Question

Imagine that the earth and the-moon have positive charges of the same magnitud. How big isäºthe charge necesary to produce an electrostati, propulsion that equals 1.00% of the-gravitational atraction between twe, bodies

Answer 1

5.7 x 10^12 C

Step-by-step explanation:

Let the charge on earth and moon is q.

mass of earth, Me = 5.972 x 10^24 kg

mass of moon, Mm = 7.35 x 10^22 kg

Let d be the distance between earth and moon.

the gravitational force between them is

`F_(g)=G(M_(e) * M_(m))/(d^(2))`

The electrostatic force between them is

`F_(e)=(Kq^(2))/(d^(2))`

According to the question

1 % of Fg = Fe

`0.01 * 6.67*10^(-11)(5.97 * 10^(24)*7.35 * 10^(22))/(d^(2))=9 * 10^(9)(q^(2))/(d^(2))`

`2.927 * 10^(35)=9 *10^(9)q^(2)`

`3.25 * 10^(25)=q^(2)`

q = 5.7 x 10^12 C

Thus, the charge on earth and the moon is 5.7 x 10^12 C.