1
Surface Chronology of Phobos – The Age of
Phobos and its Largest Crater Stickney
3MS³ Symposium,
Moscow, 08.-12.10.2012
N. Schmedemann1, G. Michael1, B. A. Ivanov2, J. Murray3 and G. Neukum1,
1Institute of Geological Sciences, Freie Universität Berlin, Berlin, Germany;
2Institute of Dynamics of Geospheres, Moscow, Russia; 3Department of Earth
Sciences, Open University, Milton Keynes, UK.
2
Characteristics & Origin of Phobos
• shape, spectral characteristics and density similar to primitive (C), D or T-type
asteroids (Jones et al., 1990; Giuranna et al., 2011)
• Inside Mars synchronous orbit
• Instable orbit and potential disintegration/crash within 30-50 Ma (Burns, 1978)
• Tidal interactions may have lowered the orbit to current state  higher orbit in the
past but likely always inside Mars synchronous orbit
• Theories on Phobos’ origin include:
 capture of an asteroid
 in-situ formation with Mars
 coalesced debris from Martian ejected material
• Irregular shape indicates major collision(s)
• Several sets of grooves with yet unexplained origin
3
Two Cases of Phobos’ Chronology
• End-member cases of Phobos’ history
 Case A: Phobos was in its current orbit since its formation
o Average projectile impact velocities are converted form Mars to Phobos’ orbit
o Average impact rate equals Martian impact rate – corrected for different
crater scaling
 Case B: Phobos is a recently captured Main Belt asteroid
o Average projectile impact velocities equals average Main Belt impact
velocities
o Average impact rate equals average Main Belt impact rates
4
The Lunar Chronology
Lunar Chronology Function
•
derived from radioisotopic
measurements of lunar rock
samples and measurements of
the cratering record at the Apollo
landing sites
Neukum (1983)
5
Scaling Laws – Conversion of Projectile to
Crater Diameters
𝐷𝑡
𝐷𝑃
𝛿
𝜌
0.43
(𝑣𝑠𝑖𝑛𝛼)0.55
=
1.21
[ 𝐷𝑠𝑔 + 𝐷𝑡
Ivanov (2001; updated 2011)
𝑔]0.28
If D < Dsimple to complex transition then Dt ~ D
If D > Dsimple to complex transition then
D
Dt
DP
G
δ
ρ
v
α
Dsg
𝐷𝑡
𝐷𝑠𝑖𝑚𝑝𝑙𝑒 𝑡𝑜 𝑐𝑜𝑚𝑝𝑙𝑒𝑥 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 0.15
– observed crater diameter
– transient crater diameter
– impactor diameter
– gravity acceleration of target body
– projectile density
– target density
– impact velocity
– impact angle
– strength to gravity transition crater diameter
(Dt>>Dsg -> gravity regime; Dt<<Dsg -> stregth regime)
=D
6
Scaling Laws – Conversion of Projectile to
Crater Diameters
Moon
Phobos (Case A)
Phobos Asteroid
Case (Case B)
Target Density (g/cm³)
2.5
(est. surface
regolith)
1.9
(Willner et al.,
2010)
1.9
(Willner et al., 2010)
Projectile Density (g/cm³)
2.5
2.5
2.5
Impact Velocity (km/s)
18
8.5
5
Impact Angle (most probable case after
Gilbert, 1893)
45
45
Surface Gravity (m/s²)
1.62
Diameter Strength to Gravity Transition
(km)
0.3
Diameter Simple to Complex (km)
15
45
6*10-3
6*10-3
(Willner et al.,
(Willner et al., 2010)
2010)
1000 (all craters are 1000 (all craters are
in the strength
in the strength
regime)
regime)
1000 (all craters are 1000 (all craters are
simple)
simple)
7
Summary Production & Chronology
Functions
Resulting production and chronology functions for cases A and B
8
Measurement Areas
HRSC Basemap: Wählisch et al. (2010)
9
Measurement Areas
Average Surface to the West of Stickney: N-S grooves stratigraphically above EW grooves
10
Measurement Areas
Area S1: Interior of Stickney
11
Measurement Areas
Area S2: SRC image of Interior of Stickney; N-S grooves stratigraphically
below solitary E-W groove
12
Randomness Analysis
Analysis according to Michael et al. (2012)
13
Surface Ages
Age of Phobos
Cumulative crater plots of average area west of Stickney
Age of Phobos equals last global resurfacing event (break-up of parent body)
14
Surface Ages
Age of Stickney
Cumulative crater plots of S1 area inside Stickney
15
Surface Ages
Cumulative crater plots of S2 area inside Stickney
16
Surface Ages
Comparison of cumulative crater plots of
average and S1 area
Stratigraphic relations suggest a formation age of E-W grooves of 3.8 – 3.85 Ga
17
Apex-/Antapex Asymmetry
Large (old) craters show apex-/antapex ratio of ~1.5  Phobos is not a recently captured
object. Form recent orbit a factor 4 is expected according to Morota et al. (2008).
