Solve Net Gravitational Force Problem: Earth-Moon Distance

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SUMMARY

The discussion centers on solving the net gravitational force problem between Earth and the Moon, specifically determining the distance from Earth where the gravitational forces cancel out for a spaceship. The Universal Law of Gravitation, represented by the equation F=G(m1)(m2)/r^2, is utilized to set up two equations for the forces exerted by Earth and the Moon. Participants confirm that the correct approach involves equating these forces, and one user, Daniel, acknowledges the need for careful calculations to avoid errors, particularly regarding negative values under the square root in his computations.

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  • Understanding of the Universal Law of Gravitation
  • Familiarity with gravitational force calculations
  • Basic algebra for solving equations
  • Concept of equilibrium in forces
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CinderBlockFist
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Hey all, I am stuck on this problem.

A spaceship is ona straight line path between Earth and its mon. At what distance from Earth is the net gravitational force on the spaceship zero?



Well, when I try to use the Universal law of gravitation. F=G(m1)(m2)/r^2, I could find the distance if only I knew the mass of the spaceship, but it is not given. So, I tried to set 2 equations equal, one using the moon, and one using the earth, since the forces would cancel on the spaceship, making it 0. But when i do the computations, I get a negative under a root symbol. Is this the correct approach? Am i missing something here? THanks in advance.
 
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Your second method is the correct one.Please post your calculations,as to figure out what u're doing wrong...


Daniel.
 
Ok, thanks dex, it's kind of lengthy, so since i know this is the correct approach, I'll try to do it more carefully and see what I get, thanks for the quick response.
 

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