asymmetries. Deep-space, multi-geometry astrometric sampling is indispensable for breaking these degeneracies. The formal uncertainty on 3I’s size related to NGA systematics remains substantial. The methodology developed here sets a stringent benchmark for future studies on the characterization of additional interstellar small bodies, where volatility, anisotropy, and activity asymmetry must be robustly disentangled in the context of limited temporal and geometric baselines.