18
Conclusion
•
Production and chronology function were derived for two end-member cases of Phobos’ evolution
 Case A: Phobos was always in its current orbit
 Case B: Phobos is a recently recently captured MB asteroid
• Oldest surface age 4.3-4.4 Ga/ ~3.7-3.8 Ga  last global resurfacing/break-up of
Phobos parent
• Age of Stickney: ~4.2 Ga/ ~3.5 Ga
•
Surface ages show multiple resurfacing events, probably connected to groove formation
•
Groove formation appears to be ancient but very young ages can’t be resolved based on current
imaging data
•
Stratigraphic relationships indicate similar formation age of E-W striking grooves in at least two areas
around 3.8-3.85 Ga/ 2.9-3.1 Ga
•
Apex-/antapex asymmetry of large/old craters indicate long cratering history in orbit about Mars
 Ratio (1.5) is more than a factor of two less than the expected value (4.1) from current orbit 
e.g. reorientation event(s with more frequent current position)
19
Questions
20
Crater Production Function
• Lunar production function is used as base line, because the main impactor
source is the same on the Moon, Phobos and Main Belt asteroids
• Case A
 𝑣𝑖𝑚𝑝𝑃 =




2
2
2
𝑣𝑖𝑚𝑝𝑀
− 𝑣𝑒𝑠𝑐𝑀
+ 𝑣𝑒𝑠𝑐𝑃
vimpM = 9.4 km/s (Ivanov, 2008)
vescM = 5 km/s
vescP = 3 km/s
vimpP = 8.5 km/s
Velocity distribution of
682 Main Belt asteroids
D>50 km
• Case B
 Average impact velocities among
Main Belt asteroids are calculated
following (Bottke et al., 1994)
 vimpP ~ 5 km/s
Bottke et al. (1994)
21
Chronology Function
• Lunar chronology is used as base line, because the main impactor source is the same
on the Moon, Phobos and Main Belt asteroids
• Case A
 Impact probability of Mars (Ivanov,
2001)  0.45 x lunar impact rate
 Correction for different crater
scaling between Mars and Phobos
 0.84 x lunar impact rate (same
projectile is forming larger craters
on Phobos than on Mars or the
same crater size is achieved by
smaller projectiles on Phobos)
22
Chronology Function
• Lunar chronology is used as base line, because
the main impactor source is the same on the
Moon, Phobos and Main Belt asteroids
1 Ga
Isochrones
• Case A
 Impact rate at Mars (Ivanov, 2001)  0.45 x
lunar impact rate
 Correction for different crater scaling between
Mars and Phobos  0.84 x lunar impact rate
(same projectile is forming larger craters on
Phobos than on Mars or the same crater size is
achieved by smaller projectiles on Phobos)
1 Ga isochrones for Phobos and Mars
23
Chronology Function
• Lunar chronology is used as base line, because the main impactor source is the
same on the Moon, Phobos and Main Belt asteroids
• Case B
 Average impact probabilities among Main Belt Asteroids are calculated following
(Bottke et al., 1994)  Pi ~ 2.9*10-18 km-2/a  2.9*10-9 km-2/Ga
 Conversion from intrinsic impact probability to chronology:
f=Pinir2mean
(O’Brien and Greenberg, 2005)
f: impact frequency forming craters ≥ 1 km/Ga
Pi: intrinsic impact probability
ni: number of projectiles forming craters ≥ 1 km
o observed number of Main Belt asteroids ≥ 10 km (obs. limit): 9554
o crater size on Phobos as average Main Belt asteroid from 10 km projectiles: 104.5 km
o correction factor for frequency of 104.5 km craters to 1 km craters based on Phobos production
function as MBA: 4*103
o  ni: 3.8*107
r: mean radius of target body scaled to unit area = (11 km)²/4π*(11 km)²
 f ~ 9*10-3
 𝑁𝑐𝑢𝑚 𝐷 ≥ 1 𝑘𝑚 = 𝑃1 𝑒 𝑃2𝑡 − 1 + 𝑃3 𝑡
(Neukum, 1983)