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Icarus 220 (2012) 297–304
Contents lists available at SciVerse ScienceDirect
Icarus
journal homepage: www.elsevier.com/locate/icarus
Surveys of elliptical crater populations on the saturnian satellites, Mercury,
and Mars
Robert R. Herrick a,⇑, Paul M. Schenk b, Stuart J. Robbins c
a
Geophysical Institute, University of Alaska Fairbanks, 903 Koyukuk Dr., Fairbanks, AK 99775-7320, United States
Lunar and Planetary Institute, 3600 Bay Area Blvd., Houston, TX 77058, United States
c
Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, United States
b
a r t i c l e
i n f o
Article history:
Received 15 December 2011
Revised 21 May 2012
Accepted 23 May 2012
Available online 31 May 2012
Keywords:
Impact processes
Cratering
Saturn, Satellites
Mercury, Surface
Mars, Surface
a b s t r a c t
Near-horizontal planetary impacts result in elliptical craters. The percentage of elliptical craters on a planet can be used to infer the impact angle at which craters become elliptical. Previous surveys of the
Moon, Mars, and Venus indicated that planetary craters become elliptical at more vertical angles than
experimental impacts into a strengthless medium, and this was attributed to a higher ratio of crater
diameter to projectile diameter. Here we determined the percentage of elliptical craters on the mid-sized
saturnian satellites and Mercury, bodies that represent Solar-System extremes of impactor velocity, target density, and target strength. On the saturnian satellites, 7.6% of the craters have ellipticities e (ratio of
major to minor axis) greater than 1.2, but only 0.4% have e > 1.5, and no craters have e > 1.75. On Mercury,
3% of the craters have e > 1.2 and 0.5% have e > 1.5. The mercurian percentages are slightly lower than the
other terrestrial planets, attributable to a higher crater diameter to projectile diameter caused by the
higher impact velocities at Mercury. We attribute the high percentage of moderately elliptical craters
on the saturnian satellites to the rugged target terrain on those bodies. We interpret enhanced crater collapse on the icy surfaces of the saturnian satellites as preventing craters with extremely high ellipticities
like the lunar crater Schiller. Finally, a reexamination of the martian crater population shows its elliptical
crater population to be consistent with the other planets, and we see little evidence for a large population
of craters formed by inward-spiraling moonlets.
Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction
Planetary impacts that occur at the lowest impact angles with
respect to horizontal produce craters that are elliptical in planform
with the long axis oriented in the downrange direction (Moore,
1976; Gault and Wedekind, 1978). A series of experimental hypervelocity impacts into a strengthless medium suggested that kmscale and larger planetary craters should be elliptical if the impact
angle is less than 5° (Gault and Wedekind, 1978). On planetary
surfaces, it is not possible to directly determine the impact angle
from the final crater. However, the critical angle for elliptical crater
formation can be inferred from a survey of the crater population. If
asteroids and comets strike a planet from random directions, then
the percentage P of impactors that strike the surface below an angle h is (Shoemaker, 1962)
2
P ¼ 100 sin h
ð1Þ
⇑ Corresponding author. Fax: +1 907 474 7290.
E-mail addresses: [email protected] (R.R. Herrick), [email protected]
(P.M. Schenk), [email protected] (S.J. Robbins).
0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.
http://dx.doi.org/10.1016/j.icarus.2012.05.027
This formula does not consider any atmospheric filtering effects on
meteoroids. Using Eq. (1), the experimental data of Gault and
Wedekind (1978) indicates that 0.8% of planetary impactors should
strike at a low enough angle to produce an elliptical crater. If crater
size decreases as h becomes more horizontal, as indicated by Gault
and Wedekind’s (1978) data and recent numerical modeling (Elbeshausen et al., 2009), then the percentage of craters that are elliptical
and larger than some chosen diameter D should be even lower than
0.8%.
