TO solve the force of attraction between the Earth and the Moon we use Newton's Law of Gravitation.
The gravitational force between two objects of mass m1 and m2 placed a distance d apart is m1*m2*G*r^2, where G is the universal gravitational constant.
So now the mass of the moon is 7.35E+22 Kg. Mass of the Earth is 5.98E+24 Kg. The Gravitational constant is 6.67E-11 nt-m2/Kg2.
The distance between the Earth and the Moon is 3.85E+08 m
Therefore the gravitational force of attraction between the Earth and the Moon is:
6.67* 10^-11 nt-m^2/Kg^2 * 7.35*10^22 kg* 5.98*10^24 kg *(3.85E+08) ^2 m^2
= 1.98* 10^20 N
So the force of attraction between the Earth and the Moon is 1.98* 10^20 N.
We'll write the Universal Law of Gravitation:
Fg = G*Mm*Me/r^2 (1)
Mm and Me are the masses of the moon and the Earth.
r^2 is the orbital radius that express the distance between the moon and the Earth.
G = 6.67*10^-6 dyne cm^2/g^2
Mm = 7.35*10^25 g
Me = 5.96*10^27 g
r = 3.84*10^10 cm
We'll substitute the values in the expression (1):
Fg = (6.67*10^-6)*(7.35*10^25)(5.96*10^27)/(3.84*10^10)^2
Fg = 2*10^25 dynes