I'm trying to find the point at which FG attracting to the moon = FG attracting to the earth...
5.98e24 kg = Earth Mass
7.35e22 kg = Moon Mass
3.84e8 m = Distance from Earth to Moon
a = 3.84e8 - b
b = 3.84e8 - a
a+b = 3.84e8
g = G m / r2
(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!