Theorem of the keplerian kinematics

As described in the literature the velocity of a Keplerian orbiter on a fixed orbit is always the sum of a uniform rotation velocity and a uniform translation velocity, both coplanar. This property is stated here as a theorem and demonstrated as true. The consequences are investigated among which the Newton's gravitational acceleration appears as its derivative with respect to time, the classical mechanical energy is deduced, the Galileo's equivalence principle is respected. However the Newton's factor $G M$ appears as a kinematics factor, the angular momentum multiplied by the rotation velocity, and this enables to consider a kinematics reason for the rotation of the galaxies, with no need for dark matter. Furthermore the kinematics demonstrate that the gravitational acceleration causes the rotation, but not the attraction, while the mechanical acceleration can only cause a translation. These two accelerations being thus of different natures, the Einstein's equivalence principle can not be correct.