OK you'd need to know the masses of the Earth and of the Moon... or at least the ratio of the masses

you've got a spacecraft on the line between the centres of mass of the earth and the moon and you need to find the position where the gravitational force on the spacecraft due to the earth is equal in size to the gravitational force on the spacecraft due to the moon - giving no net gravitational force.

to make it as simple as possible you might as well assume the spacecraft has a mass of 1kg - hopefully it's obvious the position would be the same for any mass.

so your equations for the force on the spacecraft will look like

GM_{moon}/r_{moon}^2 = GM_{earth}/r_{earth}

and G is a constant so you can cancel that on both sides

you've got a spacecraft on the line between the centres of mass of the earth and the moon and you need to find the position where the gravitational force on the spacecraft due to the earth is equal in size to the gravitational force on the spacecraft due to the moon - giving no net gravitational force.

to make it as simple as possible you might as well assume the spacecraft has a mass of 1kg - hopefully it's obvious the position would be the same for any mass.

so your equations for the force on the spacecraft will look like

GM

and G is a constant so you can cancel that on both sides

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