Schultz and Lutz-Garihan (1982) surveyed the martian crater
population and estimated the percentage of ‘‘grazing impacts’’,
meaning those craters whose appearance resembled laboratory
impacts at <5°. To be classified as a grazing impact the crater had
to satisfy at least two of four criteria: an elliptical shape, ‘‘butterfly’’ ejecta, saddle-shaped rim, and median floor ridge. They globally identified 170 such craters with diameters larger than 3 km.
They performed surveys for three plains regions on Mars and found
that 5% of the craters >5 km in diameter were grazing impacts.
Lunae Planum has 5 ± 0.4% grazing impacts, Syrtis Major Planitia
3 ± 0.5%, and plains near Uranius Tholus 8 ± 0.4%. Messier was
identified as the only grazing impact in this size range in the lunar
maria. Schultz and Lutz-Garihan (1982) concluded that there was
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R.R. Herrick et al. / Icarus 220 (2012) 297–304
Fig. 1. Mosaic of Rhea showing craters used in this study.
Fig. 2. Mosaic of Iapetus showing craters used in this study.
an excess of grazing impacts on Mars relative to the Moon, and
they attributed this to an additional population of moonlets spiraling into Mars.
Bottke et al. (2000) conducted surveys of the crater populations
on the Moon, Venus, and Mars. They defined a crater as ‘‘elliptical’’ if
the ratio of the major axis to the minor axis, the ellipticity e, was
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R.R. Herrick et al. / Icarus 220 (2012) 297–304
299
Fig. 3. Mosaic of Dione showing craters used in this study.
Fig. 4. Mosaic of Tethys showing craters used in this study.
>1.2. In Lunae Planum and Syrtis Major Planitia they found 3.9% and
2.4% elliptical craters, respectively, results for Mars that they considered consistent with Schultz and Lutz-Garihan (1982). Bottke
et al. (2000) also performed crater surveys for the lunar mare and
Venus. Crater diameters for their survey of lunar craters ranged
from 2.3 to 89 km, and they found 50 of 932 craters, or 5.4%, to be
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Fig. 5. Map of Mimas showing craters used in this study.
Fig. 6. Plots of ellipticity versus crater diameter for the saturnian satellites we examined.
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elliptical. To avoid atmospheric effects on the impactor population
for Venus, they examined only craters with D > 20 km, and they
found 4.4% of 303 craters to be elliptical. The overall interpretation
by Bottke et al. (2000) was that the percentages of elliptical craters
on all three planets were similar at 5%, and therefore Mars does
not have an excess of grazing impacts. Surveys of fresh crater populations on the Moon, Venus, and Mars have much higher error bars
(Herrick and Forsberg-Taylor, 2003; Herrick and Hessen, 2006), but
they have results consistent with those of Bottke et al. (2000).
Assuming the impactor populations are striking the planets
from random directions, these percentages suggest that planetary
craters become elliptical for impact angles as high as 12°. Bottke
et al. (2000) hypothesized that the discrepancy with the experimental data was attributable to a higher impactor/crater diameter
ratio on the planets than in the experiments of Gault and Wedekind (1978). Andrews-Hanna and Zuber (2010) developed the Bottke et al. (2000) hypothesis into a geometric model that appears to
explain the discrepancy between experimental and planetary data,
and it predicts the high abundance of elliptical giant basins on the
terrestrial planets. Using the results of experimental impacts and
numerical modeling, Collins et al. (2011) determined an empirical
relationship of the threshold angle for creating an elliptical crater
relative to the impactor/crater diameter ratio. They use the relationship to predict the percentage of elliptical craters on all of
the terrestrial planets over the complete diameter range of observable impact craters.
Here we attempt to expand the range of impact velocities and
target properties for the planetary data by conducting surveys similar to Bottke et al. (2000) for five saturnian moons and Mercury.
The saturnian moons have low surface gravities and a low-density
ice target surface. Mercury has a higher mean impact velocity than
the other terrestrial planets due to its proximity to the Sun. As we
discuss below, our results led us to reexamine martian craters
using a recently developed database that extends down to 1.0 km
diameter (Robbins and Hynek, 2012).
