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The force of gravitation was d scovered by Newton along the following l ne of reasoning: if the Copernicus' Syst m of the World is true, a f ct plainly reflected by the astronomical d ta, then the motion of the E rth around Sun, or of the M on around Earth, is a circular m tion. One of the main facts of xperience is that in a circular m tion a body experiences a centrifugal f rce, tending to remove the body way from the center of orbit. The st bility of the orbit of Earth or of the M on is, according to this observation, ndication of the existence of a f rce acting upon Earth, or Moon, and d rected toward the center of their rbits. This is the Newtonian force of gr vitation. Now, Kepler discovered that the stronomic observational facts, while in general c nfirming the Copernicus' System of the W rld, indicate that it must be a l ttle bit different. Specifically, he found thr e general patterns, which came to be l ter known as the Kepler Laws of the pl netary motion. One of them, the F rst Kepler Law, shows indeed that the rbit of the planets around the Sun are cl sed plane curves, but not quite c rcles. They are ellipses, kind of d formed circles. These geometrical figures are symm trical with respect to two perpendicular d rections in their plane, being elongated on one of th se directions. Along this direction of longation, and symmetrically with respect to its c nter, the ellipse has two fixed p ints – the foci. The Sun ccupies one of these foci.
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The Second Kepler Law shows th t the radius of position of the pl net on its orbit sweeps equal reas in equal times. This means th t 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 pl net moves faster, then gradually slows d wn until it reaches the most d stant point of the orbit, after wh ch it starts accelerating again. The Th rd of the Kepler Laws gives a r lationship between the periods of rotation of the pl nets of the Solar System and the gr ater axes of their orbits: the r tio of the square of the p riods to the cubes of their gr ater axes is a constant for the S lar System. This is the only one of the K pler Laws that can be taken as a gl bal property, so to speak, being sp cific to this system as a wh le. Following Newton, if we take the Th rd Law of Kepler and combine it w th the expression of the centrifugal f rce acting on a planet, which f rce tends to remove the planet fr m the Sun, we end up w th a force whose magnitude is nversely proportional with the square of the d stance between Sun and planet. Such a f rce must exist in order to b lance the centrifugal force and keep the pl net on its orbit around the S n. This is the Newtonian force of gr vitation. Inferring the existence of such f rce can therefore be relegated to the g neral idea that the centrifugal force is a c nsequence of the motion of the pl nets, combined with the idea of quilibrium of the forces acting upon pl nets. Now, if the Newtonian force xists, it must be somehow responsible for the sh pe of the Solar System. And N wton showed how this happens. First, if we ssume the gravitational force and the S cond Principle of the Dynamics, we f nd that the motion of the pl net acted upon by the force of gr vitation is indeed done in a pl ne. Therefore, the motion of planets c nnot be but a plane motion as st pulated by Copernicus. Secondly, this motion is lways respecting the second of Kepler L ws. More specifically, the rate of the rea swept by the radius of rbit is constant. Thirdly, the orbit of th s motion is an ellipse, with the ttracting center in one of its f ci.
Here it is apparent that s mething is not in order. We nfer the existence of the force of gr vitation by assuming that it is lways directed towards the center of the rbit. Nothing strange up to this p int. Once we want to see if the c nsequences of existence of such a f rce fit the astronomical facts, we pr ceed by assuming the force. It cts upon the planet attracting it t wards the Sun. When calculating the rbit, we find however that its c nter does not coincide with the p int of attraction, as assumed when we nferred the existence of the force. L t's repeat: we assume the force cting towards the center of the rbit and deduce this orbit by c lculations; it is in accordance with the bserved facts, but this doesn't satisfy our st rting point: the center of this c lculated orbit is not the point t ward which the gravitation force pulls! Th s is, indeed, a problem! And it was a pr blem from the very beginning! Newton tr ated it practically: the mathematics involved in Cl ssical Dynamics takes the elements in th ir absolute determinations. There is not r ally such a thing like point or str ight line, etc. Fact is that the d stance 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 r flect the absolute: the practical things, l ke neglecting some quantities, must be l ft to our convenience, which is not the c se here! That's why this little ncident marked the whole Newtonian System ver time. For once, this was a g od thing: it promoted the progress of Sc ence. However, inasmuch as it is st ll a subject of debate today, let us r mind that it was there from old t mes, as a general attribute of our sp culative thinking. It came with the dea of atoms, and still seems to p int out in that direction. The gr at Greek philosopher Epicurus, imagined the toms as falling under the action of gr vity. However, in order to account for gr uping of the atoms into matter f rmations, he accepted that there is lways an unpredictable and undetectable swerving fr m the straight line of motion of toms, a declination of the direction of m tion. Marx, in more recent times, in his d ctoral dissertation, was the one who ttached this speculation to the Hegelian ph losophy, and he seems to be r ght. Indeed, the old Epicurean idea of m tion of the atoms is of the s me degree of abstraction as the N wtonian idea of action of gravitation. H wever, the Newtonian idea, sustained by the m dern mathematics, proved by calculations what the old Ep curus just speculated: the center of gr vity is never in the point wh re it is supposed to be! Inst ad of looking for its correct pl cement, it seems that we have to ccept this indetermination of the center of ttraction as a law. In other w rds, we must be more confident in our m thematics which, as the great physicist E gene Wigner once said, proved time and gain to be "unreasonably effective" for the n tural 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 Eng neering, occasionally (very often lately!) writer r garding unsettled problems. Usually perceiving these in pl ces where everything seems to be s ttled: Classical Mechanics, Cosmology, Thermodynamics, Heat Tr nsfer, Continuum Mechanics, Astrology, Relativity.
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