Distance between moon and earth

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SUMMARY

The discussion focuses on calculating the distance between the Earth and the Moon using gravitational force equations. The mass ratio of the Moon to the Earth is established as 0.012, and the distance from the Earth to point X is given as 3.4 x 108 meters. The gravitational force equation F=GMm/r2 is identified as the primary tool for solving the problem. Participants emphasize the importance of algebraic manipulation and substitution of distances to find the total separation between the Earth and the Moon.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F=GMm/r2
  • Knowledge of mass ratios, particularly the Moon to Earth mass ratio of 0.012
  • Basic algebra skills for manipulating equations and solving for unknowns
  • Familiarity with circular motion concepts in astrophysics
NEXT STEPS
  • Study gravitational force calculations in astrophysics
  • Learn about the concept of gravitational equilibrium points
  • Explore algebraic techniques for solving equations with multiple variables
  • Investigate the implications of mass ratios in celestial mechanics
USEFUL FOR

Students studying physics, particularly those focusing on gravitational forces and celestial mechanics, as well as educators seeking to enhance their teaching methods in these topics.

phinl
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Homework Statement


I'm stuck at one of my homework questions.Basically,it says there is a line EM between the Earth's and moon's centre of masses.The moon revolves around the Earth in circular motion.Point X(somewhere in between moon and earth)represents a point where the resultant gravitational force is 0.Mass of moon/Mass of earth=0.012. Given distance EX is 3.4x10^8,determine distance of EM.

Sorry I can't show a diagram.



Homework Equations


F=GMm/r^2

I can only think of this.


The Attempt at a Solution


It's quite lengthy and after some time I realized it was wrong so I think it would be better if I just read some suggested solutions from you guys.
 
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The point X is at a distance from the centre of the Earth and at a distance from the centre of the Moon.
These 2 distances add up to the separation of the Earth and Moon.
Can you see it... it is an exercise in algebra and substitution of the appropriate distances in your equation.
 

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