What is the reason that the Moon has a larger acceleration than Earth according to Newton's second law of motion?

The reason the Moon exhibits a larger acceleration compared to Earth when considering Newton's second law of motion relates to its mass. According to the law, acceleration is directly related to the force applied to an object and inversely related to its mass. This means that for the same force, the smaller the mass of an object, the greater its acceleration will be.

In this context, the Moon has a smaller mass than Earth. Therefore, when gravitational forces act on both bodies, the acceleration experienced by the Moon is greater than that experienced by Earth because it has less mass. This relationship follows from the formula ( F = ma ), where ( F ) is the force, ( m ) is the mass, and ( a ) is the acceleration. The smaller mass of the Moon results in a larger acceleration when subjected to the gravitational force exerted by the Earth.

This principle demonstrates why the Moon accelerates more than Earth in response to the gravitational interaction between them, confirming the choice that the Moon's smaller mass is the key factor here.