Mars/moon impact rate ratio:
2000/2012 comparison
Boris Ivanov
Institute for Dynamics of Geospheres, RAS, Moscow
• Impact craters as a link to other terrestrial
planets, satellites and asteroids
• Interplanetary comparisons
• Mars/Moon impact ratio
3MS3 IKI 2012
ASTEROIDS
• Stony (several types)
• Iron
• Orbit evolution due to
close encounters and
resonances with giant
planets
• No close encounters
with Jupiter (Tisserand
T_J>3)
3MS3 IKI 2012
COMETS
• Jupiter family (JFC):
mostly from Kuiper
Belt
• 2<T_J <3
• Long-periodic comets
(LPC) drop out of
Oort cloud
• Unpredictable
3MS3 IKI 2012
(number of returns?)
Crater chronology: interplanetary comparison
Moon: crater counts and
chronology by returned
samples
Moon crossers orbits - >
impact velocity and
probability
Scaling laws: D_crater -> D_projectile
Mars crossers orbits - > impact velocity
and probability, relative number of
projectiles
Scaling laws: D_projectile -> D_crater
Mars: crater counts (beware
of secondaries!)
Bolide ratio
Rb
Of numbers of
impacts of the
same size
bodies per 1
km2 per 1 year
Mars: model chronology
3MS3 IKI 2012
2012 astorb.dat
N
Pcol, yr-1
<Uimp>
N (% of total)
Pcol, yr-1
<Uimp>
The Moon (Earth) crossers
Mars-crossers
H<18
H<16
H<18
H<16
Asteroid-like orbits TJ > 3
458
82
5774
1416
-9
-9
-9
0.16×10
0.14×10
0.23×10
0.17×10-9
17.0
19.0
9.3
10.0
JFComet-like orbits 2< TJ <3
97 (17%)
18 (25%)
336 (5.5%)
83 (5.5%)
0.051×10-9
23.4
0.045×10-9
25.5
0.07×10-9
17.3
0.06×10-9
16.7
(1) the percentage of comet-like orbits (higher impact velocities) on the Moon is about
25% to 20%, on Mars this number is factor of ~2 less;
(2) at the modern Mars orbit (e=0.094) the “bolide ratio” (the ratio of impact number per
unit area per unit time) is about Rb=5.5 in comparison with 2000 estimates of
Rb=4.9
(3) the average impact velocity for asteroid-like objects on the moon increases to ~19
km/s in comparison with 16.1 km/s in 2000 estimates.
3MS3 IKI 2012
Population of asteroid-like (TJ>3)
and comet-like orbits (TJ<3)
2005 vs. bolide survey
Below D~1 km (H~18) population of small (10 cm) projectiles the share of comet-like bodies may
increase factor of 2
3MS3 IKI 2012
Öpik-Wetherlill impact probabilities for osculating orbits
2000
2012
Planet 4= the moon
Number of bodies
58709
H_max=
18.050000
Number of impactors
160
Mean intrinsic probability =
= 1.865368E-10 1/Proj
<v_imp>
16.122780
<v_inf> 15.916600
------------------------------------Planet 5=Mars
Number of bodies
1109
Planet 4= the moon
H.ge. 18. arc_limit 20
Number of bodies 458
Average of impactors 458
Intrinsic probability =
1.58944954E-10 per body
<v_imp> 17.0044266
<v_inf> 16.8058947
-------------------------------Planet 5=Mars
H.ge. 18. arc_limit 20
Number of bodies 5774
Number of impactors
1109
Mean intrinsic probability =
2.587355E-10 1/Proj
<v_imp>
9.929664
<v_inf>
8.330708
Average of impactors 5774
Intrinsic probability =
2.29726429E-10 per body
<v_imp> 9.30803356
<v_inf> 7.60588575
3MS3 IKI 2012
2012 astorb.dat, Mars- and Moon-cossers number vs. magnitude
(H=18 approximately corresponds to Dproj ~ 1 km
In the current epoch number of Mars-crossers with asteroid like orbits is
factor of 20 larger than the number of Moon-crossers. Number of
bodies with comet-like orbits is factor of 5 larger for Mars. 3MS3 IKI 2012
From craters to projectiles
• Scaling laws for impact cratering allow us
to convert size-frequency distribution of
craters to the size-frequency distribution of
projectiles
• Crater-derived curves may be compared
with astronomical observations
3MS3 IKI 2012
Scaling laws for impact cratering
Coupling parameter:
Ivanov, B., Size-Frequency Distribution of
Asteroids and Impact Craters: Estimates of
Impact Rate, in Catastrophic Events Caused
by Cosmic Objects, edited by V. V. Adushkin
and I. V. Nemchinov, pp. 91-116, Springer,
2008.
