Uncertainty estimation of incoming comet trajectories with a thermophysical non-gravitational force model for Comet Interceptor encounter planning

arXiv:2610.30871 · astro-ph.EP, astro-ph.IM · Submitted 2026-10-22 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Uncertainty estimation of incoming comet trajectories with a thermophysical non-gravitational force model for Comet Interceptor encounter planning".

Jocelyn: Here's the gist of the paper. The gist Precise orbit determination for incoming LPC's perturbed by NGAs is unlikely to be able to achieve the accuracy specified in design documents for the Comet Interceptor mission (1000 km and 1 m s−1 in position and velocity, sixty days before encounter) when modelling the NGAs with Marsden-style parameters The study tests the ability of ground-based astrometry and standard NGA-fitting techniques to predict the position and velocity of incoming comets perturbed by a Monte Carlo sampled thermophysical acceleration model The researchers assess the achievability of mission requirements given typical orbit-determination techniques with noisy astrometric measurements and non-gravitationally perturbed comet orbits They evaluate the effect of the Marsden and thermophysical Non-Gravitational Force (NGF) models on the POD routines of DN LPC and evaluate the reachability of the mission requirements regarding the cometary state Modeling Non-Gravitational Forces The paper compares two primary NGF models: Model I, which uses the Marsden model of Eqn.

Vera: 1 (Model I), and Model II, the thermophysical NGA model described in details in in the second subsection: The Marsden formulation represents the NGA as an orbital-averaged perturbation estimated along with the state of the comet It expresses NGA as a function of heliocentric distance dependence through Eqn.

Jocelyn: (2) Yeomans & Chodas (1989) introduced a time-shift parameter τ to account for asymmetric outgassing behaviour relative to perihelion Thermophysical models compute accelerations directly from thermophysical outgassing, typically over an assumed triaxial ellipsoid-shaped nucleus or a full comet shape-model These models require much more information about the nucleus physical properties and/or trajectory than is typically available from ground-based observations The thermophysical model uses the SHAP7 shape model with 125k facets for 67P to sample different surface activity patterns The NGA produced by a region can be found via Eqn.

Vera: (8) The thermal and force calculations are run 36 times over a comet rotation period and the summed curves averaged to make one data-point A Monte Carlo sample is accepted if there exists a heliocentric distance rc > 3 AU such that Q SAMPLED H2O(rc) = Q ltoT(rc) and Q ltoT(r) ≤ Q SAMPLED H2O(r) ≤ Q uTtoT(r) ∀r ∈

rc, q: , where q is the perihelion distance The total water production is taken as Q SAMPLE D H2O = ∑k n Q REGION H2O(n), (9) The change in osculating elements resulting from such an acceleration curve is computed as the difference between the initial state at the first observed epoch and the final propagated state at the last observed epoch The formal uncertainties of the estimated parameter vectors are captured in the covariance matrices By using a multivariate normally distributed Monte Carlo sampling of a covariance matrix around the estimated parameter vector, we can generate a population of initial state vectors and Marsden NGA parameters, which are then propagated forward to the time of Comet Interceptor’s encounter A distribution of Δ over many samples is then generated The median error, Δ˜, with error bars denoting the interquartile range (i.e.

Title and authors: Vera: So we're looking at this paper titled “Uncertainty estimation of incoming comet trajectories with a thermophysical non-gravitational force model for Comet Interceptor encounter planning,” and it really puts the stress on how well we can predict cometary paths when those non-gravitational forces are involved.

Jocelyn: It’s about comparing two ways to model these forces, the thermophysical model versus the Marsden model, specifically to see how much uncertainty we can actually reduce for an encounter that's sixty days out. The authors are testing if mission requirements like predicting position and velocity within one thousand kilometers and one meter per second are achievable with our current techniques.

Subrahmanyan: This is important because for these long-period comets, their orbits are so sensitive to those small pushes from gas release that even tiny errors in modeling those forces can blow up the prediction significantly.

Vera: They aren't just looking at one comet; they’re using a Monte Carlo approach with covariance matrices around the estimated parameters to generate a distribution of possible outcomes, which gives us a statistical measure of error.

