# Newton's law of universal gravitation!

## 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!

SammyS
Staff Emeritus
Homework Helper
Gold Member

## 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 MeMm=x2*(r-x)2

from GMeMp/x2 = GMmMp/(r-x)2

???

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
Staff Emeritus
Homework Helper
Gold Member
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:
$\displaystyle\frac{M_e}{x^2}=\frac{M_m}{(r-x)^2}$​
Mm and Me should end up on opposite sides of the equation from each other.

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

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

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