If account be taken of the motion of the earth's center through space and the slight precession of the earth's axis in the terms and of Eq. (112), then the more accurate relation for the absolute acceleration of a particle whose motion relative to the earth is known is
In this equation the angular velocity represents that of a radius vector between the centers of the earth and moon and is that of a radius vector between the centers of the earth-moon system and the sun. The quantity is the radius vector from the center of the earth-moon system to the center of the earth, and is the radius vector from the sun to the earth-moon system. The complete fourth and fifth terms represent the centripetal accelerations of the earth about the center of the earth-moon system and the sun respectively. These accelerations have already arisen in the discussion ofthe tide producing forces.
In the last term, the derivatie includes any changes in magnitude of as well as the change in direction of associated with the slight wobble of the earth's axis. The magnitude of the acceleration is extremely small and can be neglected for all practical purposes.
The motions of the solar system in the Milky Way galaxy as well as the motion of the galaxy itself through absolute space are considered to be sufficiently uniform and rectilinear in character such as to lead to no additional contributions of significance to Eq. (12). At least the expression for the ``absolute acceleration'' given by Eq. (121) is considered exact from the Newtonian standpoint, which infers that it is the acceleration induced by and equivalent to a real force per unit mass. This law having been established through measurements in our solar system indeed puts it on a relativistic plane which automatically encompasses an invariant effects which are beyond the realm of measurement.