The most stricking result of our simulation is that, during a probe orbital period, the sun-comet distance variations influence dust mass, flux and fluence much more than the probe-nucleus distance changes. This is a consequence of the small comet nucleus mass and, thus, of the non negligible probe orbital period with respect to the comet revolution time. The previous result supports our assumption of circular probe orbits. Moreover, only low eccentricity probe orbits and probe-nucleus distances of tens of nucleus size may offer stability against perturbations, due to the very probable asphericity of the nucleus. Models considering very eccentric keplerian probe orbits, passing very close to the nucleus, should include corrections during each revolution which are not predictable. Therefore, they appear less realistic than our conservative model based on circular probe orbits.
We must expect strong anisotropy of the dust ejection: it is very probable that the nucleus night side will release a negligible dust mass, whereas all the dust production will be confined in the sun side. Our results are mostly sensitive to the dust ejection anisotropy. Therefore, a detailed prediction of dust mass, flux and fluence versus the probe orbit anomaly, node and inclination is impossible without detailed information on the coma anisotropy patterns. It is unlikely that such data will be available before the ROSETTA probe will explore its target. The fit of the DIDSY data, coming from the fly-by of the 1P/Halley comet (Fulle et al. 1995), has shown that, on times comparable to the assumed probe orbital periods, a satisfying approximation of the ejection anisotropy pattern is given by a gaussian function of the zenithal angle cosine. Planned observations of the ROSETTA target, 46P/Wirtanen, might provide information on the spin axis direction and coma morphology, which would allow us to improve the adopted model. For instance, if comet 46P/Wirtanen would display a fan shaped coma, due to active spots located close to the nucleus rotation pole, then the model would be improved by assuming the nucleus rotation axis as the direction of the highest dust production.
Observations of 46P/Wirtanen might allow us to better define poorly known parameters describing the comet dust environment. Some of these parameters have a predictable influence on the model results: they depend linearly on the gas loss rate or on the dust to gas ratio; so that changes of these parameters would imply a simple scaling of all the plots presented in this paper. Other parameters influence only some of the results. Changes of the dust bulk density would imply a scaling of the computed total masses and mass fluxes. Similarly, variations of fluences are produced by a dust size distribution power index change, which, instead, is ineffective on dust masses and mass fluxes, when considering the largest grains dragged by gas out of the nucleus. Other poorly known parameters strongly influence model results in a non predictable way. Information is lacking about the dust loss rate dependence on the sun-comet distance and the time of comet activity onset, that we have assumed to occur at aphelion. The gas ejection anisotropy influences the mass limit of grains dragged out by gas, which might be lower than the assumed values. This would imply cut-offs of the fluences at lower masses than those shown in the plots, mainly at large sun-comet distances, where the comet dust environment is unknown. Further observations are needed to constrain inner coma models which provide the dust ejection velocity: models predicting the dust flux which will be measured in-situ mainly depend on this poorly known quantity and on the dispersion around its most probable values.
The model presented in this work is a powerful tool for the prediction of
results we can expect from ROSETTA experiments aimed at comet dust analysis.
The reported conclusions about the dependence of dust mass, flux and fluence on
the direction, in the probe reference frame, have a general validity. On the
other hand, their absolute values have been obtained on the basis of the
presently available best estimates of cometary environment parameters. These
results will have to be updated as long as more refined information will be
available on the target comet. With concern to the experiment on board ROSETTA
expressely devoted to the dust flux monitoring, our results clearly indicate
that direct grains will be collected only when the probe will cross
the jets of the inner coma. During all other phases, the total mass of
reflected grains, collected from both the directions perpendicular to
the probe orbital plane, will be higher than that collected in the nucleus
direction. According to our computations, these two directions will be the
most suitable to monitor the reflected dust flux coming from the sun
direction. To properly constrain the velocity determination of direct
grains, an acceptance angle of about 
will be needed (Lamy et al. 1996).
On the other hand, an acceptance angle of about 
is more efficient when
measuring the flux of reflected grains. In this last case, according to
our results, for 56% of randomly oriented probe orbits the flux received from
both the directions perpendicular to the probe orbital plane is higher than
that received from the nucleus direction. Most of these favourable orbits are
not forbidden on the basis of the present mission plan. The collection of
reflected grains is crucial to get information on dust ejected at
sun-comet distances different from those characterizing the probe orbits.
Finally, according to our model results, many probe orbits, similar to those
considered in the present approach, will be needed to deposit a complete dust
monolayer on the spacecraft and/or experiment surfaces pointing to the nucleus.
Acknowledgements
This work has been supperted by ASI, CNR and MURST research contracts. We thank Dr. J.F. Crifo for providing us the digital version of the output of his comet environment modelling and for the stimulating discussion. We thank Dr. J. Crovisier for the detailed review and for the suggested improvements to the paper.