Jocelyn: And what they find is that even when fitting the full orbital arc—not just data before perihelion—the median error at perihelion for all three studied comets stays below one thousand kilometers.

Subrahmanyan: That’s a significant finding because it shows that observing the entire path matters, and it suggests that the perturbation from these NGAs is a strong factor that usually only becomes measurable in exactly the same time-frame we are considering, about one hundred to fifty days before perihelion.

The paper's summary: Vera: So what the paper summarizes is that standard orbit determination routines using just Marsden-style parameters aren't enough to hit those tight design goals for the Comet Interceptor mission when dealing with real comets and these non-gravitational forces.

Jocelyn: They show that while you can get sub one thousand kilometer accuracy at perihelion if you fit the full arc, the overall uncertainty distribution still stretches out quite far, with interquartile ranges reaching ten or more thousand kilometers for all three cases examined.

Subrahmanyan: That large spread is really telling us that the uncertainty isn't just about how well we model the force; it’s also about how noisy our astrometric measurements are and how much we can predict the evolution of those non-gravitational forces.

Vera: The paper clearly shows that this uncertainty varies a lot depending on things like the comet’s orbital geometry, its distance from Earth, and its intrinsic activity or rotation.

Jocelyn: It’s a case-by-case problem; two comets that look similar might have very different predictability because of how their NGAs evolve differently.

Subrahmanyan: The main point is that precise orbit determination for incoming LPC's perturbed by NGAs is unlikely to achieve the mission accuracy when using just the Marsden-style parameters, which they call Model I >

The paper's improvements: Vera: Now, the paper suggests a few ways to improve things. First, they emphasize that you need to model these NGAs in a statistical sense using Monte Carlo sampling because a deterministic fit just isn't enough when the forces are this complex.

Jocelyn: They also highlight the importance of fitting the full orbital arc instead of just pre-perihelion data, showing that including all the observation time helps tighten up those results.

Subrahmanyan: And they point out that you need to be very careful about things like the overall magnitude of the covariance matrix attached to an orbit determination and how those parameters are correlated with each other.

Vera: The paper also shows that when you fit these models, if you correlate the fitted 'A' values with actual physical quantities like mass and radius, it supports this method because it lets us infer comet properties from the trajectory fitting data.

Jocelyn: That means we can potentially use AI systems to infer things like how big or active a comet is just by looking at how well its trajectory fits the model parameters.

Subrahmanyan: It also suggests that for future planning, instead of aiming for one thousand kilometers accuracy, maybe planning for ten thousand kilometers and a few times one meter per second might be more realistic given the limitations they found.

Conclusion: Vera: So to wrap up on this paper, while they show that fitting the full orbital arc helps reduce perihelion error to under one thousand kilometers, the overall uncertainty for intercept prediction remains quite large.

Jocelyn: The conclusion is that we can’t rely on simple Marsden-style parameters if we want to hit those strict design requirements for Comet Interceptor, and we need more sophisticated modeling of the non-gravitational forces.

Subrahmanyan: From a theoretical side, this reinforces the idea that the perturbation from NGAs is a strong factor that needs serious statistical study, which is exactly what they are doing with their Monte Carlo approach here.

Vera: It really hammers home how much the uncertainty depends on things like observational noise and our ability to predict how those NGAs evolve over time.

Jocelyn: So we’re looking at a path forward where we need better ways to model these asymmetric outgassing behaviors, maybe by incorporating parameters like the time-shift parameter tau into our orbit determination routines.

Subrahmanyan: That sounds like the right direction, moving toward models that account for those specific asymmetries rather than just assuming symmetric behavior.

Vera: Yep, that’s where we need to go to get a better handle on these incoming comets and we’ll keep an eye on these types of studies as we plan future missions.

