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Takashi Ito (CfCA/NAOJ, Tokyo)
Renu Malhotra (LPL/U.Arizona)
keywords: Asteroid dynamics, impacts on the Moon
Origin of cratering objects
is not very well known yet
What created craters? When?
How did impactors reach here?
(restricted) N-body model
of long-term (108-109 yr)
small body impact flux
with high accuracy
We need a lot of particles
Low collision probability to the Moon
30000 resonant asteroids yield
g 10-20 collisions on the Moon over 109 yrs
Multiply test particles ("clones")
at the activity sphere of the Earth
30K particles, ~107 encounters
"cloning" x1000
lunar orbit
30M particles, ~1010 encounters
~104 impacts on Moon
Better estimate of collision probability
Better comparison with crater records
Near-Earth orbital distribution of asteroid
fragments coming from the n6 resonance
Takashi Ito1
Renu Malhotra2
1Center
for Computational Astrophysics,
National Astronomical Observatory of Japan, Tokyo
2Lunar
& Planetary Laboratory,
The University of Arizona, Tucson, AZ, USA
Motivation
Objectives
 The late heavy bombardment on
the Moon (~4 Ga): Cause unknown
 Asteroid shower? Comet shower?
 Dynamics of resonant asteroids
 Disruption at n6 g many fragments
 Collision probability on planets/Moon
 Comparison with the crater records
What's new
 Better statistics with more particles
 102-103 g >104 (for several 108 years)
 More particles around Earth (~1010)
 Direct collisional history on the Moon
Initial positions of the fragments
 Assumption Isotropic & equal-velocity disruptions
 Initial ejection velocity: v0= 0.1, 0.2 km/s
v0 of some known asteroid families (Zappala et al. 1996)
(7)
a [AU]
(5)
(6)
(1)
(2)
• "WH" symplectic map
• dt = 8 days, T ~ 100 Myr
• 8 planets (Mercury g Neptune)
n6 (i~0)
(3)
(4)
Eccentricity
• Asteroid fragment
- 3,000-6,000 particles / case
- 7 initial positions
- Total ~30,000 test particles
around n6
56%
Typical orbital evolution
a
Close encounters with planets
g Change a, q, Q
g Remove fragments from the resonance
Kozai oscillation
- Partly causes many "sun-grazers"
- Rapid collisions with the Sun
q
w
Q
Collision probability (%)
Mercury Venus Earth
(1)
(2)
(3)
(4)
(5)
(6)
(7)
1.01
0.68
1.38
0.57
0.37
0.84
0.97
6.11
5.06
4.56
3.24
2.90
5.00
3.83
4.42
3.17
2.57
2.90
2.33
3.24
2.96
Mars
Sun
0.71
0.64
0.54
0.88
0.94
0.20
0.94
66.0
71.6
73.1
47.3
52.8
75.4
65.5
Probability: PVenus > PEarth , PMercury > PMars
More particles for the Moon
~3,000 test particles
g ~100 collisions on the Earth
Earth, case (6)
g a few collisions on the Moon
g Statistically no meaning?
But: many more encounters
at the Earth's activity sphere
(rI ~ 144 REarth)
rI
g ~106 close encounters
aMoon
g Good to make orbital
distribution function
f (a,e,i, ... ; t)
More particles for the Moon
Generate many particles ("clones") from
the orbital distribution function f (a,e,i, ... ; t)
30,000 particles
n 107 encounters
x 1,000
30,000,000 clones
n 1010 encounters
rI
Orbital integration of
Earth + Moon + Sun + 1010 "cloned" asteroids
(No other planet; with lunar gravity)
Statistics at Earth's rI
vx
y
z
x
[km/s]
Fraction
vy
y
[rI]
[km/s]
y
Typical orbits in Earth's rI
aMoon
rI
x
Collisions on the Earth/Moon
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Encounters
Col (E) Col (M) Pcol,E Pcol,M
1142636(x103)
1176793(x103)
982652(x103)
777056(x103)
648519(x103)
998867(x103)
758500(x103)
87486
101766
81359
72613
58647
82014
66163
Pcol,E
Pcol,M
3708
4160
3618
2801
2388
3501
2840
2.9%
3.4%
2.7%
2.4%
2.0%
2.7%
2.2%
0.12%
0.14%
0.12%
0.09%
0.08%
0.12%
0.10%
Pcol,E
Pcol,M
23.6
24.5
22.5
25.9
24.6
23.4
23.3
= 23-26 f Close to the ratio of Earth/Moon
collisional cross sections (~21)
Impact history
Earth, case (2)
Moon, case (7)
Moon, case (2)
Moon, case (5)
Time [Myr]
Impact velocity
Impact angle
Case (2)
Earth
Moon
Fraction
[km/s]
[deg]
Case (5)
Earth
Moon
[km/s]
[deg]
Asymmetric collisions on the Moon
z
y
x
Fraction
x
[RMoon]
y
z
[RMoon]
[RMoon]
Comparison with crater distribution
apex
Moon's orbital and rotational
motion is synchronized
More craters at apex
gConfirmed by recent geological
discovery (Morota & Furumoto 2003)
1.2
relative crater density
Observation
This study
Our numerical result
 Geological record agree well
Asymmetric distribution of craters
and impactors
The model probably reproduces
vMoon/vimpactors well (by chance?)
Dcrater > 10 km
0.4
0
angle from apex
180
Lunar crater impactors have been
asteroidal, with moderate vimpactors
(cf. Comets have much larger vimpactors)
Summary
 Improved statistics of orbital evolution
of asteroid fragments from n6
 Improved impact probability on planets
Venus: ~5%, Earth: ~3%
 Impact probability on the Moon
~ 0.1%
 Asymmetric distribution of lunar craters
Matches well with observations
g Asteroidal origin of projectiles is justified
 Future work: estimate of comet impacts