Why is the acceleration of one cosmic body relative to another always greater than it would follow from the law of universal gravitation

Why is the acceleration of one cosmic body relative to another always greater than it would follow from the law of universal gravitation a = CM / r2, where M is the mass of the attracting body, and r is the distance between the centers of these bodies?

We are talking about the acceleration of a space body in a non-inertial frame of reference associated with another space body. This acceleration is found by the formula a = G (M + m) / r ^ 2, where M and m are the masses of the bodies.