A 4-D Spherical-Harmonic Polynomial Framework for EmpiricalGas-Field Modelling in Spacecraft Orbit Analysis: Case Study ofRosetta at 67P/Churyumov–Gerasimenko

This year marks the tenth anniversary of the end of the Rosetta mission at comet 67P/Churyumov–Gerasimenko [1], and the community is already preparing for the next step in cometary exploration with ESA's Comet Interceptor mission, scheduled for launch in 2029 [2]. Despite the extensive insights gained from Rosetta regarding coma structure and its impact on spacecraft dynamics, accurately and efficiently modelling the coma for orbit analysis remains a major challenge.

The cometary coma exhibits a highly complex structure driven by the nucleus shape, time-varying illumination from rotation, and changing heliocentric distance [3]. These factors produce a strong day–night asymmetry, with gas number densities differing by several orders of magnitude between the sunlit and shadowed hemispheres [4]. The nearly radial outgassing velocity shows a similar angular structure: day-side bulk speeds reach up to ~800 m/s, almost twice those on the night side. Because orbiting spacecraft move at only cm/s to low m/s relative to the nucleus, this radial gas velocity dominates the aerodynamic force and must therefore be modelled with high fidelity.

Uniform, homogeneous coma models [5] can capture only bulk quantities such as the total water production rate and lead to large propagation errors when applied to orbit determination. Direct Simulation Monte Carlo (DSMC) approaches reproduce the structure of the coma far more faithfully by accounting for nucleus shape and illumination [3], but are computationally prohibitive for a temporally continuous representation and are typically restricted to the inner coma (≲10–20 km). Consequently, neither approach is directly suitable for orbit analysis, where thousands of force evaluations are required along candidate trajectories.

To bridge this gap, we introduce a 4-D Spherical-Harmonic Polynomial Framework for empirical gas-field modelling. The framework provides a joint radial, temporal, and angular continuous expansion of the coma. Any scalar gas-field quantity, number density, bulk speed, an individual velocity component, or temperature, is expanded in surface spherical harmonics whose Stokes coefficients depend on radius and time. Diurnal variability is captured through a discrete Fourier representation over the nucleus rotation period, while the radial evolution is described by compact polynomials. Once fitted, the resulting surrogate is operationally tractable: it delivers continuous, differentiable, millisecond-scale field evaluations directly compatible with high-throughput orbit propagation routines.

In this contribution, we present the formulation of the framework and demonstrate its application to comet 67P as a case study, illustrating its ability to reproduce reference fields with high accuracy using an open-source implementation in Tudat software [6] and its utility for trajectory analysis around active small bodies in support of upcoming missions such as Comet Interceptor.

 

 

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