Finding Equal Force Distance from Moon

[sony]

So I am supposed to find the distance from the moon where the force on a particle from the Earth and sun is equal.

I get this expression (earth-moon distance is 400 000km):
yMm/(r^2) = yMm / (400000km-r)^2

But from that I get r=200 000km and the answer should be 40 000km...

whats wrong with the expression?

thanks

 

[µ³]

mass of the moon != mass of the earth

 

[sony]

but the product of the masses is the same on both sides right? don't they cancel...?

 

[Tide]

No, they are not the same and they can't cancel if they are not the same.

 

[sony]

then what is the expression...?

 

[DaveC426913]

There should be only one mass variable on each side of your equation.

 

[sony]

but Newtons gravitation law is yMm/r^2...

 

[Tide]

Yes. But do you KNOW what M and m are?

 

[sony]

M=mass of earth
m=mass of moon

?

 

[sony]

oh, heh, I don't know what caused me to be so slow... I forgot the mass of the particle at the Lagrance point...

Bah, sorry for the trouble :P