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"From the earth to the moon", Jules Verne Physics Problem

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In his novel "From the earth to the moon", Jules Verne imagined that astronauts inside a space ship would walk on the floor of the cabin when the force exerted on the ship by the earth was greater than the force exerted by the moon. When the force exerted by the moon was greater he thought the astronauts would walk on the ceiling. (A) At what distance from the center of the earth would the forces exerted on the spaceship by the earth and the moon be equal? (B) explain why Vernes description of gravitational effects is incorrect.

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Solution Summary

The distance from the center of the earth on the force exerted are given. The expert explains why vernes description of gravitational effects is incorrect.

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Part A
As you you are well aware the Gravitational Force (F) on a body(mass: m) due to another (Mass:M) separated by a distance 'r' is given by :

F = G*M*m/(r^2) ;

Now suppose our space ship has mass 'Ms', and is on a straight line path from the Earth, mass 'Me', to the Moon , mass 'Mmoon' and lets say that the distance beween the Earth and Moon is 'R'. Let us also say that some distance 'r' from the Earth, the Gravitational Forces on the spaceship due to the Moon and the Earth are equal and balance one another, and the net Gravitational Force is zero. Mathematically, it can be expressed as :

G*Me*Ms/(r^2) = ...

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