From: Spike Jones (spike66@attglobal.net)
Date: Mon Dec 03 2001 - 17:43:24 MST
hal@finney.org wrote:
> 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.
Yup. I realized it after I sent the second post.
Heres the calc with rotation included:
Mj = 1.9E27
Ms = 2E30
Ds = distance from Lagrange point to the sun
Dj = distance from Lagrange point to Jupiter
Ds + Dj = 5.2
Taking into account a rotating reference frame:
GMj/Dj^2 + wj^2Ds = GMs/Ds^2
Dj = 5.2 - Rs
Dj^2 = 27 - 10.4Ds + Ds^2
GMjDs^2 + wj^2Ds^3Dj^2 - GMsDj^2 = 0
Thats where Damien's puzzling cube term was coming from.
I just put it in excel and goal seeked (goal sought?) a
value of 0.35 AU from Jupiter, which isnt that far from
Damien's original .48 AU and over twice my original
incorrectly calculated .16 AU.
Hey instead of calculating these, isnt there a website
somewhere where this sorta thing can be found? spike
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