Re: Jupiter's L1

From: Anders Sandberg (
Date: Mon Dec 03 2001 - 14:59:36 MST

On Mon, Dec 03, 2001 at 09:22:45AM -0800, wrote:
> 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.

The equlibrium condition is that G M_sun / R^2 - G M_jup / (R-R_jup)^2 -
omega^2 R = 0
which gives:
(G M_sun - omega^2) R^2 + (omega^2 R_jup - 2 G M_sun R_jup ) R
+ (G M_sun R_jup^2 - G M_jup) = 0

I don't have a calculator with the requisite precision to solve the
equation, but omega^2 seems to be a very small factor.

Anders Sandberg                                      Towards Ascension!                  
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y

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