Why does the gravitational force between earth and moon predominate over electrical forces?

Because the Earth and the Moon are electrically neutral

Explanation:

The gravitational force between the Earth and the Moon is given by

where G is the gravitational constant, m is the mass of the Moon, M is the mass of the Earth, r is the distance between the Moon and the Earth. Since both the Earth and the Moon have large masses, m and M are big, so the gravitational force between the two objects is large.

On the contrary, the electrostatic force between the Earth and the Moon is given by

where k is the Coulomb's constant, q1 is the charge of the Moon, q2 is the charge of the Earth, r is the distance between the Moon and the Earth. However, big objects (and planets as well) are electrically neutral, which means that they have zero charge (because if they had charge, they would tend to attract charge of the opposite sign, becoming neutral again). Therefore, the values of q1 and q2 are approximately zero, so the electrostatic force is zero as well.

see earlier answer