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**The mass of the Moon is 7.35*10^22 Kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is cancelled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (centre to centre) is 3.84*10^5 Km (3.84*10^8 m), calculate where this will occur, relative to Earth.**

**Given:**

m Moon = 7.35*10^22 kg

m Earth = 5.98*10^24 kg

r = 3.84*10^8 m

G = 6.67x10^-11 N * m^2/kg^2

**Required:**r1

**Analaysis:**Fg = (G*m1*m2) / r^2

Fge = Fgm

**Solution:**

Let m2 = 1 kg (the mass of an object between the earth and the moon)

For Earth:

Fge = [(6.67*10^-11)(5.98*10^24)(1)] / r1 ^2

For the Moon:

Fgm = Fgm = [(6.67*10^-11)(7.35*10^22)(1)] / (3.84*10^8 - r1)^2

Fge = Fgm

[(5.98*10^24 kg) / r1^2] = [(7.35*10^22 kg) / (3.84*10^8 - r1)^2]

**Am I on the right track here, and if so, can someone help me finish off the equation to solve for r1? Thanks in advance.**

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