Orbital stability of a protoplanet system under a drag force proportional to the random velocity

Kazunori Iwasaki, Hiroyuki Emori, Kiyoshi Nakazawa, Hidekazu Tanaka

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


We investigated the effects of a tidal interaction with a gas disk and the dynamical friction with a planetesimal disk on the orbital instability of a protoplanet system. Both effects are expressed as the drag force, which is proportional to the random velocity of a protoplanet. We calculated numerically the orbits of 5 protoplanets with the same separation distance under the drag-force effect and examined the orbital instability time under the drag force, Tinstdf. We found that Tinstdf can become much larger than the instability time under the drag-free condition, and that the onset of the orbital instability is prevented when the separation distance exceeds a critical value. We obtained a relation between the critical separation distance and the surface density of the gas or planetesimal disk. By applying this relation, we found that, for the formation of terrestrial planets from a protoplanet system with a typical orbital separation (i.e., ∼ 10 Hill radii), the surface density of the nebular gas must be reduced to about one-thousandth of that in the minimum-mass nebula model. Terrestrial planets would be formed after such a depletion of the solar nebula.

Original languageEnglish
Pages (from-to)471-479
Number of pages9
JournalPublications of the Astronomical Society of Japan
Issue number3
Publication statusPublished - 2002
Externally publishedYes


  • Earth
  • Instabilities
  • Solar system: formation
  • Stokes-type drag force

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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