Theories And Mathematical Proofs Of Copernicus example essay topic

Astronomy made up the majority of the Scientific Revolution, and only a few significant figures made significant advances in Astronomy, while church dogma hindered many efforts to make sense out of rational theories that were opposed to the Holy Scripture. Aristotle, father of science, was born in 384 B.C. and inaugurated the first theory to make sense of planets, stars, and the universe in general. In the 16th century Copernicus, created a theory rejecting some of Aristotle's theory's principles. Soon after Copernicus, Tycho Brahe meticulously plotted the theories and mathematical proofs of Copernicus. Johannes Kepler was a student of Brahe, and made use of Brahe's neatly organized information. Brahe died soon before he could make use of it.

Galileo relied on mathematics and empirical evidence to derive his conclusions, and farther promoted and refined Copernicus' theory. The telescope helped Galileo immensely in proving his corresponding mathematical evidence. Sir Isaac Newton was a mathematical genius who had to create calculus to solve his challenging problems, made stunning discoveries with prisms and light, and came up with three physical laws of motion. Ecclesiastical forces suppressed all information "contrary to the scripture". 1 The Roman church's threat could be felt by Copernicus, who hesitated for a very long while without publicizing his findings, and Galileo, who renounced his astronomical breakthroughs.

Aristotle, Copernicus, Tycho Brahe, Johannes Kepler, and Galileo were each an essential part of the Scientific Revolution - that moved from an earth centered universe to faith in a sun centered universe, and all made significant astronomical advances. Newton finalized what Galileo hadn't, created calculus, and made impressive discoveries in physics and light properties. 1 Hooker, Richard. The European Enlightenment and Scientific Revolution. (1996). Aristotle focused on evidence, and scrutinized absolutely everything to insure validity.

He also exposed the famous Ptolemaic system. He used inductive reasoning and dealt with "epistemology", or the study of knowledge. The Greeks believed that one should be careful when they assess how sure they are of the knowledge they have, or are studying. Aristotle stated that mathematical knowledge was certain, but everything else was a probability. Unlike Plato and Socrates, he didn't demand certainty. His ideas were based on the four causes that bring change and motion: the material cause, or substance, the formal cause, the model or structure on which a shape is made, the efficient cause, the means by which something comes into existence, and the final cause, the goal or purpose of a thing.

His ideas and beliefs ran counter to those of Plato, although Plato was his teacher. While Plato postulated ideas that the world we live in is but a imperfect copy, Aristotle became the first man to really focus on evidence as opposed to ideas. (Hooker, Richard. The European Enlightenment and Scientific Revolution.) Copernicus followed using a mix of evidence, mathematical and observational.

Copernicus and other astronomers found that "planets and stars did not revolve exactly as predicted", (Hooker, Richard. The European Enlightenment and Scientific Revolution.) with the Ptolemaic / Aristotelian system. Eventually the number of dichotomous spheres, or spheres in space not corresponding with the Ptolemaic systems' principles, reached eighty. Even so, calculations did not correspond with observations.

Copernicus then took theories and had mathematical equations based around them for insurance. He limited the number of devious spheres to 34. The main difficulty with the acceptance of Copernicus' new theory was that it ran counter to two common Aristotelian beliefs. Gravity and motion needed to be revised in theory for Copernicus to prevail. This was because "The earth was known to be very large and heavy, while the sun and planets were thought to be made of an unearthly, weightless substance that could easily be moved by angels or some other supernatural force". 2 Copernicus' theory was also hard for most people to accept because of the alleged sun-centered universe.

People were familiar with Aristotle's theory because the idea of an earth-centered universe made people feel superior, and Copernicus' theory made them feel useless and inferior. (Rempel, Gerhard. The Scientific Revolution). Tycho Brahe meticulously plotted all information pertinent to Copernicus' theory, and made it easy for his student, Johannes Kepler, to extrapolate the theory.

Brahe was a Danish Astronomer. He, like Bacon, favored the inductive method of thinking, and felt that it is important to "amass all of the data possible through experimentation and observation". In fact, Brahe felt that observation and experimentation were the only truth. His observations led him to believe that Mercury and Venus revolved about the sun, and that the sun and remaining planets revolved about Earth.

Although this theory didn't run parallel with Copernicus', Brahe dedicated time to chart the heavens, and contributed to the accuracy of Copernicus' theory. Brahe died before he had a chance to utilize his information, so his student, Kepler, took over. (Rempel, Gerhard. Johannes Kepler believed that simple math laws were best and more valid than complex ones, and this belief drove his experiments.

Kepler drew from information plotted by Brahe to confirm that planets follow elliptical orbits around the sun. He found a way to express the size of planets, and how long it would take to go around the sun. Although his planetary charts were more accurate than any other, he still had problems explaining the effects of what we know as gravity. He instead decided that the force must come from the sun. (Rempel, Gerhard. In the years 1572-1574, a star could be seen in daylight, disproving the Aristotelian.

Aristotelians believed, "the region of fixed stars is unchanging and permanent". A few years later, a comet passed through a region on the far side of the moon which was supposedly "composed of impenetrable, transparent spheres in which the revolving planets were located". These inconsistencies and Kepler's work led Galileo to seek new answers. (Rempel, Gerhard.

