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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

1 answer

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.