I am not entirely certain that I understand what you are asking. I will assume that you are asking this question: Given that the gravitational pull exerted by the earth is stronger than that exerted by the moon, what are the effects of the moon's gravitational pull on the earth?
Even though we think of the moon circling the earth - as if the earth's gravity affected the moon but not vice versa - this is not strictly true. The earth and the moon actually revolve around a single common point located on the line joining their centres.
The key point is this: Any body with mass, even only a tiny mass, will exert a gravitational pull on all other objects, no matter how massive those other objects are, and in some way "affect" those other objects.
The moon's gravity is one-sixth that of the Earth's;
The moon has one-sixth of the Earths gravity.
The centre of the earth is solid iron, however the centre of the earths gravitational pull changes, due to the movement of the moon, which has an effect on the earths gravity.
Because the moon is much, much closer to the earth, so the earths immediate gravity has more of an effect on the moon. But the moon-earth "package" together both orbit the sun.
The moon's gravity is about 1/6th of the earth's.
Less, about 1/6th of Earths.
Gravity. The moon orbits the earth because the moon is stuck in earths gravational pull.
the earths gravity holds the moon so it orbits the earth.
The moon's gravity is about 1/6th of Earth's.
the earths gravitational pull keeps the moon in orbit
they are pulled by the Earths gravity
Moon gravity is less because the atmosphere and mass and the earths gravity is greater than the moon if you weight yourself in the earth and then you weighted yourself in the moon you would weight less in the moon you could actually float in the moon because of its atmosphere and mass