The force due to gravity

\(\displaystyle{F}={\frac{{{G}{M}{m}}}{{{R}^{{2}}}}}\)

G - universal gravitational constant

M - mass of the earth

m - mass of the moon

R - distance

force between the the charges

\(\displaystyle{F}={\frac{{{Q}^{{2}}}}{{{4}\sigma\pi{R}^{{2}}}}}\)

Equating and solve for Q

\(\displaystyle{F}={\frac{{{G}{M}{m}}}{{{R}^{{2}}}}}\)

G - universal gravitational constant

M - mass of the earth

m - mass of the moon

R - distance

force between the the charges

\(\displaystyle{F}={\frac{{{Q}^{{2}}}}{{{4}\sigma\pi{R}^{{2}}}}}\)

Equating and solve for Q