How Much Charge Would the Moon and Earth Need to Replace Gravity?

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SUMMARY

The discussion focuses on calculating the amount of charge required on the Moon and Earth to replicate the gravitational force between them using Coulomb's law. The gravitational force is equated to the electrostatic force, represented by the equation Fe = ke |q1||q2|/r^2. The gravitational acceleration of 9.81 m/s² is used, leading to the conclusion that a charge of approximately -0.64766 must be applied to each body to achieve the necessary force. The participants confirm that equating the gravitational pull of the Earth on the Moon with the electrostatic force is the correct approach.

PREREQUISITES
  • Understanding of Coulomb's Law
  • Familiarity with gravitational force equations
  • Basic knowledge of electrostatics
  • Concept of charge magnitude and sign
NEXT STEPS
  • Study the derivation of Coulomb's Law in detail
  • Explore gravitational force calculations in astrophysics
  • Research the implications of charge interactions in celestial mechanics
  • Learn about the constants involved, such as the electrostatic constant (ke)
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Physics students, educators, and anyone interested in the interplay between gravitational and electrostatic forces in celestial bodies.

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1. The Moon and Earth are bound together by gravity. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force.



2. Fe = ke |q1||q2|/r^2



3. 9.81 = ke |x||-x|/r^2
solving for x, I ended up getting -.64766

Not sure if I understand the problem correctly or not. Please help steer in the right direction. Thanks
 
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I think you need to equate the gravitational pull of the Earth on the moon with [tex]F_e[/tex]. Since you know the radius from the center of the Earth to the center of the moon, and you know [tex]k_e[/tex], you can find the two "q"s by a simple square root operation, making one positive and the other negative.
 
I got it..thanks
 

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