Orbital Stability of a Protoplanet System under a Drag Force Proportional to the Random Velocity

Details Orbital Stability of a Protoplanet System under a Drag Force Proportional to the Random Velocity Orbital Stability of a Protoplanet System under a Drag Force Proportional to the Random Velocity

Jun 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002pasj...54..471i&link_type=abstract

Publications of the Astronomical Society of Japan, Vol.54, No.3, pp.471-479

Astronomy and Astrophysics

Astronomy

21

Earth, Instabilities, Solar System: Formation, Stokes-Type Drag Force

Scientific paper

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, Tdfinst. We found that Tdfinst 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.

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