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

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

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 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) "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

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

Collision probability (%) Mercury Venus Earth Mars Sun (1) 1.01 6.11 4.42 0.71 66.0 (2) 0.68 5.06 3.17 0.64 71.6 (3) 1.38 4.56 2.57 0.54 73.1 (4) 0.57 3.24 2.90 0.88 47.3 (5) 0.37 2.90 2.33 0.94 52.8 (6) 0.84 5.00 3.24 0.20 75.4 (7) 0.97 3.83 2.96 0.94 65.5 Probability: PVenus > PEarth , PMercury > PMars

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)

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] vy Fraction y [rI] [km/s]

Typical orbits in Earth's rI aMoon x

Collisions on the Earth/Moon Pcol,E Pcol,M Encounters Col (E) Col (M) Pcol,E Pcol,M (1) 1142636(x103) 87486 3708 2.9% 0.12% 23.6 (2) 1176793(x103) 101766 4160 3.4% 0.14% 24.5 (3) 982652(x103) 81359 3618 2.7% 0.12% 22.5 (4) 777056(x103) 72613 2801 2.4% 0.09% 25.9 (5) 648519(x103) 58647 2388 2.0% 0.08% 24.6 (6) 998867(x103) 82014 3501 2.7% 0.12% 23.4 (7) 758500(x103) 66163 2840 2.2% 0.10% 23.3 Pcol,E Pcol,M = 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) Time [Myr]

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

Asymmetric collisions on the Moon z y x x [RMoon] Fraction z y [RMoon] [RMoon]

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

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