2. Saturnian satellites
We utilized global mosaics from 75 N to 75 S latitude constructed from Cassini flybys for the saturnian moons Mimas,
Tethys, Dione, Rhea, and Iapetus. The global mosaics were
produced with pixel sizes ranging from 400 to 1000 m/pixel,
although in some areas the image resolution was far worse than
this. The mosaics were reprojected into a Mercator projection
(shape-preserving) and then craters were outlined and fit with
an ellipse. Crater dimensions were then corrected for the Mercator
projection. We only outlined craters for which (1) the crater shape
was clearly distinguishable, meaning its planform has mostly not
been superposed by later craters; (2) the target terrain does not appear to have been so rugged as to have clearly distorted the final
crater shape; and (3) the crater has not been noticeably deformed
by subsequent tectonics (mostly rifting on these moons). Although
all of these moons are heavily cratered, only a modest percentage
of the craters were well enough preserved to meet these criteria.
We were only able to obtain reliable outlines for craters with D >
10 km in most of the mosaics. Figs. 1–5 show the outlines of craters
in our saturnian surveys plotted on the global mosaics. Fig. 6 shows
crater diameter versus ellipticity for each of the satellites. Table 1
summarizes the results of our surveys. Overall, we were able to
observe 510 adequately preserved impact craters on the saturnian
satellites, 7.6% of which had e > 1.2 and 0.4% had e > 1.5.
3. Mercury
We conducted a survey of a portion of the surface imaged by the
MESSENGER mission’s first flyby of Mercury. The Narrow Angle
Camera (NAC) Departure Mosaic #1 has a comparable resolution
(550 m/pixel) and viewing geometry to the saturnian mosaics
compiled from Cassini flybys. We conducted a survey for 25° of
longitude from 115 E to 140 E and 75 N to 75 S (Fig. 7). Fig. 8 shows
diameter versus ellipticity for the mercurian craters. Table 1 summarizes the survey results. Of 988 craters observed, 3% had e > 1.2
and 0.5% had e > 1.6.
4. Highly elliptical craters and reexamination of the martian
cratering record
As we surveyed the saturnian satellites, we noticed that there
seemed to be a paucity of extremely elliptical craters like the lunar
craters Schiller and Messier, or the mercurian crater Sveinsdottir in
our survey. We surveyed craters that are predominately complex
craters, and the most elliptical complex craters often have a medial
Table 1
Summary of surveys of elliptical craters.
e > 1.2
e > 1.3
e > 1.5
max e
min D (km)
max D (km)
Iapetus
Dione
Rhea
Tethys
Mimas
Combined
Percentages
Body
718
560
764
530
202
77
73
158
157
45
510
6
8
15
7
3
39
7.6
3
1
2
3
0
9
1.8
1
1
0
0
0
2
0.4
1.74
1.66
1.40
1.44
1.22
1.74
13
10
10
4
7
579
317
431
413
138
Mercury
Percentages
2940
988
30
3.0
6
0.6
5
0.5
1.93
10
280
1737
932
50
5.4
13
4.4
102
504
3.8
27
2.9
–
–
68
179
1.4
14
1.5
2
0.7
49
52
0.4
2.23
2.3
90
20
270
5
8
140
260
From other works
Moona
Percentages
Venusa
Percentages
Marsa
Marsc
Percentagesc
a
b
c
Radius (km)
Observations
6052
303
3397
3397
NA
13,255
Bottke et al. (2000); for Mars we show only those considered ‘‘likely’’ low-angle impacts by the authors.
Graham crater, 110 47 km, as measured in this work.
Robbins and Hynek (2012); preservation states 2, 3, and 4 (all but the most degraded craters) were used.
2.34
3.21
2.23
b
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Fig. 7. Portion of Mercury imaged by MESSENGER Flyby #1 with craters used in this
study highlighted. Note that we used an uncontrolled mosaic that is not coregistered with a later-released global mosaic, so crater locations can be inaccurate by
over 100 km; this does not affect our results.
