(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The mass of the Moon is 7.36 x 10 ^ 22 kg. At some point between Earth and the Moon, the force of Earth's gravitational attraction on an object is canceled by the Moon's force of gravitational attraction. If the distance between Earth and the Moon (center to center) is 3.84 x 10 ^ 5 km, calculate where this will occur, relative to Earth.

2. Relevant equations

Fg = Gm1m2 / r ^ 2

3. The attempt at a solution

Given:

Mass of Earth = 5.98 x 10 ^ 24 kg

Mass of Moon = 7.36 x 10 ^ 22 kg

Radius between Earth and Moon = 3.84 x 10 ^ 5 km = 3.84 x 10 ^ 8 m

So at this point, Fgmoon = Fgearth, but I need another object to calculate the point.

So assuming the object is 1kg. Fg between Moon and object = Fg between Earth and object.

I need to find the r between Earth and object. This distance is the entire distance between Earth and Moon minus distance between object and Moon.

Gm(earth)m(test) / (distance between moon and sun - r) ^ 2 = Gm(test)m(moon) / r ^ 2

I don't know either r.

I'm not sure how to find r with this equation.

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# Law of Universal Gravitation: gravitational attraction of Earth and Moon is canceled

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