Geoscience Reference
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(dominated by water), and carbonaceous particles as 0.20:0.19:0.55:
0.06 and 0.26:0.23:0.42:0.09, respectively. By assigning the densities
{
kg
/
m
3
for these compo-
nents, a total compact density of
ρ
comp
=1
,
540-1
,
650 kg
/
m
3
was obtained.
However, the assumed densities may be on the high side (e.g., the pyroxene
end member enstatite, which dominates the silicate composition of Comet
C/1995 O1 Hale-Bopp,
3
,
4
only has
ρ
sil
=2
,
700 kg/m
3
, and since water ice
by far is the most common volatile,
ρ
vol
= 930 kg/m
3
may be a more rea-
sonable value). If the lower values for
ρ
sil
and
ρ
vol
are used, the density
of compact material drops by
ρ
sil
,ρ
or
,ρ
vol
,ρ
car
}
=
{
3
,
500
,
1
,
800
,
1
,
200
,
2
,
000
}
300 kg
/
m
3
with respect to the value sug-
gested by Greenberg.
2
Therefore, the range 1
,
400
∼
ρ
comp
∼
1
,
700 kg/m
3
is
applied here.
The basic question in the current paper is, if the bulk densities
of comets are in this range, or substantially lower due to porosity.
The density expected for small planetesimals in the Solar Nebula is
discussed in Sec. 2. The subsequent evolution of these planetesimals is dis-
cussed in Sec. 3, leading to some theoretical expectations on the bulk density
of comets. Empirical estimates of cometary bulk densities are summarized
in Sec. 4, and are compared with the theoretical range in Sec. 5.
∼
2. Grain Agglomeration and Planetesimal Formation
The Solar Nebula consisted of
98% hydrogen and helium (by mass) while
heavier species predominantly were trapped in solid dust grains with a
plausible average radius
5
of
∼
0
.
1
µ
m. These grains may have had a layered
structure,
6
with a silicate core, a mantle of organic substances, and a crust
of ices (mostly H
2
O, CO, and CO
2
) mixed with very small carbonaceous
particles (e.g., polycyclic aromatic hydrocarbons).
The gas disk was supported by radial pressure gradients and therefore
orbited the Sun at sub-Keplerian velocities. The grains, slowed down further
by gas drag, had generally very small relative velocities (on the order of
V
rel
=10
−
4
m
/
s), governed by Brownian motion. Under such conditions,
laboratory experiments on ground and in microgravity
7
,
8
show that grains
readily stick to each other upon collisions and build highly porous fractal
clusters, having a fractal dimension
D
f
=1
.
3-1
.
9 (see Fig. 1). This means
that the cluster mass
m
∼
r
D
f
grows much slower with cluster size
r
,than
for solid particles (for which
D
f
= 3). As the clusters grow, their cross
section to mass ratio
σ/m
slowly decreases, leading to reduced gas drag
and higher relative cluster velocities.
∝
