University of Winnipeg History of Science 2900/6-050 Tyler Fulcher-3047465 Dr. James Hanley History of the Classical model of Gravity and its unravelling: An in-depth analysis of Gottfried Leibniz thoughts on Isaac Newtons law of universal gravitation. The understanding of Gravity has held man down for thousands of years. It was the missing key of mechanics and still is today. There have been many attempts to create laws that can aptly define what is gravity; however, none have been created. Despite the lack of understanding, over the past few thousand years we have achieved great feats of engineering and have even escaped gravitys prison that is the earth. Regardless of our achievements this missing piece of physics theory is vital in solving many metaphysical and scientific theories. As such, this piece must be found if further advancements are to be made in obtaining our ultimate goal; that is to solve, why it is, that man is? In order to understand this fundamental force completely, we must examine all concepts and arguments relating to the various theories of gravitation. The best starting place for someone to successfully tackle this problem is with reviewing what other scientists thought at the time of gravitys creation by Isaac Newton. The main character that particular attention will be paid in this time period is Gottfried Leibniz as his arguments had enough merit to overturn Newtons Universal law of gravitation, even though Newtons theory eventually prevailed. (Figure 1) (Figure 2) Projectile motion illustrated by Isaac Newton Parabola as sketched by Galileo How did Newton derive his equation for universal gravitation? Newton built on the concepts of projectile motion that Galileo had perfected. He had postulated that if an projectile was fired fast enough that it could begin to move in a circular orbit just as the Moon orbits the Earth. To explain, Newton had hypothesised that if someone were to throw an object horizontally with sufficient velocity that it would fall circularly around the earth and that it would be able to do so for an infinite amount of time (see figures 1&2), given a projectiles hyperbolic motion. Which lead him to have a great interest in the study of circular motion, thus he created a mathematical model of the moons orbit. A model which would later would bring a universal numerical value of gravity and an elementary explanation as to the workings of gravity. (Figure 3) Newtons method for determining if the Moon is in projectile motion. To begin, you should iterate yourself with respect to figure 3 and reiterate when needed. Carrying on with the discussion of satellite motion, Newton realised that just as if someone were to throw an object fast enough it would come into orbit indefinitely, some objects may already be in orbit around the Earth. Thus, he hypothesised that the moon was in orbit. He did this in order to try to test for the value that an object falls with on earth as well as, with respect to the celestial realm. Newton used the moon as a tool to attempt to mathematically determine the value of gravity. From methods similar to the following this attempt can be shown: For simplicity Newton choose t = 1 second, as well as made use of a straight line by assuming that the Sm deviation is so small in 1 second that a straight line can be assumed, which is a Taylor approximation if you are curious. eg. : The equation for Sm is Sm = (2π Rm t)/ Tm. Finally, the last bit of information that was needed, was the distance from the centre of the Earth to the centre of the Moon, Rm. All of the above information provides the requirements to solve a Pythagorean equation, where Rm2 + Sm2 = (Rm + Yo)2. Thus, Rm2 + Sm2 = Rm2 + 2 Rm Yo + Yo2 where Yo2 is negligible and Rm2 may be canceled, giving a simplified equation Sm2 = 2 Rm Yo. Which allows for a final equation: Yo= Sm2/ 2 Rm In expanded form this equation is given as Yo= [(2pi Rm t)/ Tm]2/2 Rm . Data that Newton would have had at the time includes: Re = 6378.14 km, Tm = 27.3217 days rev-1, Rm= 384467 km, ge = 9.7803185 m s-2 . Yielding a result for the distance the moon falls with respect to the earth of Yo = 1.362x10-3m, or in Newtons own words one twentieth of an inch. Which lead him to the conclusion that the force of attraction between any two bodies heavenly or earthly shall be proportional to the masses and inversely proportional to the square of the radius between the centre of the two. Providing the following formula: F ∝ m1 m2 / r2 Which stems from his 3rd law of universal motion, for every action there is an equal and opposite reaction. Later, the previous law of universal attraction would be completed by adding a constant of big G giving: F = G (m1 m2 / r2) This constant was determined by Henry Cavendish by accident in 1797, while performing an experiment to try to determine the density of the earth. Although this value was not mentioned until 75 years after the experiment was preformed, the credit for discovering the value of Newtons constant is given to Cavendish. Which is measured to be approximately 6.67 x 10-11 m3 kg-1 s-2, however this value has a high degree of uncertainty and the value is not exact. Which brings us to another problem, with respect to a deviation in Newtons calculated value for the distance that the Moon falls in one second. The theoretical value that could have been determined after the Cavendish experiment would indicate that the distance that the moon fell was off by 1.2%. This value can be determined by knowing the following: Yt = (1/2) ge (Re2/Rm2) t2 provided by the general kinematics formula for falling bodies d=1/2 a t2 where t equals 1 second. Knowing the numerical value for ge due to Galileos experiment on an inclined plane, being ge = 9.783185 m s-2. Thus, where as Yt= 1.346 m one can find [(1.362mm-1.346mm)/1.346mm] x 100% = 1.2% The value of 1.2% is much too large to be a coincidence and so Newton devised a plan to correct for this error. The method that Newton had used to propose a prediction to this problem was that the Moon does not revolve around the Earths geometrical centre but at its centre of mass. To simplify again Newton used 1D mathematics which was without a doubt unequal to the real value, but can be treated as a good approximation (see figure 4). (Figure 4) Proposal for mass centred rotation (not to scale). To be able to construct a model of the Moons orbit to determine the Earths centre of gravity one must first have known an equation for finding such a centre. In which Newton had worked furiously to find. That equation being, Xm¬ = (Σmi xi)/M, where M is the total mass of the rigid body. Thus the following equation was derived, Xcm¬= (Mm¬¬ Rm)/ (Me Mm) Which equates to Xcm = 4.672x106m and thus a revision of the previous calculation can be made to get a more accurate prediction. However Newton was not able to determine this value because the value of big G was not known at the time and thus the mass of the Earth or the Moon was not known. To demonstrate that Newton was in fact correct regardless of his ability to determine the numerical value, I have redone the corrected calculation below. Yo = (Sm)2 / 2 ( Rm - Xcm) Which equates to, Yo = 1.345 x 10-3m. Comparing with respect to Yt we get a 0.074% difference by use of the same methods employed previously. [(1.346mm-1.345mm)/1.345mm] x 100% = 0.074%. Thus, we have a much more tolerable value. Further research conducted by Isaac Newton on gravity was with respect with ocean tides and ocean currents. (Figure 5) effects of celestial bodies on the Earth Newton had explored the effects of the moons gravity on ocean currents and determined that they move in the same direction as the moons orbit. Further he had determined that the tidal periods are due to the centrifugal force of the moon, as well as the position of the earth with respect to the sun. The effect of religion on Newtons Gravitation. The members of the Royal Society believed that knowledge came from two areas that share a common purpose; Revealed truth, which comes from studying scripture, and natural theology, which seeks to learn about God by studying His creation. The conclusions of natural theology were only accepted if they agreed with revealed truth. Because of the influence of the Royal Society and the fact that publishing anything blasphemous was illegal. Newton argued that because a singular God exists always and everywhere space and time must be absolute. This means they provide a background in which things take place and would continue to exist even if the universe was devoid of all physical matter. Newton argued that Gods eternal nature implies absolute time and his infinite duration corresponds to absolute space. The belief that space and time are absolute is known as space-time substantivalism because it implies that space is composed of some kind of pseudo-substance like Aristotles aether. To reiterate further, what Newton is trying to say here, is that God fills the spaces in between particles, which is to say that something other than the mass that makes up classical molecules is in between particles. Today physicists say that empty space does not exist, they say that particles even smaller than Quarks fill the free space in between macro particles. The name of this free space particle is Dark Matter. A further problem needs to be addressed in this statement which is that of Dark energy which is the free space particles outside of the expanding universe. Leibniz thoughts on Newtons natural theology. French philosopher Gottfried Leibniz accepted that the laws of physics could be universalised, but objected to Newtons concept of absolute space. Firstly, he argued that Galileo had shown there is no such thing as absolute velocity and so there cannot be any such thing as absolute space, from which it is derived. Secondly, Leibniz objected to Newtons description of absolute space as a kind of physical entity because it has no causal powers or independent existence. Leibniz argued that space is purely a mental entity. The view that space only exists when physical objects are present is known as relationism. To explain, absolute velocity is a property of matter in which all particles, photons, Quarks or what have you, have a predetermined amount of kinetic energy which will cause motion when some action in the universe takes place this is called Cause & Effect, which is analogous to the idea of pressure. This brings us to another problem in the physics of gravity, that is in need of our attention; what is it that causes anti-matter to mutual annihilate with matter or what causes an action in the universe to take place? We know now that when a subatomic particle collides with its respective antimatter particle, a Gluon is produced and it does not disappear from the universe. However, this chain of deductive events is much too complicated and I will just say that we do not believe that the universe has absolute velocity simply because of the acceleration that the universe must have if this system is to work. As such, absolute space cannot exist with reference to absolute velocity due to the conservation of energy. Leibnizs second point on the other hand was defeated by Newton stating that God fills the space in between atoms. it is notable to describe the god that Newton speaks of. Newton did not believe in many aspects of the Bible, he believed in the Hebrew God of the old testament. Because of this it can be said that, Newton believed that what we call Dark matter and Dark energy to be God, our creator, the matter in which the universe was created from. Instead of a God that has human shape and lives in the clouds. The last argument of Leibniz refers to relative space being that the universe is infinite and that the only way we can determine an objects position is by way of reference to another object. As such, these arguments successfully defeat Newtons law of Gravitation as being one that is universal. Newtons response to Leibnizs arguments Newton countered these remarks by arguing that although there is no absolute velocity, there is absolute acceleration and absolute space can be derived from this. What this means is that the Dark energy outside of the universe, which Newton calls God, is more massive than the universe and so the universe is accelerating towards it. With respect to God this is possible because Gods mass does not need to change, because people can give God occult properties. But in logical terms this causes a problem, because if for example, the universe is expanding the Dark matter inside of the universe will not be able to fill the same volume. If Dark matter cannot fill the same volume that means that Dark energy must be converted to Dark matter or some substrate of Dark energy or even further Dark energy must be inter mixed with the Dark matter of the universe. Which means that the universe is now accelerating away from some point, the center of the universe, which now satisfies relative velocity and relative space but not absolute space. Which is why Newtons Universal Law Of Gravitation would eventually be defeated by Einsteins Theory Of General Relativity, due his introduction of Dark energy as a cosmological constant which holds back gravity. In conclusion, Leibniz had some very interesting arguments, which should not be regarded as a useless mental exercise. Leibnizs arguments from the very foundation of the theory of general relativity. As such, these arguments should be incorporated into the process in which we consider further research into the fundamental force of gravity. Newton on the other hand also had some very strong and correct arguments, however his law of universal gravitation does not hold up as universal law and should be considered only as a correct method for solving problems regarding gravity on the macro scale with limited merit. Because of the limited capacity that Newtons universal law of gravitation can cover it is safe to say that gravity does not exist. To explain, gravity will still act in the way that it always has, as in an apple will still fall from a tree; However, gravity was not described by Newton and as such the merit of him discovering what gravity is, in a dynamical sense should be limited.
Posted on: Fri, 28 Mar 2014 18:40:04 +0000
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