Gm1m2 / d2 = kq1q2 / d2What is the value of Q to maintain the present orbit?

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SUMMARY

The discussion centers on calculating the charge value (Q) required to maintain the Moon's orbit around the Earth if electrical attraction replaces gravitational force. The relevant equations are the gravitational force formula, Fg = Gm1m2 / d², and the electrostatic force formula, Fe = kq1q2 / d². Given the masses of the Earth (5.97 x 10²⁴ kg) and Moon (7.35 x 10²² kg), and the orbital radius (3.84 x 10⁸ m), the forces of gravity and electrostatic attraction must be equal for the orbit to remain stable. The solution involves equating these forces and solving for Q.

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Homework Statement



Supppose that electrical attraction, rather than gravity were responsible for holding the moon in orbit around the earth. If equal and opposite charges Q were placed on the Earth and the Moon, What should be the value of Q to maintain the present orbit?

Treat the Earth and Moon as point particles

Homework Equations



Mass of earth: 5.97x1024kg
Mass of moon: 7.35x1022kg
radius of orbit: 3.84x108m

Fg=Gm1m2 / d2
Fe= kq1q2 / d2

The Attempt at a Solution



Well I know to start by finding the force of gravity, but from there i am unsure about how to do this problem. Could someone please help?
 
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If the orbit remains the same, then so does the acceleration.
Since the masses are the same, so are the forces: Fg=Fq
 

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