The distance between earth and moon is about `3.8xx10^(5) km`. At what point or points will the gravitational field strength of earth-moon system be zero? Given mass of earth is `81` times the moon's mass.

Explanation

Let `x` be the distance of a point from the Earth where resultant gravitational field intensity is zero. So
`(Gm_(e))/(x^(2)) = (GM_(m))/((r - x)^(2))` or `(82 M_(m))/(x^(2)) = (M_(m))/((r x)^(2))`
or `(9)/(x) = (1)/((r - x))` or `9 r = 10 x`
or `x = 9 r//10 = 0.9 r`