On the Character and Consequences of Large Impacts in the Late Stage of Terrestrial Planet Formation

Abstract We perform three-dimensional N-body integrations of the final stages of terrestrial planet formation. We report the results of 10 simulations beginning with 22–50 initial planetary embryos spanning the range 0.5–1.5 AU, each with an initial mass of 0.04–0.13M⊕. Collisions are treated as inelastic mergers. We follow the evolution of each system for 2×108 years at which time a few terrestrial type planets remain. On average, our simulations produced two planets larger than 0.5M⊕ in the terrestrial region (1 simulation with one m≥0.5M⊕ planet, 8 simulations with two m≥0.5M⊕ planets, and 1 simulation with three m≥0.5M⊕ planets). These Earth-like planets have eccentricities and orbital spacing considerably larger than the terrestrial planets of comparable mass (e.g., Earth and Venus). We also examine the angular momentum contributions of each collision to the final spin angular momentum of a planet, with an emphasis on the type of impact which is believed to have triggered the formation of the Earth's Moon. There was an average of two impacts per simulation that contributed more angular momentum to a planet than is currently present in the Earth/Moon system. We determine the spin angular momentum states of the growing planets by summing the contributions from each collisional encounter. Our results show that the spin angular momentum states of the final planets are generally the result of contributions made by the last few large impacts. Our results suggest that the current angular momentum of the Earth/Moon system may be the result of more than one large impact rather than a single impact. Further, upon suffering their first collision, the planetary embryos in our simulations are spinning rapidly throughout the final accretion of the planets, suggesting the proto-Earth may have been rotating rapidly prior to the Moon-forming impact event.

[1]  V. Safronov,et al.  Evolution of the protoplanetary cloud and formation of the earth and the planets , 1972 .

[2]  S. Alexander,et al.  N-Body Simulations of Late Stage Planetary Formation with a Simple Fragmentation Model , 1998 .

[3]  George W. Wetherill,et al.  The Formation and Habitability of Extra-Solar Planets , 1996 .

[4]  K. Ohtsuki,et al.  PLANETARY ROTATION BY ACCRETION OF PLANETESIMALS WITH NONUNIFORM SPATIAL DISTRIBUTION FORMED BY THE PLANET'S GRAVITATIONAL PERTURBATION , 1998 .

[5]  R. Canup,et al.  Accretion of the Moon from an Impact-Generated Disk , 1995 .

[6]  G. Wetherill,et al.  Formation of planetary embryos: effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination. , 1993, Icarus.

[7]  L. Taylor,et al.  Age and Origin of the Moon , 1997 .

[8]  D. Davis,et al.  Accretional Evolution of a Planetesimal Swarm , 1997 .

[9]  S. Tremaine,et al.  Why Does the Earth Spin Forward? , 1993, Science.

[10]  J. Lissauer,et al.  Growth of planets from planetesimals , 1991 .

[11]  H. J. Melosh,et al.  Impact Fragmentation: From the Laboratory to Asteroids☆ , 1998 .

[12]  J. Wisdom,et al.  Symplectic maps for the N-body problem. , 1991 .

[13]  G. Wetherill,et al.  Occurrence of Giant Impacts During the Growth of the Terrestrial Planets , 1985, Science.

[14]  G. Wetherill.  An alternative model for the formation of the asteroids , 1992 .

[15]  Harold F. Levison,et al.  A Multiple Time Step Symplectic Algorithm for Integrating Close Encounters , 1998 .

[16]  W. Benz,et al.  Giant impacts on a primitive Uranus , 1992 .

[17]  William K. Hartmann,et al.  Planetesimals to planets: Numerical simulation of collisional evolution , 1978 .

[18]  S. Ida,et al.  Distribution of Planetesimals around a Protoplanet in the Nebula Gas , 1996 .

[19]  W. Ward.  Climatic variations on Mars: 1. Astronomical theory of insolation , 1974 .