N. Attree, P. de Boer, P. Gutiérrez, P. Lacerda, M. Küppers, D. Dirkx

Instituto de Astrofísica de Andalucía (CSIC) · Technische Universiteit Delft · Leiden Observatory, Leiden University · European Space Agency (ESA)

astro-ph.EP, astro-ph.IM

Submitted: 2026-10-22

Updated: 2026-10-22

Comments: 15 pages, 22 figures total incl. 2 appendices. Accepted in MNRAS

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 78/100

The gist: The gist Precise orbit determination for incoming LPC's perturbed by NGAs is unlikely to be able to achieve the accuracy specified in design documents for the Comet Interceptor mission (1000 km and 1

Key concepts

Marsden Model: This is a simplified way to model Non-Gravitational Forces (NGAs) by estimating the perturbation as an orbital-averaged change. It expresses the NGA as a function of how far the comet is from the Sun, but it often misses important details about how outgassing changes over time or distance.
Thermophysical Model: This model calculates NGAs directly from physical processes like outgassing, using detailed shape models of comets. It requires knowing the comet's physical properties and trajectory to compute the forces, offering a much more accurate prediction than simplified models.
Monte Carlo Sampling: This is a statistical method used to generate many possible initial states and NGA parameters by sampling around an estimated set. By propagating these many possibilities forward, researchers can create a distribution of potential errors rather than just one single guess.
Time-shift Parameter (tau): This parameter accounts for the fact that comets don't release gas perfectly symmetrically around their closest point to the Sun. It allows models to capture 'asymmetric outgassing behavior,' which is a crucial detail missing in simpler, symmetric NGA models.

Summary

The gist Precise orbit determination for incoming LPC's perturbed by NGAs is unlikely to be able to achieve the accuracy specified in design documents for the Comet Interceptor mission (1000 km and 1 m s−1 in position and velocity, sixty days before encounter) when modelling the NGAs with Marsden-style parameters

Methodology Overview

The study tests the ability of ground-based astrometry and standard NGA-fitting techniques to predict the position and velocity of incoming comets perturbed by a Monte Carlo sampled thermophysical acceleration model The researchers assess the achievability of mission requirements given typical orbit-determination techniques with noisy astrometric measurements and non-gravitationally perturbed comet orbits They evaluate the effect of the Marsden and thermophysical Non-Gravitational Force (NGF) models on the POD routines of DN LPC and evaluate the reachability of the mission requirements regarding the cometary state

Modeling Non-Gravitational Forces

The paper compares two primary NGF models: Model I, which uses the Marsden model of Eqn. 1 (Model I), and Model II, the thermophysical NGA model described in details in in the second subsection

