I'm not sure how to go about solving this problem the algebra gets very messy...
At what distance formt he EArth will a spacecraft on the way to the Moon experiance zero net force due to there two bodies because the Earth and Moon pull with equal and opposite force?
THANKS
Let
Distance from the earth to the moon, D=384,403km
=384,403,000 m
Mass of the earth, M1 = 5.98*10^24 kg
Mass of the moon, M2 = 7.35*10^22 kg
Mass of spacecraft, m
Gravitational constant, G
r = distance of spacecraft from (the centre of) the earth
Using Newton's law of universal gravitation,
GM1m/r² = GM2m/(D-r)²
Solve for r.
I get about 3.5*10^8 m
Check my thinking.