Question

A rocket is fired the Earth towards the Moon. At what distance from the Moon is the gravitational force on the rocket is zero. Mass of Earth is `6 xx 10^(24) kg` , mass of moon is ` 7.4xx 10^(22) kg` and distance between moon and earth is `3.8xx 10^(8)m`. Neglect the effect of the sun and other planes.

Answer 1

Let `x` be the distance between rocket and Moon, when the net gravitational force on roccket is zero, i.e., gravitational force on rocket due to Earth = gravitational force on rocket due to Moon.
Then, `(GM_(e)m)/((r - x)^(2)) = (GM_(m)m)/(x^(2))`
`(r - x)/(x) = sqrt((M_(e))/(M_(m))) = sqrt((6 xx 10^(24))/(7.4 xx 10^(22))) = 9.0`
Using `r = 3.8 xx 10^(8) m` and solving the above relation, we get `x = 3.8 xx 10^(7) m`