The ESA ROSETTA mission is planned to encounter comet 46P/Wirtanen after aphelion and to orbit around its nucleus while approaching the Sun (Bar-Nun et al. 1993). The probe orbit parameters will be very variable. The distance from the nucleus will range from thousands of km, during the approaching phase, to less than 100 km, during the mapping of the nucleus surface. In this latter phase, a complete surface sampling will be achieved by varying in a wide range the probe orbit angular parameters (i.e. inclination with respect to the comet orbital plane, pericenter argument and nodal line orientation with respect to the sun direction). Moreover, in the most probable case of an aspherical nucleus, the orbits will not be keplerian at the shortest probe-nucleus distances. Therefore, many orbit corrections might be necessary to maintain the probe in a cometocentric configuration. In order to constrain the required technical specifications for experiments included in the ROSETTA payload, the expected results must be simulated for all possible probe orbit configurations by assuming the most updated models of the 46P/Wirtanen nucleus. In the present paper, we model the dust flux expected on the Rosetta probe. The results will be primarily useful in the view of the dust flux analyser experiment, which is devoted to measuring the mass and velocity of the incoming dust. They will also be relevant both for the other experiments dealing with dust characterization and for those potentially affected by dust pollution.
So far, the only in-situ dust flux measurements were provided by the DIDSY
experiment on-board the GIOTTO spacecraft (McDonnell et al. 1987).
Fulle et
al. (1995) obtained the best available fit of the DIDSY data by using a
probabilistic model of the anisotropic dust ejection from 1P/Halley nucleus.
Their analysis was focused on the unexpected millimetric grain excess observed
in the collected fluence (i.e., the number of collected grains per unit area),
a feature most likely simulated by a wide distribution of dust velocities. The
adopted model included grains ejected over long times (from the GIOTTO fly-by
back to the 1P/Halley perihelion) and covering a mass range from 
to 
kg. The best fit of the DIDSY data provided the following
values of the model parameters: a dust size distribution power index of
; a dust velocity dispersion of 
5 m s-1 around the
most probable velocity, which agrees with predictions of hydrodynamic models
for the 1P/Halley inner coma (Crifo 1991); a dust to gas ratio of 
;
an ejection dispersion of 
around the sun direction. Since information
on the parameters required to model 46P/Wirtanen is mostly lacking, for our
modelling we have adopted the above reported data. When possible, they have
been updated with values provided by Jorda & Rickman (1995), estimated from
past visual and photographic observations of the 46P/Wirtanen coma, and with
the dust ejection velocity values obtained by Crifo & Rodionov (1996) on the
basis of a model consistent with the photometric data quoted by Jorda &
Rickman (1995). The adopted parameters of the dust environment model of
46P/Wirtanen are summarized in Table 1 (click here).
 | 300 kg s-1 |
 |  |
 | 300 m s-1 |
 |  |
 | 1 m s-1 |
| v0 | 35 m s-1 |
 | |
 | 1 |
 | -3.5 |
| s1 |  m |
| s2 |  m |
 | 103 kg m-3 |
 | 103 kg m-3 |
 |  m |
 |  kg |
Perihelion gas loss rate. ,
time-dependent gas loss
rate. r, Sun-comet distance (AU). , Perihelion dust
ejection velocity
from the inner coma for micron-sized grains. , time and size
-dependent dust ejection velocity from the inner coma. s, dust diameter
(
m). , dust escape velocity from the nucleus surface.
v0, Dust
velocity dispersion. , dust ejection dispersion around the sun
direction. , dust to gas ratio. , dust size distribution power
index. 
, minimum and maximum dust sizes considered in the model.
, bulk densities of the
dust and of the nucleus. 
,
Nucleus radius and mass
Figure 1: Sketch of the ROSETTA orbital configuration
Figure 2: Dust mass per unit surface collected during a probe orbit for
R = 100 km, starting sun-comet distance r = 1.762 AU, and 
.
The different panels refer to various pointing directions: comet nucleus
direction (+x) and its opposite (-x); probe velocity vector direction
(+y) and its opposite (-y); directions perpendicular to the probe orbital
plane (+z and -z)
Cometary dust is sensitive to the solar radiation pressure. Thus, for each
probe position in the coma, two grain populations must be considered: those
coming from the nucleus (hereafter direct grains) and those coming from
the sun direction, under the action of the solar radiation pressure (hereafter
reflected grains). The two populations are characterized by very
different times of ejection from the nucleus. The most relevant difference
between a fly-by (GIOTTO) and a rendez-vous (ROSETTA) configuration is that
in the first case the probe velocity is always much higher than the dust
velocities, so that the whole dust flux comes from the in front direction.
On the contrary, the ROSETTA probe velocity will always be lower than the dust
velocity, so that dust will impact the spacecraft from all directions. Thus,
it becomes relevant to take into account the acceptance angle, w, of the
considered experiment. The w angle is the full aperture of the covered solid
angle 
.
In this paper we investigate: i) which fraction of dust flux will be collected
by the instruments pointing towards the nucleus and characterized by a tight
acceptance angle w; ii) which other view directions may offer useful dust
flux sampling; iii) which fluences and dust masses are expected to be collected
for the comet environment parameters discussed above; iv) which is the
dependence of all these quantities on w and on the probe orbital parameters;
v) which is the total dust flux on the orbiter, evaluated for 
. Due
to the large number of free parameters and the uncertainties affecting actual
probe orbits, in this paper we assume circular orbits around the nucleus.
Future works will have to analyse the dependence of the model results on the
orbit eccentricity and on the variation of the parameters describing the dust
environment of 46P/Wirtanen.
Figure 3: Dust mass flux (left panel) and cumulated fluence (right panel)
for R = 100 km, starting sun-comet distance r = 1.762 AU, ,
and 
. The different line types refer to various pointing
directions: +x (continuous line), -x (dot dashed line); +y (short
dashed line), -y (long dashed line), and -z (three dot dashed line)
Figure 4: Dust mass flux (left panel) and cumulated fluence (right panel)
in the -z direction for R = 100 km, starting sun-comet distance
r = 1.762 AU, , 
and 
Figure 5: Dust mass flux (left panel) and cumulated fluence (right panel)
for R = 100 km, starting sun-comet distance r = 1.762 AU, ,
and 
. Pointing directions: +x (continuous line) and
-z (three dot dashed line)