QUOTE (fredk @ Oct 26 2014, 06:45 PM)
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This is still the big assumption, and could conceivably be orders of magnitude off...
Correct! There are still a few degrees of freedom in the system. Albedo/scattering and gamma-correction (for grain size estimates) are the other two, besides some minor uncertainties in image analysis.
For Rosetta's velocity relative to the center of mass of the nucleus, the
escape velocity of an object at a distance of 10 km from a mass of 1e13 kg is
sqrt(2 GM/r) = sqrt(2 * 6.672e-11 Nm²/kg² * 1e13 kg / 10,000 m) = 36.5 cm/s.
The velocity for a circular orbit is slower by a factor of sqrt(2), hence 25.8 cm/s.
At 9 km distance from the center of mass it's 27.2 cm/s for the circular orbit.
If we take the 27.2 cm/s as an estimate for the relative velocity to the dust, the distance would be (using the proportionality of velocity and distance) about 10 m * 27.2 cm/s / 1.6 cm/s = 170 m.
No idea, whether this assumption is realistic. From the geometry of the jets, it may be possible to infere the velocity of the grains causing the scattering there. But it's not clear, whether a velocity obtained that way can be used for the individual observed grains. There may be a different observational bias.
There are some faint, short streaks indicating, that there are grains further away; hence the distance for the brighter streaks should be far less than the distance to the comet. This still leaves much uncertainty.
Blur (by the optics) of the dust streaks might be another approach to find some constraints for the distance.