For the same force, the object with the larger mass will accelerate less. So the earth's motion is unmeasurably small. Section 2.5 - The Law of Gravity Newton was not finished with his three laws of motion. His range of accomplishments is astounding. He also derived a law to explain gravity.
Every mass exerts a force of attraction on every other mass.
But because of its huge mass, will have essentially zero acceleration. First accurately measured by Galileo. Aristotle believed larger objects fell faster than smaller ones. Galileo proved that idea wrong with a very simple experiment. Newton's laws of motion and law of gravity work for us on the Earth's surface.