Fig. 8. Ellipticity versus crater diameter for the area of Mercury surveyed for this
work.
ridge rather than a central peak. If we compare examples of such
craters on Iapetus, Mars, and the Moon (Fig. 9), we can see that
the crater on Iapetus is far less elliptical. We have not comprehensively surveyed medial ridge craters on the terrestrial planets, but
we have not identified any on those bodies with e < 1.8. Johun is
the most elliptical medial ridge crater of the saturnian satellites
that we surveyed, although there are other slightly elliptical craters with much shorter medial ridges. On the Galilean satellites,
so far we have been able to find one other example with a similar
ellipticity (on Callisto, center at 36 N, 6 E, 36 28 km, e = 1.3).
These observations led us to examine not only the total number
of elliptical craters, but also the number of those with high ellipticities, or e > 1.5. Table 1 summarizes the results of the surveys. Due
to the small number of craters we were able to count on a single
satellite, to obtain reliable statistics we combine the counts from
all five saturnian satellites.
Only two of the craters we surveyed on the saturnian satellites
had values of e > 1.5, and the highest ellipticity value is 1.7. Both
high-e craters are featureless in their interiors and more oval
(rounded ends, straight sides) than elliptical (see Fig. 9a). There
is nothing about their morphology that excludes the possibility
that they resulted from two independent impacts, perhaps separated in time, that combined to make a single crater. While Mercury has a lower percentage of overall elliptical craters, 17% of
the elliptical craters unambiguously have values of e > 1.5, with
the ellipticity of Sveinsdottir exceeding 1.9.
This prompted us to take a closer look at the surveys conducted
for Venus, the Moon, and Mars by Bottke et al. (2000). Maximum e
values for the surveys conducted on the Moon and Venus, the latter
being global, were 2.23 and 2.33, respectively. On Venus 15% of the
craters that were elliptical had e > 1.5 (a total of two craters with
diameter >20 km), while on the Moon 28% of the elliptical craters
pffiffiffi
had e > 1.5. Within error bars of n observations, Venus, the Moon,
and Mercury have similar ratios of elliptical to highly elliptical
craters.
The results from Bottke et al. (2000) for Mars are strikingly different. Of their elliptical craters, nearly half (49 of 102 ‘‘likely’’
elliptical craters) have e > 1.5, 10% have e > 2.0, and a few craters
have e > 3. However, a recent global survey of martian craters
compiled by one of us (Robbins and Hynek, 2012) shows different
results. In that survey, craters are allowed to be partially superposed by other craters and occur on rugged preexisting topography. However, the craters are classified into four different
preservation states, with preservation state being affected by
superposition by other craters. In Table 1 we show results from
the Robbins and Hynek (2012) survey for preservation states 2, 3,
and 4 in that survey, which includes all craters with a preserved
rim; this is most similar to the survey conditions for the surveys
we conducted and the other surveys of Bottke et al. (2000). Considering craters with D > 8 km, we observe 52 craters with e > 1.5,
similar to the near-global (between latitudes ±47.5°) results from
Bottke et al. (2000). However, we show over 500 craters with
e > 1.2, far more than Bottke et al. (2000) observed. Thus, overall
we see that about 4% of the craters are elliptical, but of the elliptical craters only 10% have e > 1.5, values more consistent with the
other surveys.
We compared in detail the observations from Bottke et al.
(2000) with those of Robbins and Hynek (2012). In a cataloging error, about a dozen of the ‘‘Likely’’ craters, mostly with e > 1.5, were
double counted, apparently because Bottke et al. (2000) drew their
survey from previous surveys by Barlow (1988) and Schultz and
Lutz-Garihan (1982). However, the main discrepancy seems to be
in the methodology employed by those previous surveys that Bottke et al. (2000) drew from. Those surveys did not fit an ellipse to
every crater or measure a semimajor and semiminor for each crater, but instead only noted ellipticity for obviously elliptical craters. Thus, the previous works captured the well-preserved and
most elliptical oblique impacts, but missed many craters that are
moderately elliptical.
