Eletric force and gravitational force question

[strawberrysk8]

Homework Statement

How many extra electrons would we have to place on Earth and moon so the electric repulsion between these bodies cancels their gravitational attraction? Assume that the numbers of extra electrons on the Earth and on the moon are in the same propotion as the radial dimensions of these bodies (6.38:1.74).

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

How many extra electrons would we have to place on Earth and moon so the electric repulsion between these bodies cancels their gravitational attraction? Assume that the numbers of extra electrons on the Earth and on the moon are in the same propotion as the radial dimensions of these bodies (6.38:1.74).

Homework Equations

The Attempt at a Solution

How would you think to address the problem? Can you think of any relevant formulas?

 

[strawberrysk8]

F=kqq/r^2

F=GmM/r^2

Constants: k,G,m,M,r

what is q1 and q2?

 

[LowlyPion]

F=kqq/r^2

F=GmM/r^2

Constants: k,G,m,M,r

what is q1 and q2?

Don't forget the additional constraint from the OP that q_earth is 6.38 to q_moon's 1.74.

$$q__{earth}$$= 6.38/1.74 * $$q__{moon}$$

With all the parameters but charge determined then what do you suggest doing with the two equations?

 

[strawberrysk8]

set them equal to each other

kqq/r^2 = GmM/r^2

kqq = GmM

k(6.38/1.74)q^2 = GmM

solve for q(moon)

then solve for q(earth)

what is the extra electons?

 

[strawberrysk8]

oh! i got it! thank you for the advice :)

 

[LowlyPion]

oh! i got it! thank you for the advice :)

Congrats then and good luck.