The gravitational force of the sun on earth is much bigger than that of the moon.
Why then are tides caused by the moon?
Ms: mass of the sun
Mm: mass of the moon
r: distance from the moon to the earth
R: distance from the sun to the earth
The gravitational force of the moon at the earth is
Tides are movement of water on the earths surface caused by variations in these forces on it.
Let Df and DF represent the differences in these forces across the earth;
the linear approximation to these differences yields:
Thus the sun's gravitational force dominates that of the moon, but the variation in the moon's gravitational force on the earth's surface dominates that of the sun.