Finding the zero gravitational force point between Earth and moon

[wow22]

Homework Statement

is there a point between the Earth and the moon for which the net gravitational force on an object is zero? Where is this point located? Note that the mass of the Earth is 5.98x10^24 kg, the mass of the moon is 7.35x10^22kg, and the distance between the centres of Earth and moon is 3.84x10^8m.

Homework Equations

Fge=Fgm

so GMeMp/x^2 = GMmMp/(r-x)^2
p being the point, x being the radius of earth

The Attempt at a Solution

i tried to rearrange...to find r. and got MeMm=x^2*(r-x)^2 ?
so that means 5.98*10^24(7.35*10^22)= x^2(3.84*10^8-x)^2 ??

Can someone tell me how to rearrange it, cause it's supposed to be rearraned to Mm/Me(x^2)=R^2-2r+x^2 ... Thanks!

Homework Statement

 

[SammyS]

Homework Statement

is there a point between the Earth and the moon for which the net gravitational force on an object is zero? Where is this point located? Note that the mass of the Earth is 5.98x10^24 kg, the mass of the moon is 7.35x10^22kg, and the distance between the centres of Earth and moon is 3.84x10^8m.

Homework Equations

Fge=Fgm

so GMeMp/x^2 = GMmMp/(r-x)^2
p being the point, x being the radius of earth

The Attempt at a Solution

i tried to rearrange...to find r. and got MeMm=x^2*(r-x)^2 ?
so that means 5.98*10^24(7.35*10^22)= x^2(3.84*10^8-x)^2 ??

Can someone tell me how to rearrange it, cause it's supposed to be rearraned to Mm/Me(x^2)=R^2-2r+x^2 ... Thanks!

How did you ever get M_eM_m=x²*(r-x)²

from GM_eM_p/x² = GM_mM_p/(r-x)²

?

 

[wow22]

GMp crosses out both sides.. to make Me/X^2 = Mm/(R-x)^2
so cross multiply, MeMm=X^2*(r-x)^2

..why? how was i supposed to do it?

 

[SammyS]

GMp crosses out both sides.. to make Me/X^2 = Mm/(R-x)^2
so cross multiply, MeMm=X^2*(r-x)^2

..why? how was i supposed to do it?

That's not what you get from cross multiplying !

Cross multiply this:

$\displaystyle\frac{M_e}{x^2}=\frac{M_m}{(r-x)^2}$​

M_m and M_e should end up on opposite sides of the equation from each other.

 

[wow22]

Oh wow.. How did I not realize that ...
haha so its Me(r-x)^2 = Mm(x^2)
Thankkss!

 

[Cecilia48]

http://www.infoocean.info/avatar2.jpg GMp crosses out both sides..