Non-gravitational force model vs observation: the trajectory and rotation-axis of comet 67P/Churyumov-Gerasimenko

The determination of non-gravitational forces based on precise astrometry is one of the main tools to establish the cometary character of interstellar and solar-system objects. The Rosetta mission to comet 67P/C-G provided the unique opportunity to benchmark Earth-bound estimates of non-gravitational forces with in-situ data. We determine the accuracy of the standard Marsden and Sekanina parametrization of non-gravitational forces with respect to the observed dynamics. Additionally we analyse the rotation-axis changes (orientation and period) of 67P/C-G. This comparison provides a reference case for future cometary missions and sublimation models for non-gravitational forces.

Orbit changes by non-gravitational forces
Among several thousand candidate orbits we have conducted an exhaustive search for the best-fit trajectory ofcomet 67P/C-G to pin down the magnitude and direction of the non-gravitational. Starting from estimates of the non-gravitational Marsden parameters A₁, A₂, A₃ from [1] and [2] (derived from Earth-bound observations of several apparitions of 67P/C-G), we determined an improved solution compatible with Rosetta telemetry [3]
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Figure 1: Error for non-gravitational force models for comet 67P/C-G [7]. The label r_ESOC denotes the (noisy) ESA provided orbit, the pink curve the best fit Marsden values, the blue curve is computed without non-gravitational forces (r₀). The reference orbit r_obs shows our best fit to the ESOC data.

Fig. 1 shows that the improved solution reduces the residual error from several hundred kilometers (Marsden parametrization) to about 20 km. This allows us to extract the magnitude anddirection of the non-gravitational acceleration (Fig. 2).

Figure 2: Total magnitude of the non-gravitational acceleration observed for 67P/C-G [7] and water production rate [8]

Comet 67P/C-G displayed a very regular activity pattern with diurnally repeating dust and gas emission [4, 5,6]. This in turn suggests a very uniform non-gravitational acceleration and smooth changes of the rotation axis.

Rotation-state changes
The rotation of comet 67P/C-G shows almost no wobbling motion and changes only by 0.5 DEG over the 2015 apparition [9]. This change is smaller than what a homogeneous emission model (i.e. Keller A model) predicts. In addition it indicates a very close alignment of the axis of inertia with the rotation axis. This requires a slightly inhomogeneous mass distribution with an increased density in the larger lobe.

Summary and Conclusions
We followed the state vector changes of the nucleus of 67P/C-G (momentum and angular momentum) in terms of a Fourier decomposition of the diurnal outgassing in the nucleus-fixed frame. Our analysis constrains the gas release and the inhomogeneity of the near surface ices. For 67P/C-G we find that the standard Marsden parametrization of the non-gravitational forces [10] can be improved considerably. No evidence for a forced precession is seen for 67P/C-G. Our methodology can be applied to other small-bodies with outgassing activity, provided that a shape and initial rotation state is known.

Acknowledgements
The work was supported by the North-German Supercomputing Alliance (HLRN). We acknowledge helpful discussions and joint work concerning the rotational state of 67P/C-G with E. Kührt, H.U. Keller, L. Jorda, andS. Hviid [9].

References
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