understood. As discussed earlier, the tensile strength of whole nuclei may be very
low but the compressive strength of the surface layers is potentially much higher and
the compressive strength of the deeper interior is essentially unknown. The importance of material strength can be illustrated by looking at crater scaling laws.
The volume of an impact crater, V imp , will depend upon impactor radius, velocity,
and density as well as the mass density of the target, the surface gravity and the
strength of the impacted material. Scaling laws have been developed to establish the
relationship between these quantities. Two regimes, the strength regime and the
gravity regime, can be distinguished. In the strength regime, gravity can be ignored
and target strength is dominant. The proportionality is then given by
V imp /
m imp
ρ N
ρ N U
2
Y
3μ imp =2 ρ N
δ imp
1À3v imp
ð2:128Þ
where m imp and U are the impactor mass and velocity, Y is a measure of the strength
of the impacted material, δ imp and ρ N are the mass densities of the impactor and
(nucleus) target respectively, and v imp and μ imp are coefficients to be determined.
In the gravity regime, the event is large and gravity’s influence dominates. The
strength of the material is then eliminated and the scaling law becomes
V imp /
m imp
ρ N
ga imp
U
2
À3μ imp = 2þμ imp
ð
Þ ρ N
δ imp
2þμ imp À6v imp
ð
Þ = 2þμ imp
ð
Þ
ð2:129Þ
where a imp is the impactor radius and g is the gravitational acceleration (Holsapple
1993, 1994). With gravity being extremely low on small bodies, the strength regime
is the most likely to be applicable and V imp increases proportionally to Y
À3μ imp =2
. Use
of the equations requires knowledge of several parameters. Examples for materials
of possible interest are shown in Table 2.6 where one can see the material strength
parameter, Y, varies by two orders of magnitude for different materials. With similar
values of μ imp for the two given materials, the crater volume varies as Y
À33/40 and
thus almost inversely to the material strength.
The high porosity inferred for comets is often (incorrectly) associated with low
material strength. Man-made, light, porous structures with significant strength are
now well known but strong, porous structures can also occur naturally. Examples
come from the gas industry where porosities greater than 50% can be found for
Table 2.6 Crater scaling law constants for materials of possible interest on comets (from https://
www.lpi.usra.edu/lunar/tools/lunarcratercalc/theory.pdf, retrieved 8 May 2019)
Constant
Soft rock
Cold ice
μ imp
0.55
0.55
ν imp
0.33
0.33
Y [MPa]
1
0.014
ρ N [kg m
À3 ]
2100
930
122
2 The Nucleus
low but the compressive strength of the surface layers is potentially much higher and
the compressive strength of the deeper interior is essentially unknown. The importance of material strength can be illustrated by looking at crater scaling laws.
The volume of an impact crater, V imp , will depend upon impactor radius, velocity,
and density as well as the mass density of the target, the surface gravity and the
strength of the impacted material. Scaling laws have been developed to establish the
relationship between these quantities. Two regimes, the strength regime and the
gravity regime, can be distinguished. In the strength regime, gravity can be ignored
and target strength is dominant. The proportionality is then given by
V imp /
m imp
ρ N
ρ N U
2
Y
3μ imp =2 ρ N
δ imp
1À3v imp
ð2:128Þ
where m imp and U are the impactor mass and velocity, Y is a measure of the strength
of the impacted material, δ imp and ρ N are the mass densities of the impactor and
(nucleus) target respectively, and v imp and μ imp are coefficients to be determined.
In the gravity regime, the event is large and gravity’s influence dominates. The
strength of the material is then eliminated and the scaling law becomes
V imp /
m imp
ρ N
ga imp
U
2
À3μ imp = 2þμ imp
ð
Þ ρ N
δ imp
2þμ imp À6v imp
ð
Þ = 2þμ imp
ð
Þ
ð2:129Þ
where a imp is the impactor radius and g is the gravitational acceleration (Holsapple
1993, 1994). With gravity being extremely low on small bodies, the strength regime
is the most likely to be applicable and V imp increases proportionally to Y
À3μ imp =2
. Use
of the equations requires knowledge of several parameters. Examples for materials
of possible interest are shown in Table 2.6 where one can see the material strength
parameter, Y, varies by two orders of magnitude for different materials. With similar
values of μ imp for the two given materials, the crater volume varies as Y
À33/40 and
thus almost inversely to the material strength.
The high porosity inferred for comets is often (incorrectly) associated with low
material strength. Man-made, light, porous structures with significant strength are
now well known but strong, porous structures can also occur naturally. Examples
come from the gas industry where porosities greater than 50% can be found for
Table 2.6 Crater scaling law constants for materials of possible interest on comets (from https://
www.lpi.usra.edu/lunar/tools/lunarcratercalc/theory.pdf, retrieved 8 May 2019)
Constant
Soft rock
Cold ice
μ imp
0.55
0.55
ν imp
0.33
0.33
Y [MPa]
1
0.014
ρ N [kg m
À3 ]
2100
930
122
2 The Nucleus