Moon and Earth Gravity Qs?

Question

The Earth and Moon 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.

Answer 1

You need to look up the values for the mass of the earth, m1,moon m2,the distance between them R,and G, the Gravitational constant and k, Coulombs constant.

For gravity the force of attraction, Fg, is

Fg =G(m1)(m2)/(R^2)

Substitute all values in on the right and get a value for Fg in newtons.

Now for the electrical force of attraction Fe

Fe = k (q1)(q2)/R^2

Let Fg=Fe

And since q1=q2; let q1=q2=q

solve for q

Fe=Fg =kq^2/R^2

q^2 = FgR^2/k

q =sqrt( FgR^2/k)  

q= Rsqrt(Fg/k)

Substitute in the values of R, Fg, and k and get the value of q in coulombs.

q= (3.85 x 10^8m) sqrt(1.98 x 10^20 N/ 9 x10^9Nm^2/C^2)

q = 5.78 x 10^14 Coulombs