[20]  J. Laskar,et al.  The chaotic obliquity of the planets , 1993, Nature.

[21]  H. Melosh,et al.  ASTEROIDS : SHATTERED BUT NOT DISPERSED , 1997 .

[22]  J. Candy,et al.  Symplectic integrators for long-term integrations in celestial mechanics , 1991 .

[23]  George W. Wetherill,et al.  Evolution of planetesimal velocities , 1988 .

[24]  A. Cameron,et al.  The Giant Impact Occurred During Earth Accretion , 1998 .

[25]  Willy Benz,et al.  Tidal disruption of inviscid planetesimals , 1991 .

[26]  George W. Wetherill,et al.  Accumulation of a swarm of small planetesimals , 1989 .

[27]  Eiichiro Kokubo,et al.  Oligarchic growth of protoplanets , 1996 .

[28]  S. Aarseth,et al.  N-body simulations of planetary formation , 1990, Monthly Notices of the Royal Astronomical Society.

[29]  S. Aarseth,et al.  A numerical simulation of the formation of the terrestrial planets , 1986 .

[30]  A. G. W. Cameron,et al.  The origin of the moon and the single-impact hypothesis III. , 1991 .

[31]  J. Lunine,et al.  O the Origin of Pluto, Charon, and the Pluto-Charon Binary , 1997 .

[32]  Junichiro Makino,et al.  N-Body simulation of gravitational interaction between planetesimals and a protoplanet. I : velocity distribution of planetesimals , 1992 .

[33]  H. Melosh,et al.  The origin of the moon and the single-impact hypothesis III. , 1991, Icarus.

[34]  K. Hourigan,et al.  On the Formation of Planetesimals , 1979, Publications of the Astronomical Society of Australia.

[35]  J. Makino,et al.  N-body simulation of gravitational interaction between planetesimals and a protoplanet II. Dynamical friction , 1992 .

[36]  S. Ida,et al.  Lunar accretion from an impact-generated disk , 1997, Nature.

[37]  J. Wisdom,et al.  The Chaotic Obliquity of Mars , 1993, Science.

[38]  Alfred Edward Ringwood,et al.  Origin of the Earth and Moon , 1979 .

[39]  P. Goldreich,et al.  The formation of planetesimals. , 1973 .

[40]  John E. Chambers,et al.  Making the Terrestrial Planets: N-Body Integrations of Planetary Embryos in Three Dimensions , 1998 .

[41]  G. Wetherill,et al.  Provenance of the terrestrial planets. , 1994, Geochimica et cosmochimica acta.

[42]  S. Weidenschilling,et al.  Formation of planetesimals in the solar nebula , 1993 .

[43]  Francesco Marzari,et al.  Accretional evolution of a planetesimal swarm: 1. A new simulation , 1991 .

[44]  W. R. Ward.  Large-Scale Variations in the Obliquity of Mars , 1973, Science.

[45]  William K. Hartmann,et al.  Satellite-Sized Planetesimals and Lunar Origin , 1975 .

[46]  G. Wetherill.  Accumulation of the terrestrial planets and implications concerning lunar origin , 1986 .

[47]  P. Goldreich,et al.  The history of the lunar orbit , 1966 .

[48]  Luke Dones,et al.  On the Origin of Planetary Spins , 1993 .

[49]  Willy Benz,et al.  Collisional stripping of Mercury's mantle , 1988 .

[50]  William R. Ward,et al.  The Origin of the Moon , 1976 .

[51]  E. Kokubo,et al.  ON RUNAWAY GROWTH OF PLANETESIMALS , 1996 .

[52]  S. Love,et al.  Catastrophic Impacts on Gravity Dominated Asteroids , 1996 .

[53]  S. Ida,et al.  Distribution of planetesimals around a protoplanet in the nebular gas. II. Numerical simulations , 1997 .

[54]  Takashi Ito,et al.  Stability and Instability of the Terrestrial Protoplanet System and Their Possible Roles in the Final Stage of Planet Formation , 1999 .