You are flying to the Moon. Find the point at which the gravitational attractions of Earth and Moon on you will be equal and opposite.

radius of the moon: 1.74*10^6 m
radius of the earth: 6.38*10^6 m
orbital radius of the moon: 3.8*10^8 m

Not enough information has been provided to answer that question. The point where gravitational attractions cancel out depends upon the relative MASSES of the Earth and Moon, bot the radii. Moon and earth have different average densities. You cannot deduce their relative masses from the relative radii.

Look up the relative masses of Earth and Moon. Call it M/m = a

Where the forces cancel, a = (d1/d2)^2

d1 is the distance to Earth and d2 is the distance to moon.
d1 + d2 = d1*(1+ 1/sqrt a)=3.8*10^8 m

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