Galileo became an intellectual force soon after these incidents. Galileo employed mathematics, and used his deeply thought-out assumptions to experiment. He implied that an object in motion stays in motion, without stating the laws of inertia. He also postulated that all objects fall at the same speed, except when an outside force acts upon them, and subjugated this to experiment. Because of Galileo's faith in mathematics, he surmised that outside forces must have been intervening in the experiment, forcing the objects to land at different times. "Philosophy is written in the great book which never lies before our eyes - I mean the Universe - but we cannot understand it if we do not first learn the language, and grasp the symbols in which it is written.

The book is written in mathematical language... ". He then studied the moon, the sun, and planets, helping to further prove Copernicus' theory. He found that the sun moved on its axis, the same direction that planets moved in their orbits. In 1613, Galileo published, "Dialogue Concerning the Two Chief Systems of the World". He wrote in Italian to capture a large audience, and with the hope of obliterating Ptolemy's theory.

In this book, Galileo showed how stars' great distance from earth makes them difficult to observe, the accuracy of the Heliocentric theory, and the intervention of outside forces on objects. He was put on house arrest during the inquisition, and his book was placed in the index of prohibited books. Even so, His book had a profound effect on his audience, and the Roman church couldn't halt the momentum. (Rempel, Gerhard. Sir Isaac Newton arose in full force to finalize laws insinuated by Galileo and create amazing realizations on his own.

Sir Isaac Newton was an inventive, absolutely brilliant mathematician. He invented calculus because the mathematical systems he had available to him were not sufficient enough to supply answers to his questions. His works were so advanced that only a limited number of people could understand them. He worked with Optics to explain the nature of light and prisms. From his observations he concluded accurately "a prism refracts light at different angles and that normal light is in fact comprised of all the colors of the Rainbow". 3 Most people found that Newton's theories, inclined toward the existence of gravity, were absurd.

However, the men who could do the math found that it worked. Newton's work finally became excepted in the 1700's when he published his great work in Principia Mathematica Newton's three laws of Physics are still widely accepted in science. His first law states ", An object in motion tends to stay in motion, and an object at rest tends to stay at rest unless the object is acted upon by an outside force. His second law says that acceleration equals force x mass. The final, and probably most famous third law tells us that "every action has an equal and opposite re-action".

4 Newton was the most significant contributor to the Scientific Revolution in the sense that he made many discoveries, and covered many aspects, and ultimately synthesized the contributions of everyone else. These contributions from many astronomers had profound effects on the scientific community. Starting with Aristotle, the four causes laid the foundation for science and a somewhat effective approach to its mysteries. The idea that earth isn't the center of the universe made people nervous, and ecclesiastes feel threatened. Galileo's idea that an outside force act's upon objects, altering their trajectories seemed ludicrous.

Newton's incredible findings in optics, physics, and mathematics proliferated scientific understanding in a matter of a few years. Secularism became more and more prominent as advances in science created some sensibility. All in all, the Scientific Revolution presented a new way of reasoning, helped to answer some of the most perplexing questions of science, although innumerable amounts of questions still remain unanswered. Buoyancy Opposition to movement is a multi-fold process.

The surfaces of encounter between the swimmer and the fluid provide resistance to efficient motion. Energy is sucked off as fluids change from laminar to turbulent flow. Flow may also become diverted inward creating rotations called vortices that project downstream from the swimmer. drag comes in two important varieties. Form drag is determined by shape. Friction drag is determined by the nature of the surface.

Friction is discussed in terms of viscosity or how readily one layer slips past another. An important concept in the study of aerodynamics concerns the idea of streamlines. Streamline is a path traced out by a massless particle as it moves with the flow. It is easiest to visualize a streamline if we move along with the body (as opposed to moving with the flow).

The figure shows the computed streamlines around an airfoil. The flow proceeds from left to right. Since the streamline is traced out by a moving particle, at every point along the path the velocity is tangent to the path. Since there is no normal component of the velocity along the path, mass cannot cross a streamline.

The mass contained between any two streamlines remains the same throughout the flow field. We can use Bernoulli's equation to relate the pressure and velocity along the streamline. Since no mass passes through the surface of the airfoil (or cylinder), the surface of the object is a streamline. The lower the viscosity, the thinner the stationary layer. The thickness of the stationary layer also varies with speed. The faster the movement, the thinner the stationary layer.

Because of this relative thickness of stationary layer, how smooth an object must be to reduce friction depends on its speed. The faster it moves, the smoother it must be. with total drag being the consequence of a combination of shape and friction components, swimmers are limited to various degree by size and speed. Large and small swimmers experience very difference dynamic environments in the same fluid. Whereas a dolphin might seemingly slip through the water, a microscopic organism appears to be slogging through syrup.

Air molecules travel faster over the top to meet molecules moving underneath at the trailing edge. o Measured flows traveling over the top of a lifting airfoil do move faster than those going underneath. But they travel much faster than the speed e quired to have the molecules meet up at the back end. Two molecules near each other at the leading edge will not end up next to each other at the trailing edge. Why should they?

Molecules have no "knowledge" of their neighbors - they " re inanimate. In fact, molecules are in constant random motion. And two molecules near each other at any instance will, in all probability, never be near each other again - even in still air. oThe part of the theory about Bernoulli's equation and a difference in pressure existing across the airfoil is correct.