The gas-drag effect on the orbital instability of a protoplanet system

Kazunori Iwasaki, Hidekazu Tanaka, Kiyoshi Nakazawa, Hiroyuki Emori

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


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, log10 Tinst can be approximately written as a linear function of the initial orbital separation distance, Δã0, where Tinst 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 Tgasinst and found that Tgasinst suddenly becomes large compared with Tinst, when Δã0 is larger than a certain critical separation distance, (Δã0)crit. Furthermore, we showed that (Δã0)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 (Δã0)crit in the nebula as being about 10 Hill radius at 1 AU.

Original languageEnglish
Pages (from-to)321-329
Number of pages9
JournalPublications of the Astronomical Society of Japan
Issue number2
Publication statusPublished - 2001
Externally publishedYes


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

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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