Study of the Non-Gravitational Forces Acting on Long-Period Comets

Active small bodies experience significant non-gravitational effects due to outgassing. While increasingly complex models have been developed to describe cometary behaviour, often requiring detailed knowledge of the shape and composition of individual objects, the general formulation of non-gravitational accelerations still largely relies on the model proposed by Marsden et al. [1]. Recent studies [2] have shown that this formulation is unable to accurately reproduce the long-term motion of cometary bodies, thereby increasing uncertainties regarding the origin and dynamical evolution of long-period comets.

This work proposes an alternative model for the non-gravitational acceleration caused by outgassing, capable of reproducing and/or improving upon the results obtained with the Marsden and Yabushita models [1,3], while offering increased interpretability and improved physical realism.

The proposed model is defined using a sample set of well-characterised bodies, for which we remeasured datasets using the zero-aperture extrapolation method for cometary astrometry [4]. The formulation builds upon the Marsden model by retaining the RTN-frame formulation and constant $A_1$, $A_2$, and $A_3$ parameters, while directly reflecting the behaviour of sublimating volatiles. The resulting model can be extended to represent the sublimation of multiple volatiles at different distances from the Sun, improving trajectory accuracy at large heliocentric distances. The model parameters are selected based on literature studies, empirical laws, and sensitivity analyses.

We introduce both a single-volatile and a multi-volatile sublimation model, and validate both formulations across a larger pool of objects and conditions. The results show that, when fitting an orbit using astrometric data, the proposed formulations generally match or outperform the Marsden model in terms of normalised weighted root-mean-square residuals. Application of these models also enables the retrieval of information about the physical properties of cometary nuclei, such as the main sublimating species and the heliocentric distance at which a comet becomes significantly active, relying exclusively on orbit estimation.

In both versions, the ability to tailor the model to individual comets through the determination of optimal model parameters offers a level of flexibility not present in the Marsden formulation, whose fixed $r_0$, $m$, $n$, and $k$ constants are less intuitively adaptable.

Overall, the proposed models are effective in representing non-gravitational accelerations due to outgassing. Their interpretability, combined with their capacity to infer physical characteristics from purely dynamical behaviour, makes them a valuable complement to direct compositional studies and contributes to a more comprehensive understanding of both cometary dynamics and cometary physics.

References

[1] Marsden, B.G., Sekanina, Z., Yeomans, D.K., The Astronomical Journal, 1973, 78, 211–225.
[2] Królikowska, M., Dybczyński, P.A., Monthly Notices of the Royal Astronomical Society, 2017, 472(4), 4634–4658.
[3] Yabushita, S., Monthly Notices of the Royal Astronomical Society, 1996, 283(1), 347–352.
[4] Tholen, D.J., Chesley, S.R., Bulletin of the American Astronomical Society, 2004, 36, 11