1. 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 ( yr)
small body impact flux
with high accuracy

2. We need a lot of particles
Low collision probability to the Moon
30000 resonant asteroids yield
g 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

3. Takashi Ito1 Renu Malhotra2
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

4. Motivation Objectives What's new 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
g >104 (for several 108 years)
More particles around Earth (~1010)
Direct collisional history on the Moon

5. 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)
"WH" symplectic map
dt = 8 days, T ~ 100 Myr
8 planets (Mercury g Neptune)
Asteroid fragment
(7)
(5)
(6)
a [AU]
n6 (i~0)
3,000-6,000 particles / case
7 initial positions
Total ~30,000 test particles
around n6
(3)
(2)
(1)
(4)
Eccentricity

6. Typical orbital evolution
56% a
Close encounters with planets
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

7. Collision probability (%)
Mercury Venus Earth Mars Sun
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Probability: PVenus > PEarth , PMercury > PMars

8. More particles for the Moon
~3,000 test particles
g ~100 collisions on the Earth
a few collisions on the Moon
Statistically no meaning?
Earth, case (6) rI
But: many more encounters
at the Earth's activity sphere
(rI ~ 144 REarth)
~106 close encounters
aMoon
Good to make orbital
distribution function
f (a,e,i, ... ; t)

9. 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 "cloned" asteroids
(No other planet; with lunar gravity)

10. Statistics at Earth's rIvx y z x
[km/s] vy
Fraction y
[rI]
[km/s]

11. Typical orbits in Earth's rI
aMoon x

12. Collisions on the Earth/Moon
Pcol,E
Pcol,M
Encounters Col (E) Col (M) Pcol,E Pcol,M
(1) (x103) % 0.12% 23.6
(2) (x103) % 0.14% 24.5
(3) (x103) % 0.12% 22.5
(4) (x103) % 0.09% 25.9
(5) (x103) % 0.08% 24.6
(6) (x103) % 0.12% 23.4
(7) (x103) % 0.10% 23.3
Pcol,E
Pcol,M
= f Close to the ratio of Earth/Moon
collisional cross sections (~21)

13. Impact history Earth, case (2) Moon, case (7) Moon, case (2)
Time [Myr]

14. Impact velocity Impact angle Case (2) Case (5) Fraction Earth Moon
[km/s]
[deg]
Fraction
Case (5)
Earth
Moon
[km/s]
[deg]

15. Asymmetric collisions on the Moonz y x x
[RMoon]
Fraction z y
[RMoon]
[RMoon]

16. Comparison with crater distribution
Moon's orbital and rotational
motion is synchronized
apex
More craters at apex
Confirmed by recent geological
discovery (Morota & Furumoto 2003)
1.2
Our numerical result
Geological record
agree well
Asymmetric distribution of craters
and impactors
The model probably reproduces
vMoon/vimpactors well (by chance?)
Lunar crater impactors have been
asteroidal, with moderate vimpactors
(cf. Comets have much larger vimpactors)
Observation
This study
relative crater density
Dcrater > 10 km
0.4
angle from apex
180

17. Summary Improved statistics of orbital evolution
of asteroid fragments from n6
Improved impact probability on planets
Impact probability on the Moon
Asymmetric distribution of lunar craters
Future work: estimate of comet impacts
Venus: ~5%, Earth: ~3%
~ 0.1%
Matches well with observations
g Asteroidal origin of projectiles is justified