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.