Where are the gravitational pulls of the Earth and the Moon equal?

On Sun, 12 Mar 2000 Evan wrote:

> i am doing a physics project. I need to know where between the earth and the
> moon are there gravitation equal. I can't find it anywhere. If u know where
> the earth and the moon have the same gravity, please write me.
> thanks

Hi Evan,

There are several points where the moon and the Earth's gravitational pull
are equal. These are called "Lagrange points" after the mathematician
Josef Lagrange who discovered them. For more detail on Lagrange points in
general, see the web site http://map.gsfc.nasa.gov/html/lagrange.html

I presume that your project is asking for the Earth-moon L1 Lagrange point
- the point lying directly between the moon and the Earth. The distance
from the center of the Earth of the L1 Lagrange point is
1/3
x = R * [ 1 - (a/3) ]
where R is the Earth moon distance, and
a = mass of the moon / (mass of Earth + mass of moon)
(see the above link for the derivation of this equation).

The Earth-moon distance is 384,400 km, the mass of the moon is
22 24
7.349 x 10 kg, and the mass of the Earth is 5.97 x 10 kg.

Filling in these values, we find that the L1 Lagrange point is at a
distance of 323,110 km from the Earth, or 84% of the distance to the moon.

Thanks for writing!

Sincerely,
Kurtis Williams

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