13 The Moon and Earth are bound together by gravity If inste

13. 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.

Solution

gravitational force between earth and moon

F = GM1*M2 / d^2

gravitational constant (G) = 6.67 x 10^-11

mass of the earth (m1) = 6.0 x 10²⁴ Kg

mass of the moon (m2) = 7.35 x 10²² Kg

The average distance from the center of the earth to the center of the moon is d = 384,400,000 m     

Force F = 1.99 x 10^20 N

now let charge on moon and earth is Q on each

F = k*q^2 / d^2

q = sqrt (F*d^2 / K)

q = sqrt(1.99x10^20* 384400000^2 / 9*10^9)

q = 5716x10^10 C