On the other hand, the SFD is important because the value of the exponent, b d ,
implies certain properties of the dust coma. The cross-sectional area of the particles
and their mass is of course a function of their size and we can crudely use πa
2 and
4πa
3
ρ d /3 for cross-sectional area and mass respectively for illustration purposes. The
total cross-sectional area at one particle size is then
σ p a
ð Þ ¼ k p π a
Àb d þ2
ð4:80Þ
and the total mass at one size is then
m a
ð Þ ¼ k p
4
3
π ρ d a
Àb d þ3
ð4:81Þ
with k p being a proportionality constant. If these equations specify the emitted
size distribution and if b d > 3 then the mass loss is dominated by the largest particles
in the distribution and if b d > 2 then both the mass and the cross-sectional area,
which is related to the scattering area, are dominated by large particles. In Fig. 4.22
left, we can see the dust size distribution (and associated area and mass plots) from
measurements made by the DIDSY and PIA experiments on Giotto (McDonnell
et al. 1991) which remains the most comprehensive data set for this purpose. The
plot shows that the quantities as the total (number density, cross-section and mass)
within a size interval equal to half a decade as a function of the logarithm of the mass
Fig. 4.22 Left: The dust size distribution in the coma derived from the PIA and DIDSY observations made from the Giotto spacecraft and normalised to 600 km (re-drawn after McDonnell et al.
1991). Right: The 269 GIADA measurements of particle masses made during the Rosetta mission.
Note that the axes have been deliberately chosen to make a comparison with the McDonnell work.
Although the x axis is the same, the y axis only covers three decades
318
4 Dust Emission from the Surface
implies certain properties of the dust coma. The cross-sectional area of the particles
and their mass is of course a function of their size and we can crudely use πa
2 and
4πa
3
ρ d /3 for cross-sectional area and mass respectively for illustration purposes. The
total cross-sectional area at one particle size is then
σ p a
ð Þ ¼ k p π a
Àb d þ2
ð4:80Þ
and the total mass at one size is then
m a
ð Þ ¼ k p
4
3
π ρ d a
Àb d þ3
ð4:81Þ
with k p being a proportionality constant. If these equations specify the emitted
size distribution and if b d > 3 then the mass loss is dominated by the largest particles
in the distribution and if b d > 2 then both the mass and the cross-sectional area,
which is related to the scattering area, are dominated by large particles. In Fig. 4.22
left, we can see the dust size distribution (and associated area and mass plots) from
measurements made by the DIDSY and PIA experiments on Giotto (McDonnell
et al. 1991) which remains the most comprehensive data set for this purpose. The
plot shows that the quantities as the total (number density, cross-section and mass)
within a size interval equal to half a decade as a function of the logarithm of the mass
Fig. 4.22 Left: The dust size distribution in the coma derived from the PIA and DIDSY observations made from the Giotto spacecraft and normalised to 600 km (re-drawn after McDonnell et al.
1991). Right: The 269 GIADA measurements of particle masses made during the Rosetta mission.
Note that the axes have been deliberately chosen to make a comparison with the McDonnell work.
Although the x axis is the same, the y axis only covers three decades
318
4 Dust Emission from the Surface