## Abstract

We have investigated numerically the orbital instability of a protoplanet system while taking account of the gasdrag force due to the solar nebula. In the present work, we considered an equally spaced five-protoplanet (with the same mass of 1 x 10^{-7} M_{⊙} ) system, in which their initial orbits are coplanar and circular, and assumed that the gas-drag force is proportional to the square of the relative velocity between the gas and a protoplanet. We first reexamined and confirmed that, under a gas-free condition, log_{10} T_{inst} can be approximately written as a linear function of the initial orbital separation distance, Δã_{0}, where T_{inst} is the time of the orbital instability (i.e., the time of the first orbital crossing between any two protoplanets). Next, we investigated the instability time under the gas-drag effect T^{gas}_{inst} and found that T^{gas}_{inst} suddenly becomes large compared with T_{inst}, when Δã_{0} is larger than a certain critical separation distance, (Δã_{0})_{crit}. Furthermore, we showed that (Δã_{0})_{crit} can be described semi-analytically as a function of the gaseous density. From a function extrapolated with a density in the minimum mass nebula model, we estimated (Δã_{0})_{crit} in the nebula as being about 10 Hill radius at 1 AU.

Original language | English |
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Pages (from-to) | 321-329 |

Number of pages | 9 |

Journal | Publications of the Astronomical Society of Japan |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 |

## Keywords

- Earth
- Gas-drag effect
- Instabilities
- Solar system: formation

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science