Let's calculate influence of Earth gravity and of Sun light on the motion of Moon.

Earth pulls Moon with the force equal to, according to Newton, F=GMm/R^2 = (6.7x10^11 N m^2/kg^2)x(6x10^24 kg)x (7.4x10^22 kg)/(3.8x10^8 m)^2 = 2x10^20 Newtons (about 5x10^19 lb, or 2x10^16 tons).

Sun light pressure is p=I/c = (1.4x10^3 watt/m^2)/(3x10^8 m/s) = 4.7x10^-6 N/m^2.

It pushes the Moon with the force F=pxS =(4.7x10^-6 N/m^2)x(3.14x(1.8x10^6 m)^2)=4.4x10^6 N which is about 10^6 lb (about 450 tons).

Comparing the force of gravity with the force of light, you may see that the gravity of Earth is 4.5x10^12 times sronger than sunlight.

So, why does the Moon have to follow Sun light rather than Earth's gravity?