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Re: [Phys-l] Lagrange points



To first order, the distances to both L1 and L2 are [M_e / (3 M_s)]^ (1/3) times the distance to the Sun. In the case of the Earth-Sun system, that turns out to be 1.00% of the distance to the Sun.

To first order, the Newtonian gravitational force balance position is [(M_e / M_s)]^(1/2) times the distance to the Sun. In the case of the Earth-Sun system, that turns out to be 0.17% of the distance to the Sun.

So there is quite a difference. The gravitational force due to the Earth at the L1 point is very small compared to that due to the Sun (only about 3% as large). This should be expected, because, after all, at the L1 point the net force must keep an object in an orbit that has the *same* period as the Earth and is just a *tiny* bit smaller in radius. It doesn't take a very large reduction in the Sun's influence to do that job.

John Mallinckrodt
Cal Poly Pomona

On Dec 2, 2009, at 7:36 PM, chuck britton wrote:

At 7:19 PM -0800 12/2/09, John Mallinckrodt wrote:
I wouldn't be too hard on them. It's not at all unreasonable to work
in a rotating frame when thinking about things like Lagrange points.
Moreover, notice that they didn't even talk about gravitational
*forces*. They simply said, "the gravity of the Earth and sun
balance out." That's really not all that far from a completely
reasonable general relativistic statement.


Just out of curiosity, how far apart ARE the L1 point and the grav.
balance point.
(In some sort of 'reduced' coordinate measure rather than miles or such)

Sounds like the earth-sun L! is getting sorta crowded?
SOHO actually circles AROUND the L1 point??
Sorta cool.
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