Stable Orbits in Binary Systems....

[Dollan]

A brief question relating to the reconstruction of my ArcBuilder add-ons (and the planets themselves in my fictional setting).

A typical measurement for stable orbits in planetary systems that I use is 1/5 the distance of the two stars' closest approach. That is, stars that come within, say, 6 AU of each other would have stable orbits out as far as 1.2 AU (this does not, of course, take into account the orbital evolution of the stars themselves which might be impossible to determin, or the gravitational interference of the forming stars on planets forming, which is beyond my knowledge to determine).

Now, the question is, is this 1/5 rule of thumb valid? I've seen it used on several world building sites, but I've never found any kind of references or documentation for it (something I'd love to have in order to have some validation for my work). If it *isn't* valid, or if it is simply too imprecise for some good solid world building, then how does one determine the distance?

...John...

[Evil Dr Ganymede]

It depends on the mass ratio of the stars. And the eccentricity of their orbits.

If the stars have equal mass and the orbits have 0 eccentricity, then planets can form within 0.274 of their separation around each star, or beyond 2.3875 times the separation around both.

If one star is 0.1 the mass of the other and they have 0 eccentricty, then planets can form within 0.43 of the separation from the more massive star, and 0.12 of the separation from the less massive star, and beyond 1.93 times the separation around both.

That all changes if the eccentricity is non-zero...

See: Long-Term Stability of Planets in Binary Systems (Holman, Matthew J.; Wiegert, Paul A.) The Astronomical Journal, Volume 117, Issue 1, pp. 621-628.