Kepler's laws of the motion of celestial bodies, and Galilei's laws for projectiles and falling bodies were not altogether compatible. According to Galilei the planetary orbits were circular, while Kepler described them as elliptical. Kepler thought that the planets were driven forwards by forces originating from the sun, while according to Galilei a body remains in its circular motion because of its inner inertia. Descartes on the other hand, assumed that this inertia maintained only linear motion.
Kepler had hit upon the thought of a universal force, a gravitating anima mundi, but for some reason he did not really dare to believe in such a fantastic idea. He thought that there was a relation between "weight" and the attraction beween two bodies, but also that the force from the sun was "magnetic".
Newton had a notion of forces between celestial bodies, in analogy with the chemical forces that act upon earthly bodies [9]. While he expected to find something like the affinities that are characteristic for different substances, acting also among celestial bodies, it turned out that gravitation is not specific for each planet, but universal. All material bodies are attracted to each other by a force proportional to the product of their masses, and to their inverse distance squared. The same force that acts on earthly bodies also acts on the heavenly bodies, echoing the hermetic "everything above is similar to everything below".
Newton's law of gravitation is however not sufficient to determine the
motion of celestial bodies. Galilei had found that the time of fall of a
falling body is proportional to its change of velocity, its acceleration.
Newton generalized this in his law of motion which relates the acceleration
and the acting force 
by 
, where 
is the mass
of the moving body.
The planetary motions are determined by Newton's law
of gravitation together with his law of motion.
The Newtonian force that "animates" matter can be conceived of as arising from a synthesis of alchemical conceptions and mathematical, mechanical ideas. Newton used the word "spirit" or "medium" for what transmits the force between two bodies at a large distance from each other. He wrote that gravity must be caused by some factor that acts constantly according to certain laws, but would not establish whether this factor is of material or immaterial nature.
That he did not get stuck with the notions of circular inertia, magnetic
forces between the planets, etc., may be due to the fact that he was not
unacquainted with the alchemical anima mundi.
Newton's concept of force was actually criticized by the French eighteenth
century rationalists, both because of its empirical foundation and its
resemblance with the occult concept of "quality" [9].
But his gravitatio mundi became a most successful successor of the anima mundi,
not least because of its convincing mathematical formulation.
The publishing of Newton's "Principia Mathematica"
brought about the greatest shift of paradigm in the Western thought since the
introduction of Christianity.
It was not only a new conception of the world, it was the very basis of truth
that was changed. A concept of truth had been established, which was
independent of worldly or spiritual authorities.
While ideas that can only be given a purely linguistic
presentation will always be threatened by arbitrariness and ideological
stains; formal, mathematical statements cannot be retouched.