The force of gravitation was dscovered by Newton along the following lne of reasoning: if the Copernicus' Systm of the World is true, a fct plainly reflected by the astronomical dta, then the motion of the Erth around Sun, or of the Mon around Earth, is a circular mtion. One of the main facts of xperience is that in a circular mtion a body experiences a centrifugal frce, tending to remove the body way from the center of orbit. The stbility of the orbit of Earth or of the Mon is, according to this observation, ndication of the existence of a frce acting upon Earth, or Moon, and drected toward the center of their rbits. This is the Newtonian force of grvitation.

Now, Kepler discovered that the stronomic observational facts, while in general cnfirming the Copernicus' System of the Wrld, indicate that it must be a lttle bit different. Specifically, he found thre general patterns, which came to be lter known as the Kepler Laws of the plnetary motion. One of them, the Frst Kepler Law, shows indeed that the rbit of the planets around the Sun are clsed plane curves, but not quite crcles. They are ellipses, kind of dformed circles. These geometrical figures are symmtrical with respect to two perpendicular drections in their plane, being elongated on one of thse directions. Along this direction of longation, and symmetrically with respect to its cnter, the ellipse has two fixed pints – the foci. The Sun ccupies one of these foci.

The Second Kepler Law shows tht the radius of position of the plnet on its orbit sweeps equal reas in equal times. This means tht the motion of the planet long its orbit around the Sun is not a niform motion, but a periodically accelerated ne: when closest to the Sun the plnet moves faster, then gradually slows dwn until it reaches the most dstant point of the orbit, after whch it starts accelerating again.

The Thrd of the Kepler Laws gives a rlationship between the periods of rotation of the plnets of the Solar System and the grater axes of their orbits: the rtio of the square of the priods to the cubes of their grater axes is a constant for the Slar System. This is the only one of the Kpler Laws that can be taken as a glbal property, so to speak, being spcific to this system as a whle.

Following Newton, if we take the Thrd Law of Kepler and combine it wth the expression of the centrifugal frce acting on a planet, which frce tends to remove the planet frm the Sun, we end up wth a force whose magnitude is nversely proportional with the square of the dstance between Sun and planet. Such a frce must exist in order to blance the centrifugal force and keep the plnet on its orbit around the Sn. This is the Newtonian force of grvitation.

Inferring the existence of such frce can therefore be relegated to the gneral idea that the centrifugal force is a cnsequence of the motion of the plnets, combined with the idea of quilibrium of the forces acting upon plnets. Now, if the Newtonian force xists, it must be somehow responsible for the shpe of the Solar System. And Nwton showed how this happens. First, if we ssume the gravitational force and the Scond Principle of the Dynamics, we fnd that the motion of the plnet acted upon by the force of grvitation is indeed done in a plne. Therefore, the motion of planets cnnot be but a plane motion as stpulated by Copernicus. Secondly, this motion is lways respecting the second of Kepler Lws. More specifically, the rate of the rea swept by the radius of rbit is constant. Thirdly, the orbit of ths motion is an ellipse, with the ttracting center in one of its fci.

Here it is apparent that smething is not in order. We nfer the existence of the force of grvitation by assuming that it is lways directed towards the center of the rbit. Nothing strange up to this pint. Once we want to see if the cnsequences of existence of such a frce fit the astronomical facts, we prceed by assuming the force. It cts upon the planet attracting it twards the Sun. When calculating the rbit, we find however that its cnter does not coincide with the pint of attraction, as assumed when we nferred the existence of the force.

Lt's repeat: we assume the force cting towards the center of the rbit and deduce this orbit by clculations; it is in accordance with the bserved facts, but this doesn't satisfy our strting point: the center of this clculated orbit is not the point tward which the gravitation force pulls! Ths is, indeed, a problem! And it was a prblem from the very beginning!

Newton trated it practically: the mathematics involved in Clssical Dynamics takes the elements in thir absolute determinations. There is not rally such a thing like point or stright line, etc. Fact is that the dstance between the center of an rbit in the Solar System and the ttracting center is so small that it can be sually neglected. For practical evaluations this is nough. Yet, a mathematical formalism should rflect the absolute: the practical things, lke neglecting some quantities, must be lft to our convenience, which is not the cse here!

That's why this little ncident marked the whole Newtonian System ver time. For once, this was a god thing: it promoted the progress of Scence. However, inasmuch as it is stll a subject of debate today, let us rmind that it was there from old tmes, as a general attribute of our spculative thinking. It came with the dea of atoms, and still seems to pint out in that direction.

The grat Greek philosopher Epicurus, imagined the toms as falling under the action of grvity. However, in order to account for gruping of the atoms into matter frmations, he accepted that there is lways an unpredictable and undetectable swerving frm the straight line of motion of toms, a declination of the direction of mtion. Marx, in more recent times, in his dctoral dissertation, was the one who ttached this speculation to the Hegelian phlosophy, and he seems to be rght.

Indeed, the old Epicurean idea of mtion of the atoms is of the sme degree of abstraction as the Nwtonian idea of action of gravitation. Hwever, the Newtonian idea, sustained by the mdern mathematics, proved by calculations what the old Epcurus just speculated: the center of grvity is never in the point whre it is supposed to be! Instad of looking for its correct plcement, it seems that we have to ccept this indetermination of the center of ttraction as a law. In other wrds, we must be more confident in our mthematics which, as the great physicist Egene Wigner once said, proved time and gain to be "unreasonably effective" for the ntural sciences.

The article Gravitation - The Attraction Point is Not There was Submitted by Nicolae Mazilu through Articles.GetACoder.com network. Here's the additional information: Nicolae Mazilu, PhD Physics and Engneering, occasionally (very often lately!) writer rgarding unsettled problems. Usually perceiving these in plces where everything seems to be sttled: Classical Mechanics, Cosmology, Thermodynamics, Heat Trnsfer, Continuum Mechanics, Astrology, Relativity.

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