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## Homework Statement

I'm trying to find the point at which F

_{G}attracting to the moon = F

_{G}attracting to the earth...

5.98e24 kg = Earth Mass

7.35e22 kg = Moon Mass

3.84e8 m = Distance from Earth to Moon

*Deductions...*

a = 3.84e8 - b

b = 3.84e8 - a

a+b = 3.84e8

## Homework Equations

g = G m / r

^{2}

(6.67e-11 * 5.98e24)/a² = (6.67e-11 * 7.35e22)/b²

## The Attempt at a Solution

*I wolfram'd this but it didn't give a step by step solution because I don't have a paid acct*

[(6.67e-11 * 5.98e24)/(3.84e8 - b)^2 = (6.67e-11 * 7.35e22)/(3.84e8 - a)^2, 3.84e8 = a+b]

a = 3.45677e8

b = 3.83233e7

This isn't for an assignment but I'm really curious as to how to do the calculus with two unknown variables. Unfortunately, I don't have calculus till next semester... If you could show your solution so I can study and figure out how you did it, I would be greatly appreciative.

Thanks for your advice and help!

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