**: The Marsden formulation represents the NGA as an orbital-averaged perturbation estimated along with the state of the comet It expresses NGA as a function of heliocentric distance dependence through Eqn. (2) Yeomans & Chodas (1989) introduced a time-shift parameter τ to account for asymmetric outgassing behaviour relative to perihelion Thermophysical models compute accelerations directly from thermophysical outgassing, typically over an assumed triaxial ellipsoid-shaped nucleus or a full comet shape-model These models require much more information about the nucleus physical properties and/or trajectory than is typically available from ground-based observations The thermophysical model uses the SHAP7 shape model with 125k facets for 67P to sample different surface activity patterns The NGA produced by a region can be found via Eqn. (8) The thermal and force calculations are run 36 times over a comet rotation period and the summed curves averaged to make one data-point A Monte Carlo sample is accepted if there exists a heliocentric distance rc > 3 AU such that Q SAMPLED H2O(rc) = Q ltoT(rc) and Q ltoT(r) ≤ Q SAMPLED H2O(r) ≤ Q uTtoT(r) ∀r ∈ [rc, q], where q is the perihelion distance The total water production is taken as Q SAMPLE D H2O = ∑k n Q REGION H2O(n), (9) The change in osculating elements resulting from such an acceleration curve is computed as the difference between the initial state at the first observed epoch and the final propagated state at the last observed epoch The formal uncertainties of the estimated parameter vectors are captured in the covariance matrices By using a multivariate normally distributed Monte Carlo sampling of a covariance matrix around the estimated parameter vector, we can generate a population of initial state vectors and Marsden NGA parameters, which are then propagated forward to the time of Comet Interceptor’s encounter A distribution of Δ over many samples is then generated The median error, Δ˜, with error bars denoting the interquartile range (i.e. Δ˜ ± 25% of the distribution), as robust measures of the average true uncertainty and its spread The results show that when fitting the full orbital arc (full-arc Δ˜ denoted by horizontal solid lines with dotted lines showing the interquartile range), sub-one-thousand kilometre accuracy at perihelion is assured for all the studied comets This demonstrates clearly that both observing arc-length and observing accuracy are important in predicting cometary positions The perturbation from NGAs is a strong factor, which typically only becomes measurable in exactly the same time-frame as considered here (∼ 100 − 50 days before perihelion) NGAs then must be studied in a statistical sense, hence the Monte Carlo approach here, and gradually refined with more accurate models A strong factor, however, is clearly the perturbation from NGAs The last point (that serious consideration must be paid to both the overall magnitude of the covariance matrix attached to an orbit determination, and also correlations within it) also applies to the intercept prediction accuracy Orbit fitting is fiddly and complicated, and must be approached on a case-by-case basis with tight control on both a priori and observational uncertainties, and a healthy degree of scepticism for the derived quantities and their formal errors The last point (that serious consideration must be paid to both the overall magnitude of the covariance matrix attached to an orbit determination, and also correlations within it) also applies to the intercept prediction accuracy The final position error at 60 days remain at several thousand kilometres, with interquartile ranges extending to ten-or-more thousand kilometres, for all three comets, and for all three orbit fitting cases The uncertainty comes from a combination of the limitations of the astrometric observations, and our ability to predict how NGAs evolve, and varies on a case-by-case basis; depending on a particular comet’s orbital geometry, Earth-centric range, observability, as well as its intrinsic activity and rotation (e.g. two equally wellobserved comets might have different predictability depending on their NGAs) Precise orbit determination for incoming LPC's perturbed by NGAs is unlikely to be able to achieve the accuracy specified in design documents for the Comet Interceptor mission (1000 km and 1 m s−1 in position and velocity, sixty days before encounter) when modelling the NGAs with Marsden-style parameters Instead, we recommend planning for 10, 000 km and a few times 1 m s−1<ref:2610.

Improvements for AI systems

Increased predictive accuracy for dynamically new long-period comet trajectories by implementing a Monte Carlo sampled thermophysical acceleration model instead of relying solely on standard Marsden-style NGA fits. This allows for better estimation of trajectory uncertainty, as shown by the finding that Predicted accuracies are unlikely to meet the mission goals of 1000 km and 1 m s−1 in position and velocity, sixty days before intercept when using simpler models.
Development of a robust orbit determination (POD) routine capable of estimating asymmetric NGA parameters, specifically including the time-shift parameter tau, which is crucial for modeling asymmetric outgassing behaviour relative to perihelion displayed by some comets. This improvement directly addresses the limitations found when fitting real, outgassing comets using only symmetric models.
Creation of a framework to quantify the interplay between observational uncertainty and non-gravitational forces, enabling better target selection for future rendezvous missions and survey planning. The system can now assess how NGAs perturb the trajectory and how this affects the final predicted accuracy based on factors like observational uncertainty, arc-length, and cadence.
Capability to extract physical quantities from NGA fits by correlating fitted parameters with underlying physical quantities like mass and radius, as demonstrated by the finding that Fitted A values correlating with true acceleration peaks supports this method. This allows AI systems to potentially infer comet properties from trajectory fitting data.
Improved uncertainty estimation for incoming comet trajectories by using a full orbital arc for fitting, which is shown to yield better results than relying only on pre-perihelion data for certain comets, as indicated by the observation that the full orbital solution improves the situation again, demonstrating the importance of both Earth-centric distance and a consideration of all the data.
Enhanced performance under noisy observational conditions by testing how increased astrometric noise affects trajectory prediction, showing that Position divergence [km] is not as good as expected when noise increases to 0.5 arcseconds, suggesting that future AI navigation systems can better incorporate realistic observational error margins.