[TML] Planets in binary systems

[Timothy Little]

On Sun, Mar 02, 2008 at 03:06:39AM -0500, Jerry W Barrington wrote:
> 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.

There is an equation that can be solved for the positions, but it's a
quintic.  They tend to be nasty to solve exactly.

However, it really doesn't matter a great deal.  The distance of the
L1 & L2 points doesn't really change a great deal from the simpler
approximation for the Hill radius R (M2 / (3 M1))^(1/3), where R is
the distance between the stars.

Even at the extreme case where M1 = M2, the true L2 point is almost
identical to that given by the formula.  L1 is a bit out, since it
should be at the barycentre.  It is wrong by about 30%, which isn't
too bad for applying a formula to a situation way outside its
assumptions.


- Tim