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There is a point roughly 90% of the distance to the moon where net gravitational force...

There is a point roughly 90% of the distance to the moon where net gravitational force is zero. How many times more massive than the moon is the Earth?

Science   Advanced-Physics   
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Answer #1

The gravitational force at the distance x at a point between the moon and the earth is
  
where, m is the mass of the test particle and D is the distance from the earth to the moon and x is the distance of the point at which the test particle of mass resides. And as the earth pulls the mass m towards itself and the moon pulls towards herself, so, there is a relative minus sign between the two forces.

Now, for
   
we have
  
  
  
   
  
Thus, mass of the Earth is 81 times greater than the mass of the Moon. And so, Earth is 81 times massive than the mass of the Moon.

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