[TML] Planets in binary systems

[shadow at shadowgard.com]

On 2 Mar 2008 at 3:06, Jerry W Barrington wrote:

> Planets can orbit far from a pair of stars, or close to either of the stars.
> "Close" is often quoted as about 1/3 of the way to the other star.  A useful
> rule of thumb, but it assumes the stars are equal mass.  Obviously, if one
> is much less massive than the other, it's planets must be much closer in.
> This is why Jupiter can't have moons 1.7 AU out!  (Even if there weren't
> other planets affecting things)
> 
> I think a more accurate figure would be 1/2 of the way to the nearest
> Lagrange point, at their closest approach.  Unfortunately, I can't seem to
> find simple equations for the locations of of L1/2/3 for arbitrary masses.
> :(

Nope, Lagrange points are very special cases.

"Simplest" is to merely figure out the distance where the gravity of 
the star and that of the planet balance. You won't find "real" 
satellites (and not much "captured" stuff either) outside that point. 


Most notable exception is the Earth/Moon system. But then again 
careful analysis shows that the moon doesn't really orbit the earth, 
it just shares an orbit with Earth.

> I tried looking at the Hill sphere too, but all the online info I can find
> on Hill and Lagrange assume one mass much greater than the other.  Any
> suggestions where I could find more general equations?  Or even an easy
> derivation?  :)

There *are* no *solvable* general equations for the three body 
problem.

The Lagrange point solution is a special case and *requires* those 
substantial mass differences to work.

--
Leonard Erickson (aka shadow)
shadow at shadowgard dot com