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Fig. 9. Examples of medial ridge craters on Iapetus, Mars, and the Moon. The crater on Iapetus is far less elliptical than its counterparts on the terrestrial planets. (a) Johun
crater on Iapetus (12.4 N, 83.4 W), 70 59 km, e = 1.2; also shown 50 km to the SE is the most elliptical crater in our survey of the saturnian satellites, 40 23 km, e = 1.7. (b)
Rahe crater on Mars (25.3 N, 97.6 W), 35 18 km, e = 1.9. (c) Schiller crater on the Moon (51.8 S, 40.0 W), 179 71 km, e = 2.5.
We also looked at the orientations of the craters with e > 1.5.
Assuming no polar wander, if a significant fraction of those craters
resulted from inward-spiraling moonlets, then we might expect
there to be a concentration of highly elliptical craters near the
equator, and we would expect that elliptical craters at near-equatorial latitudes would be preferentially East–West in orientation.
Neither of these things was observed.
5. Predictions from modeling
Collins et al. (2011) recently explored the Bottke et al. (2000)
hypothesis that the threshold angle ht (the impact angle below
which a crater is elliptical) is dependent on the ratio of projectile
diameter L to crater diameter. Using results from numerical simulations and experimental impacts, they derived an empirical formula for the threshold angle’s dependence on this ratio. They
then use the formula to predict how the percentage of elliptical
craters should vary with planetary body and crater size. We do
not wish to replicate their work; we provide here a simplified version of their findings in order to expand their predictions to the
saturnian satellites (they considered only the terrestrial planets).
Bottke et al. (2000) hypothesized that the threshold angle is
dependent on the path length of the impactor in the ground relative to the final crater size. For a nonvertical impact, the horizontal
component of the impactor path can be thought of as a line source
of kinetic energy release, and if the length of this line exceeds a
threshold relative to crater diameter, then an elliptical crater is
formed. The results of Collins et al. (2011) empirically support
the idea that impactor diameter can be used as a proxy for this
path length. Furthermore, Collins et al. (2011) were able to fit a
simple function over a wide range of physical conditions that relates the threshold angle to the ratio of the projectile diameter to
the crater diameter in a vertical impact Dv,
0:52
1:85
Dm
Dm
ht ¼ 45
þ 77
L
L
ð2Þ
If one then assumes a size–frequency distribution of impactors that
includes their impact velocities and angles, and a scaling law for
crater diameter, then one can estimate the percentage of elliptical
craters with size. Collins et al. (2011) do this for the terrestrial
planets, and we do not fully replicate their efforts here. Instead,
we simply take a scaling law and calculate how ht changes with
planetary body for a fixed transient crater diameter of 20 km.
Following Collins et al. (2011), using a scaling law for a strengthless
medium from Holsapple and Housen (2007),
Dm
V2
¼ 1:17
L
gL
!:22 :31
d
ð3Þ
q
where g is surface gravity, V is impactor velocity, q is target density,
and d is impactor density. If we assume that the inner planets are
dominated by asteroidal impactors and that the saturnian satellites
are dominated by cometary/icy impactors, then the second term in
Eq. (3) is 1.0. In Table 2 we show assumed values for g and V, and
Table 2
Predictions of the angular threshold ht, and percentage of elliptical craters Pcalc, for craters at D = 20 km, based on approach of Collins et al. (2011).
a
b
c
Planet
V (km/s)
g (m/s2)
ht (degrees from
horizontal)
Pcalc = 100 (sin2ht)
Mercury
Venus
Moon
Mars
Iapetus
Dione
Rhea
Tethys
Mimas
Mean of saturnian satellites
weighted by # observations
30a
19a
13a
10b
6c
19c
16c
21c
27c
3.7
8.9
1.6
3.7
.24
.22
.29
.19
.065
10
14
12
15
11
8
9
7
6
3.4
6.1
4.4
7.0
3.9
1.9
2.3
1.7
1.0
2.2
Bottke et al. (1994).
