I think Spike's formula is almost correct, finding the point at which
the gravitational forces would balance. However it neglects the orbital
motion of the planet.
If you consider a co-rotating coordinate system, so that the planet and
star are in fixed positions, then there is centrifugal force to consider.
Effectively this weakens the star's attractive force as you get farther
out, which is why the planet doesn't fall towards the star in this
coordinate system. Because of this weakening the L1 point of balance
will move closer towards the star than in the model Spike used where
rotation is neglected. I haven't tried to work it out exactly but if you
need a numerical result I could fire up Mathematica and get one for you.
Hal
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