Transient cavity scaling:
(1 + 2)
Crater collapse:
(3)
3MS3 IKI 2012
Modeling of impact melt in large terrestrial crater confirm
validity of scaling laws for D_crater > 1km
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2008 iteration of the scaling law for small (<1-10 km) lunar craters
Blind usage of “standard” scaling laws results in a factor of 6
difference in the R(D_crater) for the same projectile. Looks strange...
3MS3 IKI 2012
2010-2012 – hydrocode with porosity and dry friction
+ Demonstration of dry friction importance
- Modeling velocity <12 km/c
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2012 (Ivanov, LPSC): more
realistic dry friction in
fragmented rocks with thermal
softening under
shock/deformational heating
3MS3 IKI 2012
If so (need to be verified more) then
1. “Porous target” scaling is wrong
while extrapolated beyond 7 km/s.
2. “Shallow” pi_V vs. pi_2 scaling is
mostly due to dry friction, not due
to material porosity only.
3. Scaling of “regolith” lunar craters
should be redone.
4. How porous is Martian upper layer
important for 5-50 m in diameter
craters (real impact rate
available)???.
HIRISE modern impact rate
To date around 200 “new” impact cites (impact craters and crater clusters) are
found with well bounded formation time
1.E-08
1.E-09
R_Daubar
R_4years
1.E-10
RMars_1yr
R
R_Hart_1yr
R_Hart_10Years
1.E-11
Rmars_10 yr
1.E-12
1.E-13
0.001
0.01
D (km)
0.1
1
The recent data based on the discovery rate based solely on CTX/CTX image
comparison (with crater size improved with HiRISE images, 44 impacts) gives
factor of 2 to 3 lower cratering rate in the upper diameter bins (Daubar et al,
2012, under revision)
“All” craters gives better fit to Hartmann-Neukum chronology
3MS3 IKI 2012
Conclusions
 We are close to update the 2000 Mars/moon cratering rate ratio…
but not ready yet.  
Pure updating of planetary-crosser’s orbit list of crossers does not
change the Mars/moon impact ratio dramatically (despite ~6-fold
increase in the number of known objects).
 Future discussion should include possible difference in craterforming projectile properties. Small crater clusters found on Mars
witness in favor of the presence of 10% to 20% low density (high
porosity?) projectiles.
Two additional questions: (1) the difference in mechanical
properties of regolith on the dry Moon and possibly ice-saturated
Martian soil, and (2) the efficiency of lunar impacts of low-density
objects assumed from Martian strewn fields.
New observational data demands new supportive research and
modeling.
3MS3 IKI 2012
10
Asteroids,
Trojan, and JF
comets
10
10
N(>D)
• Cumulative plot for
Main Belt, Trojan
asteroids, and Jupiter
Family comets in
comparison with
cumulative N>D
distribution derived
for crater forming
projectiles (thick
curves).
10
10
7
6
5
4
Main belt
3
Trojans
100
JF comets
10
1
0.1
3MS3 IKI 2012
1
10
D, km
100
1000
10
Asteroids, Trojan,
and JF comets (2)
Jewitt et al. (2000),
comets - after Tankredy et
al. (2000).
Main Belt
6
Trojans
10
R
• R-plot for Main Belt asteroids
according to Davis et al.
(1994) and Spacewatch data
by Jedicke and Metcalfe
(1998) for all the Main Belt
and the inner belt in
comparison with the SFD for
projectiles formed lunar
craters. Trojans are after
10
7
10
5
Inner Main Belt
4
Comets
10
3
100
10
0.1
1
10
D , km
P
3MS3 IKI 2012
100
1000
RECENT
DATA
• Sloan Digital
Sky Survey
(SDSS):
Ivezic et al,
2001
• LINEAR:
Stuart, 2001
3MS3 IKI 2012
Physical mechanism of „SFD waves:
CRITICAL SPECIFIC ENERGY
(Love&Ahrens, 96; Melosh&Ryan,97)
3MS3 IKI 2012
Near-Earth
bodies (2)
1E+11
1E+10
-9 -1
H<15, P=2.42 10 ,yr
-9 -1
H<18, P=4.31 10 ,yr
Lunar projectiles for N(1km)=800
1E+9
Tunguska, 32<D(m)<64
1E+8
1E+7
N
(>D)
sky
• The lunar “projectile
curve fitted to
N(1)=800 in
comparison with
bolide data. Letters
“T” designate the
possible range of
Tunguska scale
projectiles.
1E+6
1E+5
1E+4
1E+3
1E+2
10
1
0.1
1E-4
0.001
0.01
0.1
D, km
3MS3 IKI 2012
1
10
100
Crater size-frequency distribution:
cumulative, increment, relative (R)
Incremental
Relative (R-plot)
3MS3 IKI 2012
Crater size-frequency distribution:
cumulative, increment, relative (R)
Cumulative
Relative (R-plot)
3MS3 IKI 2012