Ivanov (2001).
Zahnle et al. (2003).
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calculate ht and the resulting percentage of elliptical craters Pcalc
based on Eq. (1). For the terrestrial planets we use the same average
impact velocities as Collins et al. (2011), which are drawn from Bottke et al. (1994) and Ivanov (2001), and for the saturnian satellites
we use velocity estimates from Zahnle et al. (2003). We note that ht
in Eq. (2) is where e > 1.1, which should be a more vertical angle
than the threshold angle for e > 1.2, and thus should artificially inflate Pcalc relative to observations in Table 1. However, Pcalc does
not account for a size dependence of crater diameter on impact angle, which would lower Pcalc because low-angle impacts get put into
smaller diameter bins in a crater size–frequency distribution where
there are more craters in a smaller diameter bin. Also, the calculations in Table 2 do not account for any effects that complex crater
formation may have on crater ellipticity.
Comparisons of the observations to the predictions in Table 2
are fraught with errors, not the least of which is that the observations were made by different observers on different planetary surfaces with slightly different methodologies. We also note that the
constraints on impact velocity are fairly minimal, but the overall
trends are probably correct (higher closer to the Sun and closer
to Saturn). At best, we can say that the observations are generally
consistent with predictions, and somewhat smaller percentages of
elliptical craters are predicted on Mercury and the saturnian satellites than on the Moon, Venus, and Mars.
6. Discussion and conclusions
Table 2 predicts that the lowest percentage of elliptical craters
should exist on the saturnian satellites, but the observations show
them with higher percentages of craters with e > 1.2 than the terrestrial planets. Even though we did our best to weed out craters
clearly distorted by impact into rugged terrain, there are almost
no truly smooth target surfaces on the moons of Saturn. Furthermore, the mosaics we used to analyze the saturnian satellites often
involve reprojection, but not orthorectification, of off-nadir views.
Without full orthorectification, even circular craters in rugged
topography may falsely appear elliptical in a reprojected off-nadir
image. Our favored interpretation is that the very rugged terrains
of the icy satellites are the primary reason for those objects having
an unusually high number of craters with e > 1.2. That the numbers
for e > 1.3 on the saturnian satellites are more consistent with the
other bodies suggests the validity of our interpretation. Another
possibility is that Eqs. (2) and (3) are simply invalid for the saturnian satellites, although we do not see any obvious reason why this
would be the case. A final possibility is that there is a large population of very slow impactors from within in the saturnian system
impacting at 1–2 km/s, so that ht is large enough to significantly increase the percentage of elliptical craters.
We think that enhanced collapse due to lower crustal strengths
causes a complete lack of highly elliptical craters on the icy satellites. If we envision rim collapse during the modification stage of
crater formation expanding the crater by a fixed distance in all
directions, then increased collapse decreases ellipticity (i.e.,
(b + x)/(a + x) < b/a, where b is semimajor axis and a is semiminor
axis). This is manifested by a lower ellipticity associated with the
medial ridge craters observed on icy satellites compared to medial
ridge craters on the terrestrial planets. We note, however, that the
conclusion of enhanced collapse is based on observations involving
a small number of craters.
The slightly lower percentage of elliptical craters on Mercury
relative to the other terrestrial planets is consistent with expectations based on ellipticity being dependent on the ratio of crater
diameter to projectile diameter. A reexamination of the martian
cratering record reaffirms a lack of evidence for a significant number of craters on Mars being generated by inward-spiraling
moonlets.
Acknowledgments
Analysis of the saturnian satellites by RRH and PMS was funded
by a NASA CDAP grant. Analysis of mercurian craters was funded
by a PMDAP grant to RRH. We thank Geoff Collins for providing a
code to fit an ellipse to a set of points. We thank Jeff Andrews-Hanna and Bill Bottke for thorough and thoughtful reviews of the
manuscript.
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